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Published work

60 published item(s)

preprint2026arXiv

CktGen: Automated Analog Circuit Design with Generative Artificial Intelligence

The automatic synthesis of analog circuits presents significant challenges. Most existing approaches formulate the problem as a single-objective optimization task, overlooking that design specifications for a given circuit type vary widely across applications. To address this, we introduce specification-conditioned analog circuit generation, a task that directly generates analog circuits based on target specifications. The motivation is to leverage existing well-designed circuits to improve automation in analog circuit design. Specifically, we propose CktGen, a simple yet effective variational autoencoder that maps discretized specifications and circuits into a joint latent space and reconstructs the circuit from that latent vector. Notably, as a single specification may correspond to multiple valid circuits, naively fusing specification information into the generative model does not capture these one-to-many relationships. To address this, we decouple the encoding of circuits and specifications and align their mapped latent space. Then, we employ contrastive training with a filter mask to maximize differences between encoded circuits and specifications. Furthermore, classifier guidance along with latent feature alignment promotes the clustering of circuits sharing the same specification, avoiding model collapse into trivial one-to-one mappings. By canonicalizing the latent space with respect to specifications, we can search for an optimal circuit that meets valid target specifications. We conduct comprehensive experiments on the open circuit benchmark and introduce metrics to evaluate cross-model consistency. Experimental results demonstrate that CktGen achieves substantial improvements over state-of-the-art methods.

preprint2026arXiv

FastStair: Learning to Run Up Stairs with Humanoid Robots

Running up stairs is effortless for humans but remains extremely challenging for humanoid robots due to the simultaneous requirements of high agility and strict stability. Model-free reinforcement learning (RL) can generate dynamic locomotion, yet implicit stability rewards and heavy reliance on task-specific reward shaping tend to result in unsafe behaviors, especially on stairs; conversely, model-based foothold planners encode contact feasibility and stability structure, but enforcing their hard constraints often induces conservative motion that limits speed. We present FastStair, a planner-guided, multi-stage learning framework that reconciles these complementary strengths to achieve fast and stable stair ascent. FastStair integrates a parallel model-based foothold planner into the RL training loop to bias exploration toward dynamically feasible contacts and to pretrain a safety-focused base policy. To mitigate planner-induced conservatism and the discrepancy between low- and high-speed action distributions, the base policy was fine-tuned into speed-specialized experts and then integrated via Low-Rank Adaptation (LoRA) to enable smooth operation across the full commanded-speed range. We deploy the resulting controller on the Oli humanoid robot, achieving stable stair ascent at commanded speeds up to 1.65 m/s and traversing a 33-step spiral staircase (17 cm rise per step) in 12 s, demonstrating robust high-speed performance on long staircases. Notably, the proposed approach served as the champion solution in the Canton Tower Robot Run Up Competition.

preprint2026arXiv

RainBalance: Alleviating Dual Imbalance in GNSS-based Precipitation Nowcasting via Continuous Probability Modeling

Global navigation satellite systems (GNSS) station-based Precipitation Nowcasting aims to predict rainfall within the next 0-6 hours by leveraging a GNSS station's historical observations of precipitation, GNSS-PWV, and related meteorological variables, which is crucial for disaster mitigation and real-time decision-making. In recent years, time-series forecasting approaches have been extensively applied to GNSS station-based precipitation nowcasting. However, the highly imbalanced temporal distribution of precipitation, marked not only by the dominance of non-rainfall events but also by the scarcity of extreme precipitation samples, significantly limits model performance in practical applications. To address the dual imbalance problem in precipitation nowcasting, we propose a continuous probability modeling-based framework, RainBalance. This plug-and-play module performs clustering for each input sample to obtain its cluster probability distribution, which is further mapped into a continuous latent space via a variational autoencoder (VAE). By learning in this continuous probabilistic space, the task is reformulated from fitting single and imbalance-prone precipitation labels to modeling continuous probabilistic label distributions, thereby alleviating the imbalance issue. We integrate this module into multiple state-of-the-art models and observe consistent performance gains. Comprehensive statistical analysis and ablation studies further validate the effectiveness of our approach.

preprint2026arXiv

TideGS: Scalable Training of Over One Billion 3D Gaussian Splatting Primitives via Out-of-Core Optimization

Training 3D Gaussian Splatting (3DGS) at billion-primitive scale is fundamentally memory-bound: each Gaussian primitive carries a large attribute vector, and the aggregate parameter table quickly exceeds GPU capacity, limiting prior systems to tens of millions of Gaussians on commodity single-GPU hardware. We observe that 3DGS training is inherently sparse and trajectory-conditioned: each iteration activates only the Gaussians visible from the current camera batch, so GPU memory can serve as a working-set cache rather than a persistent parameter store. Building on this insight, we introduce TideGS, an out-of-core training framework that manages parameters across an SSD-CPU-GPU hierarchy via three synergistic techniques: block-virtualized geometry for SSD-aligned spatial locality, a hierarchical asynchronous pipeline to overlap I/O with computation, and trajectory-adaptive differential streaming that transfers only incremental working-set deltas between iterations. Experiments show that TideGS enables training with over one billion Gaussians on a single 24 GB GPU while achieving the best reconstruction quality among evaluated single-GPU baselines on large-scale scenes, scaling beyond prior out-of-core baselines (e.g., approximately 100M Gaussians) and standard in-memory training (e.g., approximately 11M Gaussians).

preprint2025arXiv

Approximation algorithms for integer programming with resource augmentation

The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{Δ,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $Δ$ and $\|\textbf{b}\|_{\infty}$ are, respectively, the largest absolute values among the entries in the constraint matrix and the right-hand side vector of the constraint. The running time is exponential in $m$, and becomes pseudo-polynomial if $m$ is a constant. In recent years, there has been extensive research on FPT (fixed parameter tractable) algorithms for the so-called $n$-fold IPs, which may possess a large number of constraints, but the constraint matrix satisfies a specific block structure. It is remarkable that these FPT algorithms take as parameters $Δ$ and the number of rows and columns of some small submatrices. If $Δ$ is not treated as a parameter, then the running time becomes pseudo-polynomial even if all the other parameters are taken as constants. This paper explores the trade-off between time and accuracy in solving an IP. We show that, for arbitrary small $\varepsilon>0$, there exists an algorithm for IPs with $m$ constraints that runs in ${f(m,\varepsilon)}\cdot\textnormal{poly}(|I|)$ time, and returns a near-feasible solution that violates the constraints by at most $\varepsilonΔ$. Furthermore, for $n$-fold IPs, we establish a similar result -- our algorithm runs in time that depends on the number of rows and columns of small submatrices together with $1/\varepsilon$, and returns a solution that slightly violates the constraints. Meanwhile, both solutions guarantee that their objective values are no worse than the corresponding optimal objective values satisfying the constraints. As applications, our results can be used to obtain additive approximation schemes for multidimensional knapsack as well as scheduling.

preprint2022arXiv

DynamicFilter: an Online Dynamic Objects Removal Framework for Highly Dynamic Environments

Emergence of massive dynamic objects will diversify spatial structures when robots navigate in urban environments. Therefore, the online removal of dynamic objects is critical. In this paper, we introduce a novel online removal framework for highly dynamic urban environments. The framework consists of the scan-to-map front-end and the map-to-map back-end modules. Both the front- and back-ends deeply integrate the visibility-based approach and map-based approach. The experiments validate the framework in highly dynamic simulation scenarios and real-world datasets.

preprint2022arXiv

Electronic chiralization as an indicator of the anomalous Hall effect in unconventional magnetic systems

The anomalous Hall effect (AHE) can appear in certain antiferromagnetic metals when it is allowed by symmetry. Since the net magnetization is usually small in such anomalous Hall antiferromagnets, it is useful to have other physical indicators of the AHE that have the same symmetry properties as the latter and can be conveniently measured and calculated. Here we propose such indicators named as electronic chiralization (EC), which are constructed using spatial gradients of spin and charge densities in general periodic crystals, and can potentially be measured directly by scattering experiments. Such constructions particularly reveal the important role of magnetic charge in the AHE in unconventional magnetic systems with vanishing net magnetization. Guided by the EC we give two examples of the AHE when magnetic charge is explicitly present: A minimum honeycomb model inspired by the magnetic-charge-ordered phase of kagome spin ice, and skew scattering of two-dimensional Dirac electrons by magnetic charge.

preprint2022arXiv

Existence and multiplicity of solutions to Dirichlet problem for semilinear subelliptic equation with a free perturbation

This paper is concerned with existence and multiplicity results for the semilinear subelliptic equation with free perturbation term. By using the degenerate Rellich-Kondrachov compact embedding theorem, precise lower bound estimates of Dirichlet eigenvalues for the finitely degenerate elliptic operator and minimax method, we obtain the existence and multiplicity of weak solutions for the problem.

preprint2022arXiv

Manifold Optimization Based Multi-user Rate Maximization Aided by Intelligent Reflecting Surface

In this work, two problems associated with a downlink multi-user system are considered with the aid of intelligent reflecting surface (IRS): weighted sum-rate maximization and weighted minimal-rate maximization. For the first problem, a novel DOuble Manifold ALternating Optimization (DOMALO) algorithm is proposed by exploiting the matrix manifold theory and introducing the beamforming matrix and reflection vector using complex sphere manifold and complex oblique manifold, respectively, which incorporate the inherent geometrical structure and the required constraint. A smooth double manifold alternating optimization (S-DOMALO) algorithm is then developed based on the Dinkelbach-type algorithm and smooth exponential penalty function for the second problem. Finally, possible cooperative beamforming gain between IRSs and the IRS phase shift with limited resolution is studied, providing a reference for practical implementation. Numerical results show that our proposed algorithms can significantly outperform the benchmark schemes.

preprint2022arXiv

Polytopic Planar Region Characterization of Rough Terrains for Legged Locomotion

This paper studies the problem of constructing polytopic representations of planar regions from depth camera readings. This problem is of great importance for terrain mapping in complicated environment and has great potentials in legged locomotion applications. To address the polytopic planar region characterization problem, we propose a two-stage solution scheme. At the first stage, the planar regions embedded within a sequence of depth images are extracted individually first and then merged to establish a terrain map containing only planar regions in a selected frame. To simplify the representations of the planar regions that are applicable to foothold planning for legged robots, we further approximate the extracted planar regions via low-dimensional polytopes at the second stage. With the polytopic representation, the proposed approach achieves a great balance between accuracy and simplicity. Experimental validations with RGB-D cameras are conducted to demonstrate the performance of the proposed scheme. The proposed scheme successfully characterizes the planar regions via polytopes with acceptable accuracy. More importantly, the run time of the overall perception scheme is less than 10ms (i.e., > 100Hz) throughout the tests, which strongly illustrates the advantages of our approach developed in this paper.

preprint2022arXiv

Quadruped Capturability and Push Recovery via a Switched-Systems Characterization of Dynamic Balance

This paper studies capturability and push recovery for quadrupedal locomotion. Despite the rich literature on capturability analysis and push recovery control for legged robots, existing tools are developed mainly for bipeds or humanoids. Distinct quadrupedal features such as point contacts and multiple swinging legs prevent direct application of these methods. To address this gap, we propose a switched systems model for quadruped dynamics, and instantiate the abstract viability concept for quadrupedal locomotion with a time-based gait. Capturability is characterized through a novel specification of dynamically balanced states that addresses the time-varying nature of quadrupedal locomotion and balance. A linear inverted pendulum (LIP) model is adopted to demonstrate the theory and show how the newly developed quadrupedal capturability can be used in motion planning for quadrupedal push recovery. We formulate and solve an explicit model predictive control (EMPC) problem whose optimal solution fully characterizes quadrupedal capturability with the LIP. Given this analysis, an optimization-based planning scheme is devised for determining footsteps and center of mass references during push recovery. To validate the effectiveness of the overall framework, we conduct numerous simulation and hardware experiments. Simulation results illustrate the necessity of considering dynamic balance for quadrupedal capturability, and the significant improvement in disturbance rejection with the proposed strategy. Experimental validations on a replica of the Mini Cheetah quadruped demonstrate an up to 100% improvement as compared with state-of-the-art.

preprint2022arXiv

Quantum sensing and imaging of spin-orbit-torque-driven spin dynamics in noncollinear antiferromagnet Mn3Sn

Novel noncollinear antiferromagnets with spontaneous time-reversal symmetry breaking, nontrivial band topology, and unconventional transport properties have received immense research interest over the past decade due to their rich physics and enormous promise in technological applications. One of the central focuses in this emerging field is exploring the relationship between the microscopic magnetic structure and exotic material properties. Here, the nanoscale imaging of both spin-orbit-torque-induced deterministic magnetic switching and chiral spin rotation in noncollinear antiferromagnet Mn3Sn films using nitrogen-vacancy (NV) centers is reported. Direct evidence of the off-resonance dipole-dipole coupling between the spin dynamics in Mn3Sn and proximate NV centers is also demonstrated with NV relaxometry measurements. These results demonstrate the unique capabilities of NV centers in accessing the local information of the magnetic order and dynamics in these emergent quantum materials and suggest new opportunities for investigating the interplay between topology and magnetism in a broad range of topological magnets.

preprint2022arXiv

Static and spherically symmetric solutions in f(Q) gravity

f(Q) gravity is the extension of symmetric teleparallel general relativity (STGR), in which both curvature and torsion vanish, and gravity is attributed to nonmetricity. This work performs theoretical analyses of static and spherically symmetric solutions with an anisotropic fluid for general f(Q) gravity. We find that the off-diagonal component of the field equation due to a coincident gauge leads to stringent restrictions on the functional form of f(Q) gravity. In addition, although the exact Schwarzschild solution only exists in STGR, we obtain Schwarzschild-like solutions in nontrivial f(Q) gravity and study its asymptotic behavior and deviation from the exact one.

preprint2021arXiv

Emergent Weyl Fermions in an Orbital Multipolar Ordering Phase

Multipolar orderings in degenerate orbital systems offer unique opportunities for emergent topological phases. The phase diagram of interacting spinless fermions in a $p$-band diamond lattice at unit filling is first studied to elucidate the essential role of orbital multipolar orderings in the evolution of multifold degenerate band nodes. The free band structure around the Brillouin zone center is described by two quadratic band nodes each with a threefold degeneracy, which are spanned by the bonding and anti-bonding $p$-orbital multiplets, respectively. Upon switching on interactions, the triply degenerate band node is split into a pair of Weyl fermions with opposite chirality due to the onset of orbital multipolar orderings. Further raising interactions ultimately drives the system into an insulating phase with the orbital quadrupolar ordering. Our study is then generalized to spin-$1/2$ fermions, which has direct relevance with solid-state materials. The system develops full spin polarization through a ferromagnetic transition at tiny interactions, leaving the remaining orbital sector activated. The ensuing transitions take place in the orbital sector as a natural consequence, qualitatively recovering the phase diagram of spinless fermions. Our findings shed new light on the realization of emergent novel fermions with a prospect being a frontier at the confluence of topology, orbital physics and strong correlation.

preprint2021arXiv

Non-Abelian braiding in spin superconductors utilizing the Aharonov-Casher effect

Spin superconductor (SSC) is an exciton condensate state where the spin-triplet exciton superfluidity is charge neutral while spin $2(\hbar/2)$. In analogy to the Majorana zero mode (MZM) in topological superconductors, the interplay between SSC and band topology will also give rise to a specific kind of topological boundary state obeying non-Abelian braiding statistics. Remarkably, the non-Abelian geometric phase here originates from the Aharonov-Casher effect of the "half-charge" other than the Aharonov-Bohm effect. Such topological boundary state of SSC is bound with the vortex of electric flux gradient and can be experimentally more distinct than the MZM for being electrically charged. This theoretical proposal provides a new avenue investigating the non-Abelian braiding physics without the assistance of MZM and charge superconductor.

preprint2021arXiv

The spectral gap to torsion problem for some non-convex domains

In this paper we study the following torsion problem \begin{equation*} \begin{cases} -Δu=1~&\mbox{in}\ Ω,\\[1mm] u=0~&\mbox{on}\ \partialΩ. \end{cases} \end{equation*} Let $Ω\subset \mathbb{R}^2$ be a bounded, convex domain and $u_0(x)$ be the solution of above problem with its maximum $y_0\in Ω$. Steinerberger proved that there are universal constants $c_1, c_2>0$ satisfying \begin{equation*} λ_{\max}\left(D^2u_0(y_0)\right)\leq -c_1\mbox{exp}\left(-c_2\frac{\text{diam}(Ω)}{\mbox{inrad}(Ω)}\right). \end{equation*} And he proposed following open problem: "Does above result hold true on domains that are not convex but merely simply connected or perhaps only bounded? The proof uses convexity of the domain $Ω$ in a very essential way and it is not clear to us whether the statement remains valid in other settings." Here by some new idea involving the computations on Green's function, we compute the spectral gap $λ_{\max}D^2u(y_0)$ for some non-convex smooth bounded domains, which gives a negative answer to above open problem. Also some extensions are given.

preprint2020arXiv

Big Bang Nucleosynthesis Hunts Chameleon Dark Matter

We study the chameleon field dark matter, dubbed \textit{scalaron}, in $F(R)$ gravity in the Big Bang Nucleosynthesis (BBN) epoch. With an $R^{2}$-correction term required to solve the singularity problem for $F(R)$ gravity, we first find that the scalaron dynamics is governed by the $R^{2}$ term and the chameleon mechanism in the early universe, which makes the scalaron physics model-independent regarding the low-energy scale modification. In viable $F(R)$ dark energy models including the $R^{2}$ correction, our analysis suggests the scalaron universally evolves in a way with a bouncing oscillation irrespective of the low-energy modification for the late-time cosmic acceleration. Consequently, we find a universal bound on the scalaron mass in the BBN epoch, to be reflected on the constraint for the coupling strength of the $R^2$ term, which turns out to be more stringent than the one coming from the fifth force experiments. It is then shown that the scalaron naturally develops a small enough fluctuation in the BBN epoch, hence can avoid the current BBN constraint placed by the latest Planck 2018 data, and can also have a large enough sensitivity to be hunted by the BBN, with more accurate measurements for light element abundances as well as the baryon number density fraction.

preprint2020arXiv

Finite-thickness effect and spin polarization of the even-denominator fractional quantum Hall states

The spin-polarized even-denominator fractional quantum Hall (FQH) states in the second Landau level (LL), i.e. 5/2 and 7/2, may possess novel quasi-particle excitations obeying non-Abelian statistics. However, the spin polarization of the 7/2 FQH state has not been investigated experimentally and the spin polarization of the 5/2 FQH state from tilted field experiments remains controversial. Using a piezo-driven sample rotator with the lowest electron temperature down to 25 mK, we studied the energy gap of the even-denominator FQH states in the second LL by precise control of the tilted angles with a resolution less than 0.1°. We observed two different energy gap dependences on the in-plane magnetic field for 5/2, 7/2, other FQH states (7/3 and 8/3) in the second LL and reentrant integer quantum Hall (RIQH) states in the third LL. Though the transition fields vary from states, their corresponding in-plane magnetic lengths are comparable to the quantum well thickness of the sample, which may result from the influence of the finite-thickness effect. At low in-plane magnetic fields, before the conjectured finite-thickness effect starts to dominate, the energy gaps of both 5/2 and 7/2 states show a non-decreasing behavior, supporting spin-polarized ground states. Our results also suggest that the 7/3, 8/3 FQH states, and the RIQH states in the third LL are spin-polarized or partially spin-polarized.

preprint2020arXiv

Linear magnetoresistance induced by intra-scattering semiclassics of Bloch electrons

The weak field magnetoresistance has seen a revived interest due to the distinct role played by the momentum-space Berry curvature of Bloch electrons. While most previous studies in this regard focus on the inter-scattering motion of semiclassical Bloch electrons in electromagnetic fields, the intra-scattering effects of the semiclassical dynamics augmented by the Berry curvature, magnetic moment and shift vector on the magnetoresistance have been largely overlooked. Here we uncover that these intra-scattering effects, which are neglected in the field-independent relaxation time approximation to the Boltzmann collision integral, can be as important as the inter-scattering ones. Concrete calculations on the two dimensional gapped Dirac model show that the sign of the negative linear magnetoresistance given by the Berry curvature alone is reversed when one considers the magnetic moment and shift vector.

preprint2020arXiv

Realization of the kagome spin ice state in a frustrated intermetallic compound

Spin ices are exotic phases of matter characterized by frustrated spins obeying local ice rules, in analogy with the electric dipoles in water ice. In two dimensions, one can similarly define ice rules for in-plane Ising-like spins arranged on a kagome lattice. These ice rules require each triangle plaquette to have a single monopole, and can lead to various unique orders and excitations. Using experimental and theoretical approaches including magnetometry, thermodynamic measurements, neutron scattering and Monte Carlo simulations, we establish HoAgGe as a crystalline (i.e. non-artificial) system that realizes the kagome spin ice state. The system features a variety of partially and fully ordered states and a sequence of field-induced phases at low temperatures, all consistent with the kagome ice rule.

preprint2019arXiv

Emergent flat band lattices in spatially periodic magnetic fields

Motivated by the recent discovery of Mott insulating phase and unconventional superconductivity due to the flat bands in twisted bilayer graphene, we propose more generic ways of getting two-dimensional (2D) emergent flat band lattices using either 2D Dirac materials or ordinary electron gas (2DEG) subject to moderate periodic orbital magnetic fields with zero spatial average. Employing both momentum-space and real-space numerical methods to solve the eigenvalue problems, we find stark contrast between Schrödinger and Dirac electrons, i.e., the former show recurring "magic" values of the magnetic field when the lowest band becomes flat, while for the latter the zero-energy bands are asymptotically flat without magicness. By examining the Wannier functions localized by the smooth periodic magnetic fields, we are able to explain these nontrivial behaviors using minimal tight-binding models on a square lattice. The two cases can be interpolated by varying the $g$-factor or effective mass of a 2DEG and by taking into account the Zeeman coupling, which also leads to flat bands with nonzero Chern numbers for each spin. Our work provides flexible platforms for exploring interaction-driven phases in 2D systems with on-demand superlattice symmetries.

preprint2019arXiv

Manipulating Anomalous Hall Antiferromagnets with Magnetic Fields

The symmetry considerations that imply a non-zero anomalous Hall effect (AHE) in certain non-collinear antiferromagnets also imply both non-zero orbital magnetization and a net spin magnetization. We have explicitly evaluated the orbital magnetizations of several anomalous Hall effect antiferromagnets and find that they tend to dominate over spin magnetizations, especially so when spin-orbit interactions are weak. Because of the greater relative importance of orbital magnetization the coupling between magnetic order and an external magnetic field is unusual. We explain how magnetic fields can be used to manipulate magnetic configurations in these systems, pointing in particular to the important role played by the response of orbital magnetization to the Zeeman-like spin exchange fields.

preprint2016arXiv

Emergent classical geometries on boundaries of randomly connected tensor networks

It is shown that classical spaces with geometries emerge on boundaries of randomly connected tensor networks with appropriately chosen tensors in the thermodynamic limit. With variation of the tensors, the dimensions of the spaces can be freely chosen, and the geometries, which are curved in general, can be varied. We give the explicit solvable examples of emergent flat tori in arbitrary dimensions, and the correspondence from the tensors to the geometries for general curved cases. The perturbative dynamics in the emergent space is shown to be described by an effective action which is invariant under the spatial diffeomorphism due to the underlying orthogonal group symmetry of the randomly connected tensor network. It is also shown that there are various phase transitions among spaces, including extended and point-like ones, under continuous change of the tensors.

preprint2016arXiv

Hermite-Hadamard and Hermite-Hadamard-Fejér type Inequalities for Generalized Fractional Integrals

In this paper we obtain the Hermite-Hadamard and Hermite-Hadamard-Fejér type inequalities for fractional integrals which generalize the two familiar fractional integrals namely, the Riemann-Liouville and the Hadamard fractional integrals into a single form. We prove that, in most cases, we obtain the Riemann--Liouville and the Hadamard equivalence just by taking limits when a parameter $ρ\rightarrow 1$ and $ρ\rightarrow 0^+$, respectively.

preprint2016arXiv

Quantum Cosmology via Quantization of Point-Like Lagrangian

The purpose of this paper is to introduce a new way to inquire the quantum cosmology for a certain gravitational theory. Normally, the quantum cosmological model is introduced as the minisuperspace theory which is obtained by reducing the superspace where the Wheel-DeWitt equation is defined on using the symmetry provided by cosmological principle. Unlike that, the key of our approach is to reinterpret the cosmology in a classical dynamical way using a point-like Lagrangian and then quantize the point-like model. We apply the method into Einstein gravity, gravity with a cosmological constant and the $f(R)$-gravity, and get their wave equations respectively. By analsysing the exact solution for the quantum cosmology with and without a cosmological constant we demonstrate that the cosmological constant is essential and being a tiny positive number. We also show the possibility of explaining inflation under the quantum version of cosmology.

preprint2015arXiv

A cosmological model from emergence of space

Many studies have been carried out since T.Padmanabhan proposed that the cosmic acceleration can be understood from the perspective that spacetime dynamics is an emergent phenomenon. Motivated by such a new paradigm, we firstly study the de Sitter universe from emergence of space. After that we investigate the universes in general cases and then narrow down our discussions into one of them with a detailed discussion of the possibility in describing our real universe classically. Furthermore, a constraint on $Ht$ and a estimated value of $\tildeΩ_Λ$ (caused by $ρ_{vac}$) can be derived from our model, the comparison with experiments is also presented. The results show the validity of our model.

preprint2015arXiv

Chern Kondo Insulator in an Optical Lattice

We propose to realize and observe Chern Kondo insulators in an optical superlattice with laser-assisted $s$ and $p$ orbital hybridization and synthetic gauge field, which can be engineered based on the recent cold atom experiments. Considering a double-well square optical lattice, the localized $s$ orbitals are decoupled from itinerant $p$ bands and are driven into a Mott insulator due to strong Hubbard interaction. Raman laser beams are then applied to induce tunnelings between $s$ and $p$ orbitals, and generate a staggered flux simultaneously. Due to the strong Hubbard interaction of $s$ orbital states, we predict the existence of a critical Raman laser-assisted coupling, beyond which the Kondo screening is achieved and then a fully gapped Chern Kondo phase emerges, with the topology characterized by integer Chern numbers. Being a strongly correlated topological state, the Chern Kondo phase is different from the single-particle quantum anomalous Hall state, and can be identified by measuring the band topology and double occupancy of $s$ orbitals. The experimental realization and detection of the predicted Chern Kondo insulator are also proposed.

preprint2015arXiv

Formation of Molecular-Orbital Bands in a Twisted Hubbard Tube: Implications for Unconventional Superconductivity in K2Cr3As3

We study a twisted Hubbard tube modeling the [CrAs] structure of quasi-one-dimensional superconductors A2Cr3As3 (A = K, Rb, Cs). The molecular-orbital bands emerging from the quasi-degenerate atomic orbitals are exactly solved. An effective Hamiltonian is derived for a region where three partially filled bands intersect the Fermi energy. The deduced local interactions among these active bands show a significant reduction compared to the original atomic interactions. The resulting three-channel Luttinger liquid shows various interaction-induced instabilities including two kinds of spin-triplet superconducting instabilities due to gapless spin excitations, with one of them being superseded by the spin-density-wave phase in the intermediate Hund's coupling regime. The implications of these results for the alkali chromium arsenides are discussed.

preprint2015arXiv

Fractional-order Generalized Principle of Self-Support (FOG PSS) in Control Systems Design

This paper reviews research that studies the principle of self-support (PSS) in some control systems and proposes a fractional-order generalized PSS framework for the first time. The existing PSS approach focuses on practical tracking problem of integer-order systems including robotic dynamics, high precision linear motor system, multi-axis high precision positioning system with unmeasurable variables, imprecise sensor information, uncertain parameters and external disturbances. More generally, by formulating the fractional PSS concept as a new generalized framework, we will focus in the possible fields on the fractional-order control problems such as practical tracking, $λ$-tracking, etc. of robot systems, multiple mobile agents, discrete dynamical systems, time delay systems and other uncertain nonlinear systems. Finally, the practical tracking of a first-order uncertain model of automobile is considered as a simple example to demonstrate the efficiency of the fractional-order generalized principle of self-support (FOGPSS) control strategy.

preprint2015arXiv

Heavy surface state in a possible topological Kondo insulator: Magneto-thermoelectric transport on the (011)-plane of SmB$_6$

Motivated by the high sensitivity to Fermi surface topology and scattering mechanisms in magneto-thermoelectric transport, we have measured the thermopower and Nernst effect on the (011)-plane of the proposed topological Kondo insulator SmB$_6$. These experiments, together with electrical resistivity and Hall effect measurements, demonstrate that the (011)-plane also harbors a metallic surface with the effective mass in the order of 10-10$^2$ $m_0$. The surface and bulk conductances are well distinguished in these measurements and are categorized into metallic and non-degenerate semiconducting regimes, respectively. Electronic correlations play an important role in enhancing scattering and also contribute to the heavy surface state.

preprint2015arXiv

High-Temperature Quantum Anomalous Hall Effect in n-p Codoped Topological Insulators

The quantum anomalous Hall effect (QAHE) is a fundamental quantum transport phenomenon that manifests as a quantized transverse conductance in response to a longitudinally applied electric field in the absence of an external magnetic field, and promises to have immense application potentials in future dissipation-less quantum electronics. Here we present a novel kinetic pathway to realize the QAHE at high temperatures by $n$-$p$ codoping of three-dimensional topological insulators. We provide proof-of-principle numerical demonstration of this approach using vanadium-iodine (V-I) codoped Sb$_2$Te$_3$ and demonstrate that, strikingly, even at low concentrations of $\sim$2\% V and $\sim$1\% I, the system exhibits a quantized Hall conductance, the tell-tale hallmark of QAHE, at temperatures of at least $\sim$ 50 Kelvin, which is three orders of magnitude higher than the typical temperatures at which it has been realized so far. The proposed approach is conceptually general and may shed new light in experimental realization of high-temperature QAHE.

preprint2015arXiv

Measurement-Device-Independent Quantum Coin Tossing

Quantum coin tossing (QCT) is an important primitive of quantum cryptography and has received continuous interest. However, in practical QCT, Bob's detectors can be subjected to detector-side channel attacks launched by dishonest Alice, which will possibly make the protocol completely insecure. Here, we report a simple strategy of a detector-blinding attack based on a recent experiment. To remove all the detector side channels, we present a solution of measurement-device-independent QCT (MDI-QCT). This method is similar to the idea of MDI quantum key distribution (QKD). MDI-QCT is loss tolerant with single-photon sources and has the same bias as the original loss-tolerant QCT under a coherent attack. Moreover, it provides the potential advantage of doubling the secure distance for some special cases. Finally, MDI-QCT can also be modified to fit the weak coherent-state sources. Thus, based on the rapid development of practical MDI-QKD, our proposal can be implemented easily.

preprint2015arXiv

On Weak Topology for Optimal Control of Switched Nonlinear Systems

Optimal control of switched systems is challenging due to the discrete nature of the switching control input. The embedding-based approach addresses this challenge by solving a corresponding relaxed optimal control problem with only continuous inputs, and then projecting the relaxed solution back to obtain the optimal switching solution of the original problem. This paper presents a novel idea that views the embedding-based approach as a change of topology over the optimization space, resulting in a general procedure to construct a switched optimal control algorithm with guaranteed convergence to a local optimizer. Our result provides a unified topology based framework for the analysis and design of various embedding-based algorithms in solving the switched optimal control problem and includes many existing methods as special cases.

preprint2015arXiv

Quantum Anomalous Hall Effect in Graphene Proximity Coupled to an Antiferromagnetic Insulator

We propose realizing the quantum anomalous Hall effect by proximity coupling graphene to an antiferromagnetic insulator that provides both broken time-reversal symmetry and spin-orbit coupling. We illustrate our idea by performing ab initio calculations for graphene adsorbed on the (111) surface of BiFeO3. In this case, we find that the proximity-induced exchange field in graphene is about 70 meV, and that a topologically nontrivial band gap is opened by Rashba spin-orbit coupling. The size of the gap depends on the separation between the graphene and the thin film substrate, which can be tuned experimentally by applying external pressure.

preprint2015arXiv

Strong interface-induced spin-orbit coupling in graphene on WS2

Interfacial interactions allow the electronic properties of graphene to be modified, as recently demonstrated by the appearance of satellite Dirac cones in the band structure of graphene on hexagonal boron nitride (hBN) substrates. Ongoing research strives to explore interfacial interactions in a broader class of materials in order to engineer targeted electronic properties. Here we show that at an interface with a tungsten disulfide (WS2) substrate, the strength of the spin-orbit interaction (SOI) in graphene is very strongly enhanced. The induced SOI leads to a pronounced low-temperature weak anti-localization (WAL) effect, from which we determine the spin-relaxation time. We find that spin-relaxation time in graphene is two-to-three orders of magnitude smaller on WS2 than on SiO2 or hBN, and that it is comparable to the intervalley scattering time. To interpret our findings we have performed first-principle electronic structure calculations, which both confirm that carriers in graphene-on-WS2 experience a strong SOI and allow us to extract a spin-dependent low-energy effective Hamiltonian. Our analysis further shows that the use of WS2 substrates opens a possible new route to access topological states of matter in graphene-based systems.

preprint2015arXiv

Topological Superconductivity induced by Ferromagnetic Metal Chains

Recent experiments have provided evidence that one-dimensional (1D) topological superconductivity can be realized experimentally by placing transition metal atoms that form a ferromagnetic chain on a superconducting substrate. We address some properties of this type of systems by using a Slater-Koster tight-binding model. We predict that topological superconductivity is nearly universal when ferromagnetic transition metal chains form straight lines on superconducting substrates and that it is possible for more complex chain structures. The proximity induced superconducting gap is $\sim ΔE_{so} / J$ where $Δ$ is the $s$-wave pair-potential on the chain, $E_{so}$ is the spin-orbit splitting energy induced in the normal chain state bands by hybridization with the superconducting substrate, and $J$ is the exchange-splitting of the ferromagnetic chain $d$-bands. Because of the topological character of the 1D superconducting state, Majorana end modes appear within the gaps of finite length chains. We find, in agreement with experiment, that when the chain and substrate orbitals are strongly hybridized, Majorana end modes are substantially reduced in amplitude when separated from the chain end by less than the coherence length defined by the $p$-wave superconducting gap. We conclude that Pb is a particularly favorable substrate material for ferromagnetic chain topological superconductivity because it provides both strong $s-$wave pairing and strong Rashba spin-orbit coupling, but that there is an opportunity to optimize properties by varying the atomic composition and structure of the chain. Finally, we note that in the absence of disorder a new chain magnetic symmetry, one that is also present in the crystalline topological insulators, can stabilize multiple Majorana modes at the end of a single chain.

preprint2014arXiv

Emergence of space and the general dynamic equation of Friedmann-Robertson-Walker universe

A novel idea that the cosmic acceleration can be understood from the perspective that spacetime dynamics is an emergent phenomena was proposed by T. Padmanabhan. The Friedmann equations of FRW universe can be derived from different gravity theories with different modifications of Padmanabhan's proposal. In this paper, a unified formula is proposed, in which those modifications can be treated as special cases when the formula is applied to different universe radii. Furthermore, the dynamic equations of FRW universe in the $ f(R) $ theory and deformed Ho{ř}ava-Lifshitz theory are investigated. The results show the validity of our proposed formula.

preprint2014arXiv

Field and long-term demonstration of a wide area quantum key distribution network

A wide area quantum key distribution (QKD) network deployed on communication infrastructures provided by China Mobile Ltd. is demonstrated. Three cities and two metropolitan area QKD networks were linked up to form the Hefei-Chaohu-Wuhu wide area QKD network with over 150 kilometers coverage area, in which Hefei metropolitan area QKD network was a typical full-mesh core network to offer all-to-all interconnections, and Wuhu metropolitan area QKD network was a representative quantum access network with point-to-multipoint configuration. The whole wide area QKD network ran for more than 5000 hours, from 21 December 2011 to 19 July 2012, and part of the network stopped until last December. To adapt to the complex and volatile field environment, the Faraday-Michelson QKD system with several stability measures was adopted when we designed QKD devices. Through standardized design of QKD devices, resolution of symmetry problem of QKD devices, and seamless switching in dynamic QKD network, we realized the effective integration between point-to-point QKD techniques and networking schemes.

preprint2014arXiv

Generalized Holographic Equipartition for Friedmann-Robertson-Walker Universes

The novel idea that spatial expansion of our universe can be regarded as the consequence of the emergence of space was proposed by Padmanabhan. By using of the basic law governing the emergence, which Padmanabhan called holographic equipartition, he also arrives at the Friedmann equation in a flat universe. When generalized to other gravity theories, the holographic equipartition need to be generalized with an expression of $f(ΔN,N_{sur})$. In this paper, we give general expressions of $f(ΔN,N_{sur})$ for generalized holographic equipartition which can be used to derive the Friedmann equations of the Friedmann-Robertson-Walker universe with any spatial curvature in higher (n+1)-dimensional Einstein gravity, Gauss-Bonnet gravity and more general Lovelock gravity. The results support the viability of the perspective of holographic equipartition.

preprint2014arXiv

Mapping Hawking into Unruh for global embeddings

We study the mechanism of global embeddings into the Minkowski spacetime(GEMS) with the Hawking into Unruh mapping. We find a constraint that the extrinsic acceleration of the static observer in the Riemann space must satisfy for such embeddings. Thus the question raised by Paston in Ref.\cite{1}, that is, when does the Hawking into Unruh mapping for global embeddings work, is partly addressed. We also calculate the potential barrier of a scalar field to reach r $\rightarrow\infty$ in the ambient space. The results show that the potential barrier is finite, hence the static observer at r $\rightarrow\infty$ can indeed detect the radiation caused by the Unruh effect from the embedding view. However the potential barriers calculated in both the Riemann background and the Minkowski background are not coincident, therefore the GEMS approach is not complete and the Hawking effect can be distinguished from the Unruh effect of the GEMS in principle.

preprint2014arXiv

Non-Local Transport Mediated by Spin-Supercurrents

In thin film ferromagnets with perfect easy-plane anisotropy, the component of total spin perpendicular to the easy plane is a good quantum number and the corresponding spin supercurrent can flow without dissipation. In this Letter we explain how spin supercurrents couple spatially remote spin-mixing vertical transport channels, even when easy-plane anisotropy is imperfect, and discuss the possibility that this effect can be used to fabricate new types of electronic devices.

preprint2014arXiv

Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor

Majorana fermions are predicted to localize at the edge of a topological superconductor, a state of matter that can form when a ferromagnetic system is placed in proximity to a conventional superconductor with strong spin-orbit interaction. With the goal of realizing a one-dimensional topological superconductor, we have fabricated ferromagnetic iron (Fe) atomic chains on the surface of superconducting lead (Pb). Using high-resolution spectroscopic imaging techniques, we show that the onset of superconductivity, which gaps the electronic density of states in the bulk of the Fe chains, is accompanied by the appearance of zero energy end states. This spatially resolved signature provides strong evidence, corroborated by other observations, for the formation of a topological phase and edge-bound Majorana fermions in our atomic chains.

preprint2014arXiv

Proximity Effects in Topological Insulator Heterostructures

Topological insulators (TIs) are bulk insulators that possess robust helical conducting states along their interfaces with conventional insulators. A tremendous research effort has recently been devoted to TI-based heterostructures, in which conventional proximity effects give rise to a series of exotic physical phenomena. This paper reviews our recent works on the potential existence of topological proximity effects at the interface between a topological insulator and a normal insulator or other topologically trivial systems. Using first-principles approaches, we have established the tunability of the vertical location of the topological helical state via intriguing dual-proximity effects. To further elucidate the control parameters of this effect, we have used the graphene-based heterostructures as prototypical systems to reveal a more complete phase diagram. On the application side of the topological helical states, we have presented a catalysis example, where the topological helical state plays an essential role in facilitating surface reactions by serving as an effective electron bath. These discoveries lay the foundation for accurate manipulation of the real space properties of the topological helical state in TI-based heterostructures and pave the way for realization of the salient functionality of topological insulators in future device applications.

preprint2014arXiv

Semiparametric Inference of the Complier Average Causal Effect with Nonignorable Missing Outcomes

Noncompliance and missing data often occur in randomized trials, which complicate the inference of causal effects. When both noncompliance and missing data are present, previous papers proposed moment and maximum likelihood estimators for binary and normally distributed continuous outcomes under the latent ignorable missing data mechanism. However, the latent ignorable missing data mechanism may be violated in practice, because the missing data mechanism may depend directly on the missing outcome itself. Under noncompliance and an outcome-dependent nonignorable missing data mechanism, previous studies showed the identifiability of complier average causal effect for discrete outcomes. In this paper, we study the semiparametric identifiability and estimation of complier average causal effect in randomized clinical trials with both all-or-none noncompliance and the outcome-dependent nonignorable missing continuous outcomes, and propose a two-step maximum likelihood estimator in order to eliminate the infinite dimensional nuisance parameter. Our method does not need to specify a parametric form for the missing data mechanism. We also evaluate the finite sample property of our method via extensive simulation studies and sensitivity analysis, with an application to a double-blinded psychiatric clinical trial.

preprint2013arXiv

Anomalous Hall effect arising from noncollinear antiferromagnetism

In most conductors current flow perpendicular to electric field direction (Hall current) can be explained in terms of the Lorentz forces present when charged particles flow in an external magnetic field. However, as established in the very early work of Edwin Hall, ferromagnetic conductors such as Fe, Co, and Ni have an anomalous Hall conductivity contribution that cannot be attributed to Lorentz forces and therefore survives in the absence of a magnetic field. Although the anomalous Hall effect is experimentally strong, it has stood alone among metallic transport effects for much of the last century because it lacked a usefully predictive, generally accepted theory. Progress over the past decade has explained why. It is now clear that the anomalous Hall effect in ferromagnets has contributions from both extrinsic scattering mechanisms similar to those that determine most transport coefficients, and from an intrinsic mechanism that is independent of scattering. The anomalous Hall effect is also observed in paramagnets, which have nonzero magnetization induced by an external magnetic field. Although no explicit relationship has been established, the anomalous Hall effect in a particular material is usually assumed to be proportional to its magnetization. In this work we point out that it is possible to have an anomalous Hall effect in a noncollinear antiferromagnet with zero net magnetization provided that certain common symmetries are absent, and predict that Mn3Ir, a technologically important antiferromagnetic material with noncollinear order that survives to very high temperatures, has a surprisingly large anomalous Hall effect comparable in size to those of the elemental transition metal ferromagnets.

preprint2013arXiv

Gate-Tunable Exchange Coupling Between Cobalt Clusters on Graphene

We use spin-density-functional theory (SDFT) ab initio calculations to theoretically explore the possibility of achieving useful gate control over exchange coupling between cobalt clusters placed on a graphene sheet. By applying an electric field across supercells we demonstrate that the exchange interaction is strongly dependent on gate voltage, but find that it is also sensitive to the relative sublattice registration of the cobalt clusters. We use our results to discuss strategies for achieving strong and reproducible magneto-electric effects in graphene/transition-metal hybrid systems.

preprint2013arXiv

Tuning the vertical location of helical surface states in topological insulator heterostructures via dual-proximity effects

In integrating topological insulators (TIs) with conventional materials, one crucial issue is how the topological surface states (TSS) will behave in such heterostructures. We use first-principles approaches to establish accurate tunability of the vertical location of the TSS via intriguing dual-proximity effects. By depositing a conventional insulator (CI) overlayer onto a TI substrate (Bi2Se3 or Bi2Te3), we demonstrate that, the TSS can float to the top of the CI film, or stay put at the CI/TI interface, or be pushed down deeper into the otherwise structurally homogeneous TI substrate. These contrasting behaviors imply a rich variety of possible quantum phase transitions in the hybrid systems, dictated by key material-specific properties of the CI. These discoveries lay the foundation for accurate manipulation of the real space properties of TSS in TI heterostructures of diverse technological significance.

preprint2012arXiv

Impurity Quantum Phase Transition in a Current-Carrying d-Wave Superconductor

We study an Anderson impurity embedded in a d-wave superconductor carrying a supercurrent. The low-energy impurity behavior is investigated by using the numerical renormalization group method developed for arbitrary electronic bath spectra. The results explicitly show that the local impurity state is completely screened upon the non-zero current intensity. The impurity quantum criticality is in accordance with the well-known Kosterlitz-Thouless transition.

preprint2012arXiv

Interaction Driven Quantum Phase Transitions in Fractional Topological Insulators

We study two species of (or spin-1/2) fermions with short-range intra-species repulsion in the presence of opposite (effective) magnetic field, each at Landau level filling factor 1/3. In the absence of inter-species interaction, the ground state is simply two copies of the 1/3 Laughlin state, with opposite chirality, representing the fractional topological insulator (FTI) phase. We show this phase is stable against moderate inter-species interactions. However strong enough inter-species repulsion leads to phase separation, while strong enough inter-species attraction drives the system into a superfluid phase. We obtain the phase diagram through exact diagonalization calculations. The FTI-superfluid phase transition is shown to be in the (2+1)D XY universality class, using an appropriate Chern-Simons-Ginsburg-Landau effective field theory.

preprint2012arXiv

Regularity of traveling free surface water waves with vorticity

We prove real analyticity of all the streamlines, including the free surface, of a gravity- or capillary-gravity-driven steady flow of water over a flat bed, with a Hölder continuous vorticity function, provided that the propagating speed of the wave on the free surface exceeds the horizontal fluid velocity throughout the flow. Furthermore, if the vorticity possesses some Gevrey regularity of index $s$, then the stream function admits the same Gevrey regularity throughout the fluid domain; in particular if the Gevrey index $s$ equals to 1, then we obtain analyticity of the stream function. The regularity results hold for both periodic and solitary water waves.

preprint2011arXiv

Block spin magnetism and metal-insulator transition in a two-dimensional Hubbard model with perfect vacancy superstructure

We study the phase diagram of a square lattice Hubbard model with a perfect vacancy superstructure. The model can be also defined on a new bipartite lattice with each building blocks consisting of a minimal square. The non-interacting model is exactly solved and a mid-band gap opens at the Fermi energy in the weak inter-block hopping regime. Increasing the Coulomb interaction will develop the Néel antiferromagnetic order with varying block spin moments. The metal-insulator transition with $U_{\rm MI}$ smaller than the one without vacancies occurs above the magnetic instability $U_{\rm M}$. The emergent intermediate magnetic metal phase develops substantially in the moderate inter-block hopping regime. Drastic increases in the ordered moment and gap magnitude on the verge of non-interacting band insulator signal a possible distinction between the magnetic semi-conductor and the Mott-insulator. The implications of these results for the recent discovered (A,Tl)$_{y}$Fe$_{2-x}$Se$_2$ compounds are discussed.

preprint2011arXiv

CO Oxidation Facilitated by Robust Surface States on Au-Covered Topological Insulators

Surface states refer to electronic states emerging as a solid material terminates at a surface, and can be present in many systems. Despite their spatial proximity to material surfaces, surface states have been largely overlooked in fundamental understanding of surface catalysis and potential real-world applications, because of their vulnerability to local impurities or defects. In contrast, the recently discovered three-dimensional topological insulators (3DTI) have exceptionally robust metallic surface states that are topologically protected against surface contamination and imperfection. The robust topological surface state(s) (TSS) provides a perfect platform for exploiting novel physical phenomena and potential applications of surface states in less stringent environments. Here we employ first-principles density functional theory to demonstrate that the TSS can play a vital and elegant role in facilitating surface reactions by serving as an effective electron bath. We use CO oxidation on gold-covered Bi2Se3 as a prototype example, and first show that the TSS is preserved when a stable ultrathin Au film is deposited onto a Bi-terminated Bi2Se3 substrate. Furthermore, the TSS can significantly enhance the adsorption energy of both CO and O2 molecules, by promoting different directions of electron transfer. For CO, the TSS accepts electrons from the CO-Au system, thereby decreasing the undesirable occupation of the CO antibonding states. For O2, the TSS donates the needed electrons to promote the molecule towards dissociative adsorption. The present study adds a new arena to the technological potentials of 3DTI, and the central concept of TSS as an electron bath as revealed here may lead to new design principles beyond the conventional d-band theory of heterogeneous catalysis.

preprint2011arXiv

Exponential type Nagumo norms and summability of formal solutions of singular partial differential equations

In this paper, we study a class of first order nonlinear degenerated partial differential equations with singularity at $(t,x)=(0,0)\in \CC^2$. By means of exponential type Nagumo norm approach, Gevrey asymptotic analysis extends to case of holomorphic parameters by a natural way. A sharp condition is then established to deduce the $k$-summability for the formal solutions. Furthermore, analytical solutions in conical domains are found for each type of these nonlinear singular PDEs.

preprint2011arXiv

On a family of symmetric hypergeometric functions of several variables and their Euler type integral representation

This paper is devoted to the family $\{G_n\}$ of hypergeometric series of any finite number of variables, the coefficients being the square of the multinomial coefficients $(\ell_1+...+\ell_n)!/(\ell_1!...\ell_n!)$, where $n\in\ZZ_{\ge 1}$. All these series belong to the family of the general Appell-Lauricella's series. It is shown that each function $G_n$ can be expressed by an integral involving the previous one, $G_{n-1}$. Thus this family can be represented by a multidimensional Euler type integral, what suggests some explicit link with the Gelfand-Kapranov-Zelevinsky's theory of $A$-hypergeometric systems or with the Aomoto's theory of hypermeotric functions. The quasi-invariance of each function $G_n$ with regard to the action of a finite number of involutions of $\CC^{*n}$ is also established. Finally, a particular attention is reserved to the study of the functions $G_2$ and $G_3$, each of which is proved to be algebraic or to be expressed by the Legendre's elliptic function of the first kind.

preprint2011arXiv

Suppression of Grain Boundaries in Graphene Growth on Superstructured Mn-Cu(111) Surface

As undesirable defects, grain boundaries (GBs) are widespread in epitaxial graphene using existing growth methods on metal substrates. Employing density functional theory calculations, we first identify that the misorientations of carbon islands nucleated on a Cu(111) surface lead to the formation of GBs as the islands coalesce. We then propose a two-step kinetic pathway to effectively suppress the formation of GBs. In the first step, large aromatic hydrocarbon molecules are deposited onto a $\sqrt{3}\times\sqrt{3}$ superstructured Cu-Mn alloyed surface to seed the initial carbon clusters of a single orientation; in the second step, the seeded islands are enlarged through normal chemical vapor deposition of methane to form a complete graphene sheet. The present approach promises to overcome a standing obstacle in large scale single-crystal graphene fabrication.

preprint2011arXiv

Topological insulators with perfect vacancy superstructure and possible implications for iron chalcogenide superconductors

Motivated by the newly-discovered intercalated iron chalcogenide superconductors, we construct a single orbital tight-binding model for topological insulators on the square lattice with a perfect vacancy superstructure. We find that such lattice structure naturally accommodates a non-vanishing geometry phase associated with the next-nearest-neighbor spin-orbit interaction. By calculating the bulk band structures and the finite stripe edge states, we show that the topological insulator phases can be tuned at certain electron fillings in a wide range of the model parameters. The possible implications of these results for the iron deficient compounds $(A,Tl)_{y}Fe_{2-x}Se_2$ have been discussed.

preprint2009arXiv

Contrasting Behavior of Carbon Nucleation in the Initial Stages of Graphene Epitaxial Growth on Stepped Metal Surfaces

Using first-principles calculations within density functional theory, we study the energetics and kinetics of carbon nucleation in the early stages of epitaxial graphene growth on three representative stepped metal surfaces: Ir(111), Ru(0001), and Cu(111). We find that on the flat surfaces of Ir(111) and Ru(0001), two carbon atoms repel each other, while they prefer to form a dimer on Cu(111). Moreover, the step edges on Ir and Ru surfaces cannot serve as effective trapping centers for single carbon adatoms, but can readily facilitate the formation of carbon dimers. These contrasting behaviors are attributed to the delicate competition between C-C bonding and C-metal bonding, and a simple generic principle is proposed to predict the nucleation sites of C adatoms on many other metal substrates with the C-metal bond strengths as the minimal inputs.

preprint1994arXiv

Coulomb Correlations and Instability of Spinless Fermion Gas in 1D and 2D

We study the stability of the ordinary Landau Fermi liquid phase for interacting, spinless electrons. We require causality and demand that the Pauli principle be obeyed. We find a phase diagram determined by two parameters: the particle density and the interaction strength. We find that the homogeneous, constant density Fermi liquid phase of a spinless Fermion gas is {\em never} stable in 1D, but that it may have a restricted domain of stability in 2D.