arXiv subjects

Xiaorong Zou

Publications and source records attributed to Xiaorong Zou.

13 recordsLinked to original sources

arXiv2026

Higher-Order Topological Phase in the Two-Dimensional Type-IV Magnet MgCr$_2$O$_4$

Type-IV two-dimensional (2D) magnetism-a newly classified collinear magnetic phase featuring nonrelativistic spin degeneracy and spin-orbit-coupling-induced momentum-dependent spin splitting-extends the symmetry classification of collinear magnets, opening new opportunities for unconventional topological quantum states. Here, we reveal that the recently proposed two-dimensional type-IV 2D magnet MgCr$_2$O$_4$ hosts an intrinsic higher-order topological insulating phase, featuring $\mathcal{C}_{3z}$-protected corner states and a nontrivial rotational topological invariant of $χ^{(3)}$ = $\{-2,4\}$ with a quantized fractional corner charge of $4e/3$. Spin-orbit coupling breaks the spin-degeneracy-enforcing symmetry $[C_{2}||M_z]$ while preserving the crystalline $\mathcal{C}_{3z}$ rotational symmetry that protects the higher-order topological phase, thereby enabling spin splitting to coexist with the nontrivial topology. Furthermore, the higher-order topological phase remains intact throughout a wide range of biaxial strains without band-gap closing and topological phase transition, demonstrating the robustness of the symmetry-protected topological state against external perturbations. Our work establishes a direct connection between type-IV magnetic system and higher-order topology, providing a new route for symmetry-engineered magnetic topological quantum states.

physics.comp-ph↗

arXiv2026

An attractive analytic solution of the Maxwell's equation

In this paper, we aim to develop a closed-form solution of the standard Maxwell's equations that describe the propagation of electromagnetic waves in an isotropic homogeneous medium such as a vacuum. The proposed solution has a simple analytic structure that explains how initial conditions characterize the underlying electromagnetic wave. As such, it can be used as a tool to generate suitable electromagnetic waves in practice. The clean structure of the solution can also help us to derive closed-form solutions in a general medium with a non-zero current term. In this paper, we enhance the solution to cover a special case where the current comes from the contribution of an independent generator. We shall leverage the tools developed in this paper to derive similar closed-form solutions of Maxwell's equations in general mediums with non-zero currents in a separate paper.

math.AP↗

arXiv2026

On analytic solution of the Maxwell's equation with non-zero currents

An analytic solution has been recently developed for the Maxwell's equation in a medium with zero currents such as vacuum. The solution is attractive in the sense that it is formulated based on the Fourier expansion of the initial value. It has been used to study the properties of solutions like certain conservative laws and construct electromagnetic waves with certain features. In this paper, we study Maxwell's equation in a medium with non-zero currents. The structure of solutions in this setting turns out to be much more complicated than what has been achieved without currents, and a clean structure of analytic solutions as with zero current is no longer available in general. Nevertheless, we can still develop an algorithm to construct the solution effectively. Our efforts in seeking analytic solution focus on two special cases. First, we develop analytic solution under the assumption that Ohm's law is satisfied, i.e. the current density is proportional to electronic density; secondly, we add skew symmetric components under generalized Ohm's law, which is also refereed as Hall effect in literature, and study the properties of solutions. In addition, we consider the case where an independent local electromagnetic field is included and derive the analytical solution accordingly. As an application, we provide an example to use the analytic solution to construct parallel electronic and magnetic waves.

math.AP↗

arXiv2026

Accelerated Discovery of Nitrogen-Coordinated Dual-Atom Hydrogen Evolution Reaction Electrocatalysts via Machine Learning Potentials

The hydrogen evolution reaction (HER) is central to sustainable hydrogen production, and nitrogen coordinated dual atom catalysts (DACs) offer a promising route to noble metal activity at low cost. Yet their vast compositional and coordination design space remains underexplored, as density functional theory (DFT) screening at scale is prohibitive. Here, we map the HER landscape of graphene supported TM2@Nx-Gr DACs, screening 23 transition metals across 20 nitrogen coordination motifs using a machine learning potential (MLP) benchmarked against DFT. Intermediate coordination (2N to 4N) consistently yields near-optimal ΔGH*, with Ti2@2Na, Mn2@2Na, Fe2@2Na, Cu2@2Na, Rh2@2Na, Zr2@2Na, Zr2@2Nb, Zr2@2Nc, Nb2@2Nc, Zr2@2Nd, Mn2@2Ne, Mn2@2Nf, Ti2@3Na, Au2@3Na, Fe2@3Na, Pd2@3Nb, Rh2@3Nc, Rh2@3Nd, Au2@3Nd, V2@4Na, Ti2@4Nb, Pd2@4Nb, Ti2@4Nc, Cr2@4Nd, Ni2@4Nd, Cu2@4Nd emerging as standout, synthesizable candidates, most exhibiting metallic or narrow gap (<0.25 eV) character. The MLP reaches near-DFT accuracy, with a mean absolute error of 80 meV for Gibbs binding free energies at orders of magnitude lower computational cost, establishing MLP driven screening as a practical engine for next-generation catalyst discovery.

cond-mat.mtrl-sci↗

arXiv2026

Floquet-Engineered Odd-Parity Altermagnetic Higher-Order Topology in a Two-Dimensional Antiferromagnet Cr$_2$CH$_2$

Periodic driving provides a platform to dynamically tailor quantum states of matter, yet its impact on symmetry-protected topological phases remains incompletely understood. Here, we demonstrate that periodic driving enables the realization of an odd-parity altermagnetic (AM) higher-order topological insulator (HOTI) phase in the Cr$_2$CH$_2$ monolayer. In equilibrium, Cr$_2$CH$_2$ is a 2D antiferromagnetic (AFM) HOTI protected by $\mathcal C_3$ rotational symmetry, characterized by a symmetry indicator $χ^{(3)}$ = $\{-2,1\}$ and robust corner states. Under circularly polarized light (CPL), the system develops a f-wave altermagnetic state governed by the symmetry $[C_{2}||\overline{3}_{001}]$ with odd-parity spin splitting. Despite substantial Floquet-induced band renormalization, the $\mathcal C_3$-protected corner states remain intact over a broad range of driving strengths, highlighting the altermagnetic higher-order topology under Floquet driving. As the light intensity increases, the system gradually evolves into an altermagnetic semimetallic state. These results establish a direct connection between magnetism and topology in a periodically driven AFM system, offering a route toward the control of coupled spin and topological transport.

physics.comp-ph↗

arXiv2026

Second-order topology in two-dimensional azulenoid kekulene carbon lattices

The discovery of higher-order topological insulator (HOTI) has established a new paradigm for understanding symmetry-constrained boundary electronic states. Here, based on first-principles calculations, we demonstrate the emergence of HOTI phase in organic lattices of two-dimensional azulenoid-kekulene-type carbon allotropes, namely AKC-[3,3] and AKC-[6,0]. Enabled by the $C_6$ rotational symmetry, the nontrivial bulk topology is confirmed through the topological invariant and fractionally quantized corner charge, giving $\{[M^{(I)}_{2}],[K^{(3)}_{2}]\}$ = $\{0,2\}$ and $Q_{\mathrm{corner}} = e/3$, respectively, accompanied by the emergence of exotic corner states in nanoflakes. Notably, the structural modifications are explored, revealing that in the derived structure PAK-[6,0], whose corner-localized states are preserved, highlighting the robustness of the higher-order topological phase. These findings highlight azulenoid-kekulene-based carbon allotropes as a promising platform to explore the interplay between structural design, crystalline symmetry, and higher-order topological boundary responses in two dimensional carbon systems.

cond-mat.mtrl-sci↗

arXiv2026

Stochastic Loop Corrections to Belief Propagation for Tensor Network Contraction

Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces systematic errors on graphs with loops. Here, we introduce a hybrid method that achieves accurate results by stochastically sampling loop corrections to BP and showcase our method by applying it to the two-dimensional ferromagnetic Ising model. For any pairwise Markov random field with symmetric edge potentials, our approach exploits an exact factorization of the partition function into the BP contribution and a loop correction factor summing over all valid loop configurations, weighted by edge weights derived directly from the potentials. We sample this sum using Markov chain Monte Carlo with moves that preserve the loop constraint, combined with umbrella sampling to ensure efficient exploration across all correlation strengths. Our stochastic approach provides unbiased estimates with controllable statistical error in any parameter regime.

cond-mat.str-el↗

arXiv2025

Trigonometric-Interpolation Based Approach for Second-Order Volterra Integro-Differential Equations

The trigonometric interpolation has been recently applied to solve a second-order Fredholm integro-differentiable equation (FIDE). It achieves high accuracy with a moderate size of grid points and effectively addresses singularities of kernel functions. In addition, it work well with general boundary conditions and the framework can be generalized to work for FIDEs with a high-order ODE component. In this paper, we apply the same idea to develop an algorithm for the solution of a second-order Volterra integro-differentiable equation (VIDE) with the same advantages as in the study of FIDE. Numerical experiments with various boundary conditions are conducted with decent performances as expected.

math.NA↗

arXiv2025

Trigonometric Interpolation Based Approach for Second Order Fredholm Integro-Differential Equations

A trigonometric interpolation algorithm for non-periodic functions has been recently proposed and applied to study general ordinary differential equation (ODE). This paper enhances the algorithm to approximate functions in $2$-dim space. Performance of the enhanced algorithm is expected to be similar as in $1$-dim case and achieve accuracy aligned with the smoothness of the target function, which is confirmed by numerical examples. As an application, the $2$-dim trigonometric interpolation method is used to develop an algorithm for the solution of a second order Fredholm integro-differential equation (FIDE). There are several advantages of the algorithm. First of all, it converges quickly and high accuracy can be achieved with a moderate size of grid points; Secondly, it can effectively address singularities of kernel functions and work well with general boundary conditions. Finally, it can be enhanced to copy with other IDE such as Volterra IDE or IDE with high order ODE component. The tests conducted in this paper include various boundary conditions with both continuous kernels and integrable ones with singularity. Decent performance is observed across all covered scenarios with a moderate size of grid points.

math.NA↗

arXiv2025

Trigonometric Interpolation Based Approach for Second Order ODE with Mixed Boundary Conditions

This paper proposes a trigonometric interpolation-based approach (TIBA) to approximate solutions of mixed boundary value problems of second-order ODEs. TIBA leverages the analytic attractiveness of a trigonometric polynomial to reformulate the dynamics of $y, y',y''$ implied by ODE and boundary conditions. TIBA is particularly attractive for a linear ODE where the solution can be obtained directly by solving a linear system. The framework can be used to solve integro-differential equations. Numerical tests have been conducted to assess TIBA's performance regarding convergence, existence, and uniqueness of solution under various boundary conditions with expected results.

math.NA↗

arXiv2025

On Trigonometric Interpolation and Its Applications

In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform (FFT) to enhance efficiency. The algorithm can be formulated in a way such that certain cancellation effects can be effectively leveraged for error analysis, which enables us not only to obtain the desired uniform convergent rate of the approximation to a function, but desired uniform convergent rates for its derivatives as well. We further enhance the algorithm so it can be applied to non-periodic functions defined on bounded intervals. Numerical testing results confirm decent accurate performance of the algorithm. For its application, we demonstrate how it can be applied to estimate integrals and solve linear/non-linear ordinary differential equation (ODE). The test results show that it significantly outperforms Trapezoid/Simpson method on integral and standard Runge-Kutta algorithm on ODE. In addition, we show some numerical evidences that estimation error of the algorithm likely exhibits ``local property", i.e. error at a point tends not to propagate, which avoids significant compounding error at some other place, as a remarkable advantage compared to polynomial-based approximations.

math.NA↗

arXiv2025

Trigonometric Interpolation Based Optimization for Second Order Non-Linear ODE with Mixed Boundary Conditions

In this paper, we propose a trigonometric-interpolation approach for solutions of second order nonlinear ODEs with mixed boundary conditions. The method interpolates secondary derivative $y''$ of a target solution $y$ by a trigonometric polynomial. The solution is identified through an optimization process to capture the dynamics of $y,y',y''$ characterized by the underlying differential equation. The gradient function of the optimization can be carried out by Fast Fourier Transformation and high-degree accuracy can be achieved effectively by increasing interpolation grid points. In case that solution of ODE system is not unique, the algorithm has flexibility to approach to a desired solution that meets certain requirements such as being positive. Numerical tests have been conducted under various boundary conditions with expected performance. The algorithm can be extended for nonlinear ODE of a general order $k$ although implementation complexity will increase as $k$ gets larger.

math.NA↗

arXiv2022

Ferroelectric higher-order topological insulator in two dimensions

The interplay between ferroelectricity and band topology can give rise to a wide range of both fundamental and applied research. Here, we map out the emergence of nontrivial corner states in two-dimensional ferroelectrics, and remarkably demonstrate that ferroelectricity and corner states are coupled together by crystallographic symmetry to realize the electric control of higher-order topology. Implemented by density functional theory, we identify a series of experimentally synthesized two-dimensional ferroelectrics, such as In$_2$Se$_3$, BN bilayers, and SnS, as realistic material candidates for the proposed ferroelectric higher-order topological insulators. Our work not only sheds new light on traditional ferroelectric materials but also opens an avenue to bridge the higher-order topology and ferroelectricity that provides a nonvolatile handle to manipulate the topology in next-generation electronic devices.

cond-mat.mtrl-sci↗