Magnetic properties of HgTe quantum wells

TL;DR

This paper investigates the magnetic properties and edge states of HgTe quantum wells under magnetic fields, revealing differences between normal and inverted regimes, and analyzing magnetization and susceptibility behaviors including oscillations and discontinuities.

Contribution

It provides analytical and numerical analysis of magnetic edge states and magnetization in HgTe quantum wells, highlighting differences between normal and inverted band structures and their magnetic responses.

Findings

Counterpropagating spin-polarized states exist only in the inverted regime.

Magnetization exhibits de Haas-van Alphen oscillations with temperature-dependent amplitude.

Discontinuity in ground-state magnetization occurs at the band crossover in the inverted regime.

Abstract

Using analytical formulas as well as a finite-difference scheme, we investigate the magnetic field dependence of the energy spectra and magnetic edge states of HgTe/CdTe-based quantum wells in the presence of perpendicular magnetic fields and hard walls, for the band-structure parameters corresponding to the normal and inverted regimes. Whereas one cannot find counterpropagating, spin-polarized states in the normal regime, below the crossover point between the uppermost (electron-like) valence and lowest (hole-like) conduction Landau levels, one can still observe such states at finite magnetic fields in the inverted regime, although these states are no longer protected by time-reversal symmetry. Furthermore, the bulk magnetization and susceptibility in HgTe quantum wells are studied, in particular their dependence on the magnetic field, chemical potential, and carrier densities. We find that for fixed chemical potentials as well as for fixed carrier densities, the magnetization and magnetic susceptibility in both the normal and the inverted regimes exhibit de Haas-van Alphen oscillations, whose amplitude decreases with increasing temperature. Moreover, if the band structure is inverted, the ground-state magnetization (and consequently also the ground-state susceptibility) is discontinuous at the crossover point between the uppermost valence and lowest conduction Landau levels. At finite temperatures and/or doping, this discontinuity is canceled by the contribution from the electrons and holes and the total magnetization and susceptibility are continuous. In the normal regime, this discontinuity of the ground-state magnetization does not arise and the magnetization is continuous for zero as well as finite temperatures.