Quantum Electrodynamics of Non-Hermitian Dirac Fermions

TL;DR

This paper develops a quantum electrodynamics framework for non-Hermitian Dirac materials interacting with photons, revealing an emergent Lorentz symmetry and a universal terminal velocity in the infrared regime.

Contribution

It introduces a novel effective QED theory for non-Hermitian Dirac systems, highlighting emergent Lorentz invariance and velocity renormalization effects.

Findings

Emergent Lorentz symmetry in non-Hermitian Dirac materials.

Existence of a universal terminal velocity equal to the speed of light.

Nonuniversal terminal velocities in three-dimensional systems due to dynamic screening.

Abstract

We develop an effective quantum electrodynamics for non-Hermitian (NH) Dirac materials interacting with photons. These systems are described by nonspatial symmetry protected Lorentz invariant NH Dirac operators, featuring two velocity parameters $v_{_{\rm H}}$ and $v_{_{\rm NH}}$ associated with the standard Hermitian and a masslike anti-Hermitian Dirac operators, respectively. They display linear energy-momentum relation, however, in terms of an effective Fermi velocity $v_{_{\rm F}}=\sqrt{v^2_{_{\rm H}}-v^2_{_{\rm NH}}}$ of NH Dirac fermions. Interaction with the fluctuating electromagnetic radiation then gives birth to an emergent Lorentz symmetry in this family of NH Dirac materials in the deep infrared regime, where the system possesses a unique terminal velocity $v_{_{\rm F}}=c$, with $c$ being the speed of light. While in two dimensions such a terminal velocity is set by the speed of light in the free space, dynamic screening in three spatial dimensions permits its nonuniversal values. Manifestations of such an emergent spacetime symmetry on the scale dependence of various physical observables in correlated NH Dirac materials are discussed.