arXiv subjects

Peigen Li

Publications and source records attributed to Peigen Li.

9 recordsLinked to original sources

arXiv2026

On the relations among algebraic models for the MinRank problem

In this article, we study the relations between algebraic models for the MinRank problem, which is a well-known NP-hard problem. We establish connections between the minors modeling, the Kipnis-Shamir modeling, and the support minors modeling, providing insights into their equivalences and differences. Our results contribute to a deeper understanding of the algebraic structures underlying the MinRank problem and may inform future research on efficient algorithms for solving it.

math.AC↗

arXiv2025

Exotic Surface Stripe Orders in Correlated Kagome Metal CsCr3Sb5

The newly discovered kagome superconductor CsCr3Sb5 exhibits distinct features with flat bands and unique magnetism, providing a compelling platform for exploring novel quantum states of correlated electron systems. Emergent charge order in this material is a key for understanding unconventional superconductivity, but it remains unexplored at the atomic scale and the underlying physics is elusive. Here, we identify and unreported stripe orders on the surface which are distinct from the bulk and investigate the underlying bulk electronic properties using a combination of scanning tunneling microscopy (STM), angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations. Specifically, a mixture of 2a0 * a0 and 3a0 * a0 stripe order is found on Cs-terminated surface while 4a0 * root3a0 stripe order is found on the Sb-terminated surface. The electronic spectra exhibit strongly correlated features resembling that of high temperature superconductors, with kagome flat bands lying about 330 meV above EF, suggesting that the electron correlations arise from Coulomb interactions and Hund's coupling. Moreover, a distinct electron-boson coupling mode is observed at approximately 100 meV. These findings provide new insights into the interplay between surface and bulk charge orders in this strongly correlated kagome system.

cond-mat.str-el↗

arXiv2024

Direct observation of topological magnon edge states

Magnon Chern insulators (MCIs) exhibit unique topological magnon band structures featuring chiral edge states. Direct observations of the topologically protected magnon edge states have long been pursued. Here, we report the spatially resolved detection of magnon edge states in a two-dimensional ferromagnet with honeycomb lattice (single-layer chromium triiodide). Using scanning tunneling microscopy, we observed magnon-assisted inelastic tunneling conductance and revealed the gapped magnon spectra with enhanced signals at the van Hove singularities. Extra tunneling conductance contributed from the magnon edge states was detected at three different edge configurations. Our work provided direct evidence proving the existence of MCI states down to the single-layer limit, initiating spatially-resolved explorations on exotic properties arising from topological edge states of MCIs.

cond-mat.mes-hall↗

arXiv2024

Observation of in-gap states in a two-dimensional CrI2/NbSe2 heterostructure

Low-dimensional magnetic structures coupled with superconductors are promising platforms for realizing Majorana zero modes, which have potential applications in topological quantum computing. Here, we report a two-dimensional (2D) magnetic-superconducting heterostructure consisting of single-layer chromium diiodide (CrI2) on a niobium diselenide (NbSe2) superconductor. Single-layer CrI2 nanosheets, which hold antiferromagnetic (AFM) ground states by our first-principles calculations, were epitaxially grown on the layered NbSe2 substrate. Using scanning tunneling microscopy/spectroscopy, we observed robust in-gap states spatially located at the edge of the nanosheets and defect-induced zero-energy peaks inside the CrI2 nanosheets. Magnetic-flux vortices induced by an external field exhibit broken threefold rotational symmetry of pristine NbSe2 superconductor, implying the efficient modulation of the interfacial superconducting states by the epitaxial CrI2 layer. A phenomenological model suggests the existence of chiral edge states in a 2D AFM-superconducting hybrid system with an even Chern number, providing a qualitatively plausible understanding for our experimental observation.

cond-mat.supr-con↗

arXiv2022

The $p$-adic Gelfand-Kapranov-Zelevinsky hypergeometric complex

To a torus action on a complex vector space, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, which are now called the GKZ hypergeometric system. Its solutions are GKZ hypergeometric functions. We study the $p$-adic counterpart of the GKZ hypergeometric system. The $p$-adic GKZ hypergeometric complex is a twisted relative de Rham complex of over-convergent differential forms with logarithmic poles. It is an over-holonomic object in the derived category of arithmetic $\mathcal D$-modules with Frobenius structures. Traces of Frobenius on fibers at Techmüller points of the GKZ hypergeometric complex define the hypergeometric function over the finite field introduced by Gelfand and Graev. Over the non-degenerate locus, the GKZ hypergeometric complex defines an over-convergent $F$-isocrystal. It is the crystalline companion of the $\ell$-adic GKZ hypergeometric sheaf that we constructed before. Our method is a combination of Dwork's theory and the theory of arithmetic $\mathcal D$-modules of Berthelot.

math.AG↗

arXiv2021

Exponential sums and rigid cohomology

In this article, we prove a comparison theorem between the Dwork cohomology introduced by Adolphson and Sperber and the rigid cohomology. As a corollary, we can calculate the rigid cohomology of Dwork isocrystal on torus.

math.AG↗

arXiv2021

Robba's method on exponential sums

In this article, we use Robba's method to give an estimate of the Newton polygon for the L function on torus and we can draw the Newton polygon in some special cases.

math.AG↗

arXiv2019

Single-Layer CrI3 Grown by Molecular Beam Epitaxy

Single- and few-layer chromium triiodide (CrI3), which has been intensively investigated as a promising platform for two-dimensional magnetism, was usually prepared by mechanical exfoliation. Here, we report on the growth of single-layer CrI3 by molecular beam epitaxy under ultrahigh vacuum. The atomic structures and local density of states have been revealed by scanning tunneling microscopy (STM). Iodine trimers, each of which consists of three I atoms surrounding a three-fold Cr honeycomb center, have been identified as the basic units of the topmost I layer. Different superstructures of single-layer CrI3 with characteristic periodicity around 2-4 nm were obtained on Au(111), but only pristine structure was observed on graphite. At elevated temperatures (423 K), CrI3 was partially decomposed, resulting in the formation of single-layer chromium diiodide. Our bias-dependent STM images suggest that the unoccupied and occupied states are distributed spatial-separately, which is consistent with our density functional theory calculations. The effect of charge distribution on the superexchange interaction in single-layer CrI3 was discussed.

cond-mat.mtrl-sci↗

arXiv2018

Topology optimization of micro-structured materials featured with the specific mechanical properties

Micro-structured materials consisting of an array of microstructures are engineered to provide the specific material properties. This present work investigates the design of cellular materials under the framework of level set, so as to optimize the topologies and shapes of these porous material microstructures. Firstly, the energy-based homogenization method (EBHM) is applied to evaluate the material effective properties based on the topology of the material cell, where the effective elasticity property is evaluated by the average stress and strain theorems. Secondly, a parametric level set method (PLSM) is employed to optimize the microstructural topology until the specific mechanical properties can be achieved, including the maximum bulk modulus, the maximum shear modulus and their combinations, as well as the negative Poisson's ratio (NPR). The complicated topological shape optimization of the material microstructure has been equivalent to evolve the sizes of the expansion coefficients in the interpolation of the level set function. Finally, several numerical examples are fully discussed to demonstrate the effectiveness of the developed method. A series of new and interesting material cells with the specific mechanical properties can be found.

cs.CE↗