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Yuhan Ye

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2 published item(s)

preprint2026arXiv

Electronic procrystalline state in moire structures

Solid state materials can display varieties of atomic structural orders ranging from crystalline to amorphous, underlying their properties and diverse functionalities. Procrystal has emerged as a new category of solids, featuring a long-range ordered lattice framework tiled with disordered atomic or molecular structures on the lattice sites, arousing great interest due to its novel structural and physical properties. However, the electronic analogue of a procrystal, dubbed as an electronic procrystalline (EPC) state, has never been experimentally observed. Here, we report the observation of an EPC state in a moire superstructure formed between a monolayer metallic NiTe2 and a superconductor NbSe2 with incommensurate lattice wavevectors. The observed EPC state exhibits a long-range periodic charge modulation at the moire scale inlaid with short-range irregular orders within each moire cell. Strikingly, the short-range charge orders inside the moire unit cells have proximately root3*root3 quasi-period, which is absent in pristine NiTe2. Intriguingly, the EPC order is also observed in the superconducting state of the moire superstructure. Furthermore, the emergent EPC state and short-range charge order, coexisting with the proximity induced superconductivity, can be precisely modulated with the thickness of NiTe2. Our findings uncover the potential of moire platform for understanding and tuning novel correlated quantum phases with this exotic procrystalline order.

preprint2026arXiv

Parameterized Complexity of Stationarity Testing for Piecewise-Affine Functions and Shallow CNN Losses

We study the parameterized complexity of testing approximate first-order stationarity at a prescribed point for continuous piecewise-affine (PA) functions, a basic task in nonsmooth optimization. PA functions form a canonical model for nonsmooth stationarity testing and capture the local polyhedral geometry that appears in ReLU-type training losses. Recent work by Tian and So (SODA 2025) shows that testing approximate stationarity notions for PA functions is computationally intractable in the worst case, and identifies fixed-dimensional tractability as an open direction. We address this direction from the viewpoint of parameterized complexity, with the ambient dimension $d$ as the parameter. In this paper, we give XP algorithms in fixed dimension for the tractable sides, and prove W[1]-hardness for the complementary sides. Moreover, lower bounds under the Exponential Time Hypothesis rule out algorithms running in time $ρ(d)\size^{o(d)}$ for any computable function $ρ$, where $\size$ denotes the total binary encoding length of the stationarity-testing instance. As a further consequence, our results yield the corresponding parameterized complexity picture for testing local minimality of continuous PA functions. We further extend our hardness results to a family of shallow ReLU CNN training losses, with stationarity tested in the trainable weight space. Thus, the same parameterized-complexity picture also appears for simple CNN training losses.