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This research investigates the macroscopic magnetoelectric response of axion topological insulators using surface variable techniques and boundary finite element methods. By deriving exact analytic solutions for axial-symmetric geometries, the study provides a rigorous mathematical framework to describe effective surface charges and currents in these quantum materials under external fields. The work advances our theoretical understanding of how topology influences electromagnetic responses at material boundaries without introducing speculative applications or hype.
Surface Variables Description of Axion Topological Materials
arXiv:2607.10509v1 Announce Type: cross Abstract: We study the response of axion topological materials under the presence of external static electric and magnetic fields. We focus on the macroscopic quasi-static magnetoelectric response of topological insulators. We use techniques based on surface variables that have been previously employed in soft condensed matter problems for the description of heterogeneous systems composed of multiple homogeneous materials. A complete description of the whole system is written in terms of surface degrees of freedom, which in this case correspond to effective surface charge and surface current densities. We obtain a set of integral equations satisfied by these variables. We present exact analytic solutions for axial-symmetric cases. We develop a numerical method for the solution of the integral equations by means of a boundary finite element method. We apply the numerical method to topological insulators with different geometries such as spheres, hollow spheres and toroidal surfaces. We show that that a variational principle can be used to recover the surface variables equations.
Abstract:We study the response of axion topological materials under the presence of external static electric and magnetic fields. We focus on the macroscopic quasi-static magnetoelectric response of topological insulators. We use techniques based on surface variables that have been previously employed in soft condensed matter problems for the description of heterogeneous systems composed of multiple homogeneous materials. A complete description of the whole system is written in terms of surface degrees of freedom, which in this case correspond to effective surface charge and surface current densities. We obtain a set of integral equations satisfied by these variables. We present exact analytic solutions for axial-symmetric cases. We develop a numerical method for the solution of the integral equations by means of a boundary finite element method. We apply the numerical method to topological insulators with different geometries such as spheres, hollow spheres and toroidal surfaces. We show that that a variational principle can be used to recover the surface variables equations.
Materials Science (cond-mat.mtrl-sci); Other Condensed Matter (cond-mat.other); High Energy Physics - Theory (hep-th); Applied Physics (physics.app-ph); Quantum Physics (quant-ph)
arXiv:2607.10509 [cond-mat.mtrl-sci]
(or arXiv:2607.10509v1 [cond-mat.mtrl-sci] for this version)
From: Francisco J. Solis [view email] [v1] Sun, 12 Jul 2026 00:01:26 UTC (1,003 KB)
Full text under the publisher's open licence · 202 words
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