Detecting winding and Chern numbers in topological matter using spectral function

TL;DR

This paper introduces a method to measure topological invariants like winding and Chern numbers directly from the spectral function in momentum space, using ARPES, applicable to various topological models.

Contribution

It derives how to extract topological quantum numbers from the spectral function in different models, linking experimental spectral data to topological properties.

Findings

Spectral function contains information about topological invariants.

Method applicable to several topological models including Kitaev, SSH, and Haldane.

Limitations exist for higher-dimensional systems, requiring additional measurements.

Abstract

We propose a method to directly probe bulk topological quantum numbers in topological matter by measuring the momentum-space single-particle spectral function (SPSF). Angle-resolved photoemission spectroscopy (ARPES) can detect SPSF and is often used to determine the bulk band structure of quantum materials. Here, we show that while one part of the momentum-space SPSF gives band structure, it also contains the knowledge of winding and Chern numbers of various topological materials. For this, we derive SPSF in different models of topological systems, such as the Kitaev model of topological superconductors, the long-range Su-Schrieffer-Heeger model, the Qi-Wu-Zhang model, the Haldane model on a hexagonal lattice and a four-band model that is a physical realization of the Kitaev chain and explain how to extract the winding or Chern numbers in different topological phases from the SPSF. Such information from SPSF seems experimentally accessible due to the recent advancement of ARPES and scanning tunneling spectroscopy techniques. While the detection of bulk topological quantum numbers using the SPSF works well for one-dimensional systems, it has certain limitations for higher-dimensional systems, where it must be complementary with another measurement to ensure the matter under investigation is topological, i.e., having a non-zero Chern number.