2D compressibility of surface states on 3D topological insulators

TL;DR

This paper develops a theoretical framework to measure the surface state compressibility of 3D topological insulators, proposing scanning single electron transistor microscopy as a practical experimental method to explore their topological properties.

Contribution

It introduces a detailed theory for surface state compressibility, incorporating electron interactions and experimental comparisons, enabling new insights into topological insulator surface states.

Findings

The theory matches experimental dμ/dn measurements from ARPES.

Interaction effects can be observed through Fermi velocity renormalization.

Surface probes can effectively access topological surface states.

Abstract

We develop a theory for the compressibility of the surface states of 3D topological insulators and propose that surface probes of the compressibility via scanning single electron transistor microscopy will be a straightforward way to access the topological states without interference from the bulk states. We describe the single-particle nature of the surface states taking into account an accurate Hamiltonian for the bands and then include the contribution from electron--electron interactions and discuss the implications of the ultra-violet cutoff, including the universality of the exchange contribution when expressed in dimensionless units. We also compare the theory with experimentally obtained d{\mu}/dn as extracted from angle-resolved photoemission spectroscopy measurements. Finally, we point out that interaction-driven renormalization of the Fermi velocity may be discernible via this technique.