Quantum capacitance of an HgTe quantum well as an indicator of the topological phase

TL;DR

This paper investigates how quantum capacitance measurements can distinguish between topological phases in HgTe quantum wells by analyzing the thermodynamic density of states in different band structures.

Contribution

It provides a theoretical calculation of the density of states in HgTe quantum wells, linking quantum capacitance to topological phase detection.

Findings

Distinct density of states behavior in normal vs. inverted regimes

Quantum capacitance as an indicator of topological order

Unique collective electronic properties in HgTe quantum wells

Abstract

Varying the quantum-well width in an HgTe/CdTe heterostructure allows to realize normal and inverted semiconducting band structures, making it a prototypical system to study two-dimensional (2D) topological-insulator behavior. We have calculated the zero-temperature thermodynamic density of states $D_\mathrm{T}$ for the electron-doped situation in both regimes, treating interactions within the Hartree-Fock approximation. A distinctively different behavior for the density dependence of $D_\mathrm{T}$ is revealed in the inverted and normal cases, making it possible to detect the system's topological order through measurement of macroscopic observables such as the quantum capacitance or electronic compressibility. Our results establish the 2D electron system in HgTe quantum wells as unique in terms of its collective electronic properties.