1/2 Z Topological Invariants and the Half Quantized Hall Effect

TL;DR

This paper introduces a new topological invariant, the 1/2 Z class, which characterizes the half-quantized Hall phase in topological materials, distinguishing it from ordinary metallic ferromagnets and validated through experimental systems.

Contribution

The paper identifies a novel 1/2 Z topological invariant linked to the half-quantized Hall phase, expanding the classification of topological states in metallic systems.

Findings

Existence of a 1/2 Z topological invariant for half-quantized Hall phase

Validation of the invariant in topological insulator and crystalline insulator films

Connection between the invariant and the anomalous Hall conductance line integral

Abstract

The half-quantized Hall phase represents a unique metallic or semi-metallic state of matter characterized by a fractional quantum Hall conductance, precisely half of an integer $\nu$ multiple of $e^{2}/h$. Here we demonstrate the existence of a novel $\frac{1}{2}\mathbb{Z}$ topological invariant that sets the half-quantized Hall phase apart from two-dimensional ordinary metallic ferromagnets. The $\frac{1}{2}\mathbb{Z}$ classification is determined by the line integral of the intrinsic anomalous Hall conductance, which is safeguarded by two distinct categories of local unitary and anti-unitary symmetries in proximity to the Fermi surface of electron states. We further validate the $\frac{1}{2}\mathbb{Z}$ topological order in the context of the quantized Hall phase by examining semi-magnetic topological insulator $\mathrm{Bi}_{2}\mathrm{Te}_{3}$ and $\mathrm{Bi}_{2}\mathrm{Se}_{3}$ film for $\nu=1$ and topological crystalline insulator SnTe films for $\nu=2$ or $4$. Our findings pave the way for future exploration and understanding of topological metals and their unique properties.