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Gang Xu

Gang Xu contributes to research discovery and scholarly infrastructure.

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Published work

26 published item(s)

preprint2026arXiv

ORACLE: Anticipating Scams from Partial Trajectories in Streaming App Usage

Smartphone scams are increasingly prevalent and typically manifest as multi-stage, cross-application processes with gradually emerging intent. Effective intervention thus requires anticipating scams before the intent becomes explicit. This is inherently challenging, as decisions must rely on partial trajectories with temporally distributed evidence. In this paper, we propose \textbf{ORACLE} Online Reasoning for Anticipating Cross-temporal Latent thrEats, the first agentic framework for early scam anticipation from \textit{streaming app-usage} trajectories. To support this setting, we curate a real-world long-horizon benchmark of streaming app-usage trajectories, covering 12 scam types, spanning extended periods (15 days on average), involving diverse applications (95 apps), and interleaving normal and scam behaviors. To address fragmented evidence, we introduce a self-evolving context manager that adaptively consolidates entity-centric interactions over time, enabling more effective reconstruction of cross-temporal evidence from partial observations. To enhance sensitivity to latent early-stage signals, we propose an on-policy self-distillation scheme in which a teacher model, conditioned on summarized anti-scam reflections and clues by skills, supervises a student model without access to such reflections. This scheme thereby distills evidence-informed knowledge and improves recognition of emerging fraud patterns from partial trajectories. Experiments show that \method{} consistently improves early scam anticipation, yielding timely warnings while reducing false alerts in realistic streaming scenarios.

preprint2026arXiv

Unexpected type-II multiferroic phase in GdMnO3 under high magnetic fields

Perovskite manganites with small A-site ions, as the first and canonical branch of type-II multiferroics, are ideal systems to exhibit magnetism-induced ferroelectricity. Despite their established magnetoelectric phase diagrams under low magnetic fields, here an unidentified phase with a large magnetism-induced polarization (up to 1500 μC/m2) is revealed in GdMnO3 under high magnetic fields up to 60 T. Based on multiprobe experiments, a complete phase diagram is constructed with successive polar-nonpolar-polar-nonpolar transitions. Such a nonmonotonic evolution is well mimicked by model simulation, while the spin-lattice coupling is the key ingredient for the reentrant ferroelectric phase.

preprint2023arXiv

Chiral Topological superconductivity in the OAI/SC/FMI heterostructure avoiding the subband problem

Implementing topological superconductivity (TSC) and Majorana states (MSs) is one of the most significant and challenging tasks in both fundamental physics and topological quantum computations. In this work, taking the obstructed atomic insulator (OAI) Nb3Br8, s-wave superconductor (SC) NbSe2 and ferromagnetic insulator (FMI) as example, we propose a new setup to realize the 2D chiral TSC and MSs in the OAI/SC/FMI heterostructure, which could avoid the subband problem effectively and has the advantage of huge Rashba spin-orbit coupling. As a result, the TSC phase can be stabilized in a wide region of chemical potential and Zeeman field, and four distinct TSC phases with superconducting Chern number N= -1, -2, -3, 3 can be achieved. Moreover, a 2D BdG Hamiltonian based on the triangular lattice of obstructed Wannier charge centers, combined with the s-wave superconductivity paring and Zeeman field, is constructed to understand the whole topological phase diagram analytically. These results expand the application of OAIs and pave a new way to realize the TSC and MSs with unique advantages.

preprint2023arXiv

Field-Induced Lifshitz Transition in the Magnetic Weyl Semimetal Candidate PrAlSi

Lifshitz transition (LT) refers to an abrupt change in the electronic structure and Fermi surface, and is associated to a variety of emergent quantum phenomena. Amongst the LTs observed in known materials, the field-induced LT has been rare and its origin remains elusive. To understand the origin of field-induced LT, it is important to extend the material basis beyond the usual setting of heavy fermion metals. Here, we report on a field-induced LT in PrAlSi, a magnetic Weyl semimetal candidate with localized 4$f$ electrons, through a study of magnetotransport up to 55 T. The quantum oscillation analysis reveals that across a threshold field $B^*\approx$14.5 T the oscillation frequency ($F_1$ = 43 T) is replaced by two new frequencies ($F_2$ = 62 T and $F_3$ = 103 T). Strikingly, the LT occurs well below quantum limit, with obvious temperature-dependent oscillation frequency and field-dependent cyclotron mass. Our work not only enriches the rare examples of field-induced LTs, but also paves the way for further investigation on the interplay among topology, magnetism and electronic correlation.

preprint2022arXiv

Fragile topologically flat band in the checkerboard antiferromagnetic monolayer FeSe

By means of the first-principles calculations and magnetic topological quantum chemistry, we demonstrate that the low energy physics in the checkerboard antiferromagnetic (AFM) monolayer FeSe, very close to an AFM topological insulator that hosts robust edge states, can be well captured by a double-degenerate fragile topologically flat band just below the Fermi level. The Wilson loop calculations identify that such fragile topology is protected by the $S_{4z}$ symmetry, which gives rise to an AFM higher-order topological insulator that support the bound state with fractional charge $e/2$ at the sample corner. This is the first reported $S_{4z}$-protected fragile topological material, which provides a new platform to study the intriguing properties of magnetic fragile topological electronic states. Previous observations of the edge states and bound states in checkerboard AFM monolayer FeSe can also be well understood in our work.

preprint2022arXiv

Gate-Tunable Spin-Orbit Coupling in a Germanium Hole Double Quantum Dot

Hole spins confined in semiconductor quantum dot systems have gained considerable interest for their strong spin-orbit interactions (SOIs) and relatively weak hyperfine interactions. Here we experimentally demonstrate a tunable SOI in a double quantum dot in a Germanium (Ge) hut wire (HW), which could help enable fast all-electric spin manipulations while suppressing unwanted decoherence. Specifically, we measure the transport spectra in the Pauli spin blockade regime in the double quantum dot device.By adjusting the interdot tunnel coupling, we obtain an electric field tuned spin-orbit length lso = 2.0 - 48.9 nm. This tunability of the SOI could pave the way toward the realization of high-fidelity qubits in Ge HW systems.

preprint2022arXiv

LASOR: Learning Accurate 3D Human Pose and Shape Via Synthetic Occlusion-Aware Data and Neural Mesh Rendering

A key challenge in the task of human pose and shape estimation is occlusion, including self-occlusions, object-human occlusions, and inter-person occlusions. The lack of diverse and accurate pose and shape training data becomes a major bottleneck, especially for scenes with occlusions in the wild. In this paper, we focus on the estimation of human pose and shape in the case of inter-person occlusions, while also handling object-human occlusions and self-occlusion. We propose a novel framework that synthesizes occlusion-aware silhouette and 2D keypoints data and directly regress to the SMPL pose and shape parameters. A neural 3D mesh renderer is exploited to enable silhouette supervision on the fly, which contributes to great improvements in shape estimation. In addition, keypoints-and-silhouette-driven training data in panoramic viewpoints are synthesized to compensate for the lack of viewpoint diversity in any existing dataset. Experimental results show that we are among the state-of-the-art on the 3DPW and 3DPW-Crowd datasets in terms of pose estimation accuracy. The proposed method evidently outperforms Mesh Transformer, 3DCrowdNet and ROMP in terms of shape estimation. Top performance is also achieved on SSP-3D in terms of shape prediction accuracy. Demo and code will be available at https://igame-lab.github.io/LASOR/.

preprint2022arXiv

On the blowup mechanism of smooth solutions to 1D quasilinear strictly hyperbolic systems with large initial data

For the first order 1D $n\times n$ quasilinear strictly hyperbolic system $\partial_tu+F(u)\partial_xu=0$ with $u(x, 0)=\varepsilon u_0(x)$, where $\varepsilon>0$ is small, $u_0(x)\not\equiv 0$ and $u_0(x)\in C_0^2(\mathbb R)$, when at least one eigenvalue of $F(u)$ is genuinely nonlinear, it is well-known that on the finite blowup time $T_{\varepsilon}$, the derivatives $\partial_{t,x}u$ blow up while the solution $u$ keeps to be small. For the 1D scalar equation or $2\times 2$ strictly hyperbolic system (corresponding to $n=1, 2$), if the smooth solution $u$ blows up in finite time, then the blowup mechanism can be well understood (i.e., only the blowup of $\partial_{t,x}u$ happens). In the present paper, for the $n\times n$ ($n\geq 3$) strictly hyperbolic system with a class of large initial data, we are concerned with the blowup mechanism of smooth solution $u$ on the finite blowup time and the detailed singularity behaviours of $\partial_{t,x}u$ near the blowup point. Our results are based on the efficient decomposition of $u$ along the different characteristic directions, the suitable introduction of the modulated coordinates and the global weighted energy estimates.

preprint2022arXiv

Ultrafast coherent control of a hole spin qubit in a germanium quantum dot

Operation speed and coherence time are two core measures for the viability of a qubit. Strong spin-orbit interaction (SOI) and relatively weak hyperfine interaction make holes in germanium (Ge) intriguing candidates for spin qubits with rapid, all-electrical coherent control. Here we report ultrafast single-spin manipulation in a hole-based double quantum dot in a germanium hut wire (GHW). Mediated by the strong SOI, a Rabi frequency exceeding 540 MHz is observed at a magnetic field of 100 mT, setting a record for ultrafast spin qubit control in semiconductor systems. We demonstrate that the strong SOI of heavy holes (HHs) in our GHW, characterized by a very short spin-orbit length of 1.5 nm, enables the rapid gate operations we accomplish. Our results demonstrate the potential of ultrafast coherent control of hole spin qubits to meet the requirement of DiVincenzo's criteria for a scalable quantum information processor.

preprint2021arXiv

Electron-phonon coupling in the charge density wave state of CsV$_3$Sb$_5$

Metallic materials with kagome lattice structure are interesting because their electronic structures can host flat bands, Dirac cones, and van Hove singularities, resulting in strong electron correlations, nontrivial band topology, charge density wave (CDW), and unconventional superconductivity. Recently, kagome lattice compounds AV$_3$Sb$_5$ (A = K, Rb, Cs) are found to have intertwined CDW order and superconductivity. The origin of the CDW has been suggested to be purely electronic, arising from Fermi-surface instabilities of van Hove singularity (saddle point) near the M points. Here we use neutron scattering experiments to demonstrate that the CDW order in CsV$_3$Sb$_5$ is associated with static lattice distortion and a sudden hardening of the B3u longitudinal optical phonon mode, thus establishing that electron-phonon coupling must also play an important role in the CDW order of AV$_3$Sb$_5$.

preprint2021arXiv

Image-based Textile Decoding

A textile fabric consists of countless parallel vertical yarns (warps) and horizontal yarns (wefts). While common looms can weave repetitive patterns, Jacquard looms can weave the patterns without repetition restrictions. A pattern in which the warps and wefts cross on a grid is defined in a binary matrix. The binary matrix can define which warp and weft is on top at each grid point of the Jacquard fabric. The process can be regarded as encoding from pattern to textile. In this work, we propose a decoding method that generates a binary pattern from a textile fabric that has been already woven. We could not use a deep neural network to learn the process based solely on the training set of patterns and observed fabric images. The crossing points in the observed image were not completely located on the grid points, so it was difficult to take a direct correspondence between the fabric images and the pattern represented by the matrix in the framework of deep learning. Therefore, we propose a method that can apply the framework of deep learning via the intermediate representation of patterns and images. We show how to convert a pattern into an intermediate representation and how to reconvert the output into a pattern and confirm its effectiveness. In this experiment, we confirmed that 93% of correct pattern was obtained by decoding the pattern from the actual fabric images and weaving them again.

preprint2021arXiv

Prediction of topological superconductivity in 1$T$-TiTe$_2$ under pressure

Topological superconductivity has attracted intensive interest for its ability of hosting Majorana zero mode and implementing in topological quantum computations. Based on the first-principles calculations and the analysis of the effective BdG Hamiltonian, we demonstrate that 1$T$-TiTe$_2$ is a topological metal hosting Dirac cone type of surface states near the Fermi level, and it exhibits a normal-topological-normal superconductivity phase transition as a function of the chemical potential. These results point out a new promising topological superconductor without random dopant, in which the influence of the impurity may be greatly reduced. Furthermore, our calculations also suggest that the transition metal intercalated Ti(Se$_{1-y}$Te$_y$)$_2$ is also a highly possible route to realize TSC and MZMs.

preprint2021arXiv

Structural instability and charge modulations in the Kagome superconductor $A$V$_3$Sb$_5$

Recently, both charge density wave (CDW) and superconductivity have been observed in Kagome compounds $A$V$_3$Sb$_5$. However, the nature of CDW that results in many novel charge modulations is still under hot debate. By means of the first-principles calculations, we discover two kinds of CDW states, the trimerized and hexamerized 2$\times$2 phase and dimerized 4$\times$1 phase existing in $A$V$_3$Sb$_5$. Our phonon excitation spectrum and electronic Lindhard function calculations reveal that the most intensive structural instability in $A$V$_3$Sb$_5$ originates from a combined in-plane vibration mode of V atoms through the electron-phonon coupling, rather than the Fermi surface nesting effect. Crucially, a metastable 4$\times$1 phase with V-V dimer pattern and twofold symmetric bowtie shaped charge modulation is revealed in CsV$_3$Sb$_5$, implying that both dimerization and trimerization exist in the V Kagome layers. These results provide essential understanding of CDW instability and new thoughts for the novel charge modulation patterns.

preprint2021arXiv

Topological Luttinger semimetallic phase accompanied with surface states realized in silicon

By means of systematically first-principles calculations and model analysis, a complete phase diagram of the body-centered silicon(BC8-Si) via lattice constant a and internal atomic coordinate x is explored, which demonstrates that BC8-Si is a topological Luttinger semimetal(LSM) accompanied with topologically nontrivial surface states, and the electronic properties of BC8-Si can be further tuned to a normal insulator or topological Dirac semimetal by very tiny changing of a and x. These results successfully explain the contradictory transport reports of BC8-Si. More importantly, the topological surface states in the LSM phase fill in the gap between the topological matters and silicon, which provide an opportunity to integrate the topological quantum devices and silicon chips together.

preprint2020arXiv

Assessing the attraction of cities on venture capital from a scaling law perspective

Cities are centers for the integration of capital and incubators of invention, and attracting venture capital (VC) is of great importance for cities to advance in innovative technology and business models towards a sustainable and prosperous future. Yet we still lack a quantitative understanding of the relationship between urban characteristics and VC activities. In this paper, we find a clear nonlinear scaling relationship between VC activities and the urban population of Chinese cities. In such nonlinear systems, the widely applied linear per capita indicators would be either biased to larger cities or smaller cities depends on whether it is superlinear or sublinear, while the residual of cities relative to the prediction of scaling law is a more objective and scale-invariant metric. %(i.e., independent of the city size). Such a metric can distinguish the effects of local dynamics and scaled growth induced by the change of population size. The spatiotemporal evolution of such metrics on VC activities reveals three distinct groups of cities, two of which stand out with increasing and decreasing trends, respectively. And the taxonomy results together with spatial analysis also signify different development modes between large urban agglomeration regions. Besides, we notice the evolution of scaling exponents on VC activities are of much larger fluctuations than on socioeconomic output of cities, and a conceptual model that focuses on the growth dynamics of different sized cities can well explain it, which we assume would be general to other scenarios.

preprint2020arXiv

Confinement effect enhanced Stoner ferromagnetic instability in monolayer 1T-VSe2

Monolayer 1T-VSe2 has been reported as a room-temperature ferromagnet. In this work, by using first-principles calculations, we unveil that the ferromagnetism in monolayer 1T-VSe2 is originated from its intrinsic huge Stoner instability enhanced by the confinement effect, which can eliminate the interlayer coupling, and lead to a drastic increase of the density of states at the Fermi level due to the presence of Van Hove singularity. Our calculations also demonstrate that the Stoner instability is very sensitive to the interlayer distance. These results provide a useful route to modulate the nonmagnetic to ferromagnetic transition in few-layers or bulk 1T-VSe2, which also shed light on the enhancement of its Curie temperature by enlarging the interlayer distance.

preprint2020arXiv

Dipole coupling of a tunable hole double quantum dot in germanium hut wire to a microwave resonator

The germanium (Ge) hut wire system has strong spin-orbit coupling, a long coherence time due to a very large heavy-light hole splitting, and the advantage of site-controlled large-scale hut wire positioning. These properties make the Ge hut wire a promising candidate for the realization of strong coupling of spin to superconducting resonators and scalability for multiple qubit coupling. We have coupled a reflection line resonator to a hole double quantum dot (DQD) formed in Ge hut wire. The amplitude and phase responses of the microwave resonator revealed that the charge stability diagrams of the DQD are in good agreement with those obtained from transport measurements. The DQD interdot tunneling rate is shown to be tunable from 6.2 GHz to 8.5 GHz, which demonstrates the ability to adjust the frequency detuning between the qubit and the resonator. Furthermore, we achieved a hole-resonator coupling strength of up to 15 MHz, with a charge qubit decoherence rate of 0.28 GHz. Meanwhile the hole spin-resonator coupling rate was estimated to be 3 MHz. These results suggest that holes of a DQD in a Ge hut wire are dipole coupled to microwave photons, potentially enabling tunable hole spin-photon interactions in Ge with an inherent spin-orbit coupling.

preprint2020arXiv

Electronic structure of a Si-containing topological Dirac semimetal CaAl2Si2

There has been an upsurge in the discovery of topological quantum materials, where various topological insulators and semimetals have been theoretically predicted and experimentally observed. However, only very few of them contains silicon, the most widely used element in electronic industry. Recently, ternary compound CaAl2Si2 has been predicted to be a topological Dirac semimetal, hosting Lorentz-symmetry-violating quasiparticles with a strongly tilted conical band dispersion. In this work, by using high-resolution angle-resolved photoemission spectroscopy (ARPES), we investigated the comprehensive electronic structure of CaAl2Si2. A pair of topological Dirac crossings is observed along the kz direction, in good agreement with the ab initio calculations, confirming the topological Dirac semimetal nature of the compound. Our study expands the topological material family on Si-containing compounds, which have great application potential in realizing low-cost, nontoxic electronic device with topological quantum states.

preprint2020arXiv

Hole spin in tunable Ge hut wire double quantum dot

Holes in germanium (Ge) exhibit strong spin-orbit interaction, which can be exploited for fast and all-electrical manipulation of spin states. Here, we report transport experiments in a tunable Ge hut wire hole double quantum dot. We observe the signatures of Pauli spin blockade (PSB) with a large singlet-triplet energy splitting of ~1.1 meV and extract the g factor. By analyzing the the PSB leakage current, we obtain a spin-orbit length l_so of ~ 40-100 nm. Furthermore, we demonstrate the electric dipole spin resonance. These results lay a solid foundation for implementing high quality tunable hole spin-orbit qubits.

preprint2020arXiv

In the Pursuit of Majorana Modes in Iron-based High-$T_c$ Superconductors

Majorana zero mode is an exotic quasi-particle excitation with non-Abelian statistics in topological superconductor systems, and can serve as the cornerstone for topological quantum computation, a new type of fault-tolerant quantum computation architecture. This review paper highlights recent progress in realizing Majorana modes in iron-based high-temperature superconductors. We begin with the discussion on topological aspect of electronic band structures in iron-based superconductor compounds. Then we focus on several concrete proposals for Majorana modes, including the Majorana zero modes inside the vortex core on the surface of Fe(Te,Se), helical Majorana modes at the hinge of Fe(Te,Se), the Majorana zero modes at the corner of the Fe(Te,Se)/FeTe heterostructure or the monolayer Fe(Te,Se) under an in-plane magnetic field. We also review the current experimental stage and provide the perspective and outlook for this rapidly developing field.

preprint2020arXiv

Phase transitions of photon fluid flows driven by a virtual all-optical piston

The piston problem, i.e. the dynamics in a uniform gas at rest under the action of a moving piston is fundamental problem of physics and a canonical case study in shock wave physics. We investigate theoretically and experimentally the analogous problem for a photon fluid, which turns out to be strongly influenced by the dispersive character of the problem. The experiment makes use of a fiber optics setup where an all-optically controlled quasi instantaneous change of frequency of the input light mimics the piston action. We show that the flow exhibits phase transitions which involve cross-over from regimes characterized by 2-shocks (pushing piston) to 2-rarefaction waves (retracting piston), with the appearance of cavitating states at critical amplitudes of the jump. Importantly, the appearance of vacuum points into the 2-shock marks the transition to a regime which is unique to the photon fluid. Our observations allow for the extensive and quantitative test of the state of the art description of the dispersive Riemann problem, i.e. Whitham modulation theory, applied to the universal defocusing nonlinear Schrödinger equation.

preprint2020arXiv

Polar state of 0.67BiFeO3-0.33BaTiO3 near the morphotropic phase boundary

The symmetric studies on the structure-property relationship of the unpoled and poled states of 0.67BiFeO3-0.33BaTiO3 (0.67BF-0.33BT) were conducted to understand the origin of the morphotropic phase boundary (MPB) in BF-BT. A typical relaxor-type dielectric anomaly was observed (Tf, ~627 K). The remnant polarization (Pr) and maximum value of electro-strain (Sm) increase clearly during heating (Pr, ~40 uC/cm2; Sm, 0.191 % under 40 kV/cm at 453 K). The first-cycle electro-strain loops indicate the difference in the polar state between 0.67BF-0.33BT and 0.94BiNaTiO3-0.06BaTiO3. Both the unpoled and poled samples have the similar frequency dispersion behaviors. Even in the poled samples, the transition between the ergodic relaxor state and ferroelectric-like state does not involve a clear dielectric anomaly. Analyses based on the Rietveld refinement of XRD patterns, bright-field images and selected-area electron diffractions (SAED) demonstrated that the formation of the long-range ferroelectric domains was difficult under the poling field.

preprint2019arXiv

Enhanced higher harmonic generation from nodal topology

Among topological materials, nodal loop semimetals (NLSMs) are arguably the most topologically sophisticated, with their valence and conduction bands intersecting along arbitrarily intertwined nodes. But unlike the well-known topological band insulators with quantized edge conductivities, nodal loop materials possess topologically nontrivial Fermi surfaces, not bands. Hence an important question arises: Are there also directly measurable or even technologically useful physical properties characterizing nontrivial nodal loop topology? In this work, we provide an affirmative answer by showing, for the first time, that nodal linkages protect the higher harmonic generation (HHG) of electromagnetic signals. Specifically, nodal linkages enforce non-monotonicity in the intra-band semi-classical response of nodal materials, which will be robust against perturbations preserving the nodal topology. These nonlinearities distort incident radiation and produce higher frequency peaks in the teraHertz (THz) regime, as we quantitatively demonstrate for a few known nodal materials. Since THz sources are not yet ubiquitous, our new mechanism for HHG will greatly aid applications like material characterization and non-ionizing imaging of object interiors.

preprint2019arXiv

Magnetotransport properties of the layered CaAl2Si2 semimetal hosting multiple nontrivial topological states

Combination of different nontrivial topological states in a single material is capable of realizing multiple functionalities and exotic physics, but such materials are still very sparse. We report herein the results of magnetotransport measurements and ab initio calculations on single crystalline CaAl2Si2 semimetal. The transport properties could be well understood in connection with the two-band model, agreeing well with the theoretical calculations indicating four main sheets of Fermi surface consisting of three hole pockets centered at the Γ point and one electron pocket centered at the M point in the Brillouin zone. The single fundamental frequency imposed in the quantum oscillations of magnetoresistance corresponds to the electron Fermi pocket. Without spin-orbit coupling (SOC), the ab initio calculations suggest CaAl2Si2 as a system hosting a topological nodal-line setting around the Γ point in the Brillouin zone close to the Fermi level. Once including the SOC, the fragile nodal-line will be gapped and a pair of Dirac points emerge along the high symmetric Γ-A direction, which is about 1.22 eV below the Fermi level. The SOC can also induce a topological insulator state along the Γ-A direction with a gap of about 3 meV. The results demonstrate CaAl2Si2 as an excellent platform for the study of novel topological physics with multiple topological states.

preprint2019arXiv

Mott phase in a van der Waals transition-metal halide at single layer limit

Two-dimensional materials offer opportunities for unravelling unprecedented ordered states at single layer limit. Among such ordered states, Mott phase is rarely explored. Here, we report the Mott phase in van der Waals chromium (II) iodide (CrI2) films. High quality CrI2 films with atomically flat surface and macro size are grown on graphitized 6H-SiC(0001) substrate by molecular beam epitaxy. By in situ low temperature scanning tunneling microscopy and spectroscopy (STM/STS), we reveal that the film has a band gap as large as ~3.2 eV, which is nearly thickness independent. Density functional plus dynamic mean field theory calculations suggest that CrI2 films may be a strong Mott insulator with a ferromagnetically ordered ground state. The Mott phase is corroborated by the spectral band splitting, that is consistent with the extended Hubbard model, and gap reduction at charge dopants. Our study provides a platform for studying correlated electron states at single layer limit.

preprint2019arXiv

New types of topological superconductors under local magnetic symmetries

We classify gapped topological superconducting (TSC) phases of one-dimensional quantum wires with local magnetic symmetries (LMSs), in which the time-reversal symmetry $\mathcal{T}$ is broken but its combinations with certain crystalline symmetry such as $M_x \mathcal{T}$, $C_{2z} \mathcal{T}$, $C_{4z}\mathcal{T}$, and $C_{6z}\mathcal{T}$ are preserved. Our results demonstrate that an equivalent BDI class TSC can be realized in the $M_x \mathcal{T}$ or $C_{2z} \mathcal{T}$ superconducting wire, which is characterized by a chiral $Z^c$ invariant. More interestingly, we also find two types of totally new TSC phases in the $C_{4z}\mathcal{T}$, and $C_{6z}\mathcal{T}$ superconducing wires, which are beyond the known AZ class, and are characterized by a helical $Z^h$ invariant and $Z^h\oplus Z^c$ invariants, respectively. In the $Z^h$ TSC phase, $Z$-pairs of MZMs are protected at each end. In the $C_{6z}\mathcal{T}$ case, the MZMs can be either chiral or helical, and even helical-chiral coexisting. The minimal models preserving $C_{4z}\mathcal{T}$ or $C_{6z}\mathcal{T}$ symmetry are presented to illustrate their novel TSC properties and MZMs.