A Quantized Interband Topological Index in Two-Dimensional Systems

TL;DR

This paper introduces a new gauge-invariant, quantized interband index for 2D multiband systems that enables bulk topological classification of parameter submanifolds, confirmed through numerical models and applicable to edge state analysis.

Contribution

It presents a novel topological index that overcomes previous characterization difficulties and links to known topological invariants in various models.

Findings

The index is gauge-invariant and quantized.

It corresponds to valley and Chern numbers in models.

It enables analysis of edge states via band-resolved topological charge.

Abstract

We introduce a novel gauge-invariant, quantized interband index in two-dimensional (2D) multiband systems. It provides a bulk topological classification of a submanifold of parameter space (e.g., an electron valley in a Brillouin zone), and therefore overcomes difficulties in characterizing topology of submanifolds. We confirm its topological nature by numerically demonstrating a one-to-one correspondence to the valley Chern number in $k\cdot p$ models (e.g., gapped Dirac fermion model), and the first Chern number in lattice models (e.g., Haldane model). Furthermore, we derive a band-resolved topological charge and demonstrate that it can be used to investigate the nature of edge states due to band inversion in valley systems like multilayer graphene.