Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor

TL;DR

This paper proposes a novel electric measurement scheme using spin-polarized STM to fully characterize the quantum geometric tensor of two-dimensional solid-state systems, demonstrated on topological insulator surface states.

Contribution

The paper introduces a new method to measure the complete quantum geometric tensor in solid-state systems via spin-polarized STM, including both quantum metric and Berry curvature.

Findings

Successfully derives the QGT from spin texture measurements.

Demonstrates the scheme on topological insulator surface states.

Shows the method works even with external magnetic fields.

Abstract

The quantum geometric tensor (QGT) embodies the geometry of the eigenstates of a system's Hamiltonian, and its full characterization across diverse quantum systems is essential. However, it is challenging to characterize the QGT of solid-state systems. Here we present an electric scheme to measure the complete QGT of two-dimensional solid-state systems by using spin-polarized scanning tunneling microscopy (STM), in which the spin texture is extracted from geometric amplitudes of Friedel oscillations induced by the intentionally introduced magnetic impurity, and then the QGT is derived from the momentum differential of spin texture. As a canonical spin model, the surface states of a topological insulator offer a promising way to demonstrate the scheme. In a slab of topological insulator, the gapped surface states host complete QGT, i.e., nonvanishing quantum metric and Berry curvature as its symmetric real part and the antisymmetric imaginary part. Thus, a detailed derivation guides the use of the developed scheme to measure the QGT of gapped surface states, even with an external magnetic field. This study opens a new avenue to directly measure the complete QGT of two-dimensional solid-state systems by using spin-polarized STM.