Geometric Model of Topological Insulators from the Maxwell Algebra

TL;DR

This paper introduces a geometric model for 3D topological insulators incorporating electromagnetic effects, using the Maxwell algebra to unify symmetries and derive a relativistic Wen-Zee term consistent with quantum Hall phenomena.

Contribution

It develops a novel geometric framework based on the Maxwell algebra to describe topological insulators and their boundary states, extending previous models to include relativistic and electromagnetic effects.

Findings

Derived a relativistic Wen-Zee term for topological insulators.

Showed the non-minimal coupling aligns with relativistic quantum Hall properties.

Unified Lorentz and magnetic-translation symmetries in a geometric model.

Abstract

We propose a novel geometric model of three-dimensional topological insulators in presence of an external electromagnetic field. The gapped boundary of these systems supports relativistic quantum Hall states and is described by a Chern-Simons theory with a gauge connection that takes values in the Maxwell algebra. This represents a non-central extension of the Poincar\'e algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, we derive a relativistic version of the Wen-Zee term, and we show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space.