Engineering topological phases in triple HgTe/CdTe quantum wells

TL;DR

This paper explores the theoretical and experimental properties of triple HgTe quantum wells, revealing multiple topological phases with varying edge states and analyzing their transport characteristics, including the coexistence of parabolic and Dirac bands.

Contribution

It introduces a comprehensive model for triple HgTe quantum wells, identifying topological phase transitions and experimentally validating the coexistence of different electronic bands through transport measurements.

Findings

Identification of multiple topological phases with varying edge states

Experimental evidence of coexistence of parabolic and Dirac bands

Transport measurements show bulk conduction complicates edge state detection

Abstract

Quantum wells formed by layers of HgTe between Hg$_{1-x}$Cd$_x$Te barriers lead to two-dimensional (2D) topological insulators, as predicted by the BHZ model. Here, we theoretically and experimentally investigate the characteristics of triple HgTe quantum wells. We describe such heterostructure with a three dimensional $8\times 8$ Kane model, and use its eigenstates to derive an effective 2D Hamiltonian for the system. From these we obtain a phase diagram as a function of the well and barrier widths and we identify the different topological phases composed by zero, one, two, and three sets of edge states hybridized along the quantum wells. The phase transitions are characterized by a change of the spin Chern numbers and their corresponding band inversions. Complementary, transport measurements are experimentally investigated on a sample close to the transition line between the phases with one and two sets of edges states. Accordingly, for this sample we predict a gapless spectrum with low energy bulk conduction bands given by one parabolic and one Dirac band, and with edge states immersed in the bulk valance bands. Consequently, we show that under these conditions, local and non-local transport measurements are inconclusive to characterize a sole edge state conductivity due to bulk conductivity. On the other hand, Shubnikov-de Haas (SdH) oscillations show an excellent agreement with our theory. Particularly, we show that the measured SdH oscillation frequencies agrees with our model and show clear signatures of the coexistence of a parabolic and Dirac bands.