Half-Quantized Hall Effect and Power Law Decay of Edge Current Distribution

TL;DR

This paper explores the unique topological and transport properties of parity anomalous semimetals, revealing a bulk-edge correspondence for the half-quantized Hall effect and a power law decay of edge current distribution.

Contribution

It uncovers a novel bulk-edge correspondence in parity anomalous semimetals and characterizes the power law decay of edge currents, linking these phenomena to physical systems.

Findings

Half-quantized Hall effect realized via bulk massless Dirac fermions.

Edge current distribution decays as a power law, not exponentially.

Relevance to topological insulators and photonic crystals.

Abstract

The half-quantized Hall conductance is characteristic of quantum systems with parity anomaly. Here we investigate topological and transport properties of a class of parity anomalous semimetals, in which massive Dirac fermions coexist with massless Dirac fermions in momentum space or real space, and uncovered a distinct bulk-edge correspondence that the half-quantized Hall effect is realized via the bulk massless Dirac fermions while the nontrivial Berry curvature is provided by the massive Dirac fermions. The spatial distribution of the edge current decays away from the boundary in a power law instead of an exponential law in integer quantum Hall effect. We further address physical relevance of parity anomalous semimetal to three-dimensional semi-magnetic topological insulators and two-dimensional photonic crystals.