Vacuum polarization at the boundary of a topological insulator

TL;DR

This paper investigates the quantum vacuum polarization effects on the surface of a topological insulator under magnetic and electric fields, revealing a force that tends to shrink the boundary due to topological properties.

Contribution

It introduces a modified Gauss law incorporating axionlike pseudoscalar effects to analyze vacuum polarization on topological insulator surfaces.

Findings

Vacuum energy depends on boundary length, inducing a surface shear stress.

The topological pseudoscalar modifies induced charge and vacuum energy.

A force tending to shrink the boundary is identified.

Abstract

In this paper we study the polarized vacuum energy on the conducting surface of a topological insulator characterized by both $Z_2$ topological index and time reversal symmetry. This boundary is subject to the action of a static and spatially homogeneous magnetic field perpendicular to it as well as of an electric field that is uniform near the considered surface and produced by a biased voltage, at zero temperature. To do this, we consider modifications in the Gauss law that arise due to the nonzero gradient of the axionlike pseudoscalar factor coupled to the applied magnetic field, which accounts for the topological properties of the system. Such a term allows us to find a correction to the induced charges which modifies the quantum vacuum of the spinor field regarding an ordinary surface. The polarized vacuum energy is calculated in both the weak-field approximation and in the general case, and since the found energy depends on a length defined on the boundary, we show that there is a radial density of force or a surface shear stress that tends to shrink it.