Abstract
Quantum wells formed by layers of HgTe between Hg_{1-x}Cd_xTe 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 8times 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 subbands given by one parabolic and one Dirac subband, and with edge states immersed in the bulk valence subbands. 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 subbands.
Highlights
Quantum wells formed by layers of HgTe between Hg1−xCdx Te barriers lead to two-dimensional (2D) topological insulators, as predicted by the BHZ model
I.e. double HgTe quantum wells (QWs) (DQWs), an intuitive 2D model for coupled QWs has been introduced by Refs.[42,43], with Ref.[23] showing that a variety of topological phases can be obtained depending upon the QW geometrical parameters
Triple quantum wells based on HgTe/CdxHg1−x Te with [013] surface orientation and equal well widths of d0 = 6.7 nm and barrier thickness t = 3 nm were prepared by molecular beam epitaxy (MBE)
Summary
Quantum wells formed by layers of HgTe between Hg1−xCdx Te barriers lead to two-dimensional (2D) topological insulators, as predicted by the BHZ model. We theoretically and experimentally investigate the characteristics of triple HgTe quantum wells We describe such heterostructure with a three dimensional 8 × 8 Kane model, and use its eigenstates to derive an effective 2D Hamiltonian for the system. I.e. double HgTe QWs (DQWs), an intuitive 2D model for coupled QWs has been introduced by Refs.[42,43], with Ref.[23] showing that a variety of topological phases can be obtained depending upon the QW geometrical parameters It has been recently proposed[44] that these DQWs could host second-order topological insulators with excitonic nodal phases that support flat band edge states, which could lead to s uperconductivity[45]. In contrast to the DQW case, the additional layer of the TQW allows for an interplay between the hybridization of the inner and outer layers, which can be controlled by its geometric parameters (wells and barrier widths), external electric fields and gates
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