Optical absorption measurement of spin Berry curvature and spin Chern marker

TL;DR

This paper introduces a measurable optical method to determine the spin Chern number and topological invariants in two-dimensional topological insulators using spin-resolved circular dichroism and ARPES, enabling real-space and criticality analysis.

Contribution

It develops a linear response theory for spin Berry curvature, proposes experimental techniques to measure topological invariants, and introduces spatially-resolved markers for topological phase transitions.

Findings

Spectral function measurable via pump-probe experiments.

Sign of the Pfaffian of the ${f Z}_2$ invariant can be directly detected.

Spatial variation of spin Chern marker characterized by circular dichroism.

Abstract

In two-dimensional time-reversal symmetric topological insulators described by Dirac models, the ${\mathbb Z}_{2}$ topological invariant can be described by the spin Chern number. We present a linear response theory for the spin Berry curvature that integrates to the spin Chern number, and introduce its spectral function that can be measured at finite temperature by momentum- and spin-resolved circular dichroism, which may be achieved by pump-probe type of experiments using spin- and time-resolved ARPES. As a result, the sign of the Pfaffian of the ${\mathbb Z}_{2}$ invariant can be directly measured. The spin Chern number expressed in real space yields a spin Chern marker, whose spatial variation may be measured by circular dichroism and spin-resolved photoemission with a spatial resolution. A spin Chern correlator and a nonlocal spin Chern marker are further proposed to characterize the quantum criticality near topological phase transitions, which are shown to take the form of overlaps between spin-selected Wannier states.