Theory of a quantum critical phenomenon in a topological insulator: (3+1)-dimensional quantum electrodynamics in solids

TL;DR

This paper develops a theoretical framework for understanding the quantum critical point in (3+1)-dimensional topological insulators, revealing how electromagnetic interactions influence the phase transition and related physical properties.

Contribution

It derives and solves RG equations for a Dirac fermion coupled to electromagnetic fields, uncovering novel scaling behaviors and crossover scales in topological insulators.

Findings

c and v approach a common value with c^2v nearly unrenormalized

RG flow of alpha is similar to QED with modified c^2v

Two crossover scales separate different scaling regimes

Abstract

We study theoretically the quantum critical phenomenon of the phase transition between the trivial insulator and the topological insulator in (3+1) dimensions, which is described by a Dirac fermion coupled to the electromagnetic field. The renormalization group (RG) equations for the running coupling constant \alpha, the speed of light c and electron v are derived. The almost exact analytic solutions to these RG equations are obtained to reveal that (i) c and v approach to the common value with combination c^2v being almost unrenormalized, (ii) the RG flow of \alpha is the same as that of usual QED with c^3 being replaced by c^2v, and (iii) there are two crossover momentum/energy scales separating three regions of different scaling behaviors. The dielectric and magnetic susceptibilities, angle-resolved photoemission spectroscopy (ARPES), and the behavior of the gap are discussed from this viewpoint.