Strain Engineering of the Band Gap of HgTe Quantum Wells Using Superlattice Virtual Substrates

Abstract

The HgTe quantum well (QW) is a well-characterized two-dimensional topological insulator (2D-TI). Its band gap is relatively small (typically on the order of 10 meV), which restricts the observation of purely topological conductance to low temperatures. Here, we utilize the strain-dependence of the band structure of HgTe QWs to address this limitation. We use CdTe-Cd0.5Zn0.5Te strained-layer superlattices on GaAs as virtual substrates with adjustable lattice constant to control the strain of the QW. We present magneto-transport measurements, which demonstrate a transition from a semimetallic to a 2D-TI regime in wide QWs, when the strain is changed from tensile to compressive.Most notably, we demonstrate a much enhanced energy gap of 55 meV in heavily compressively strained QWs. This value exceeds the highest possible gap on common II-VI substrates by a factor of 2-3, and extends the regime where the topological conductance prevails to much higher temperatures.The transport properties of molecular-beam epitaxially (MBE) grown HgTe QWs embedded in Cd 0.7 Hg 0.3 Te barriers have attracted considerable attention due to the discovery of the quantum-spin-Hall (QSH) effect in these structures [1][2][3]. The QSH effect is the landmark property of a 2D-TI and is characterized by the presence of a pair of one-dimensional, counter-propagating ("helical") channels along the edges of the mesa, giving rise to a quantized longitudinal conductanceA prerequisite for the formation of edge channels is atopologically nontrivial -inverted band structure, as is present in HgTe QWs when the thickness d QW exceeds d c = 6.3 nm [1]. Inverted HgTe QWs have a relatively small band gap E G (typically lower than 15 meV), which can make it difficult to gate homogeneously into the gap over the whole mesa, and also prevents applications at elevated temperatures. Here we present a way to increase E G well above the thermal energy at room temperature (k B T = 25 meV). This is achieved by applying compressive strain to HgTe QWs through coherent growth on virtual substrates with a freely tunable lattice constant.The crucial influence of strain on the band structure of HgTe has been demonstrated previously for bulk layers (layer thickness d > 40 nm): epitaxy of HgTe on CdTe substrates exerts tensile strain (ε = −0.3 %), which causes a gap-opening of the Γ 8 doublet, transforming the bulk semimetal into a three-dimensional topological insulator [4,5]. However, these previous experiments used commercially available MBE quality substrates, limiting the options to Cd 0.96 Zn 0.04 Te[1-3] and CdTe [4,5][6]. In both cases, the lattice constant of the substrate material is larger than that of HgTe, resulting in a tensile strain in the epilayers. Under such conditions, the largest gaps that can be obtained in inverted QWs are E G = 17 meV and 25 meV for wells grown on CdTe and Cd 0.96 Zn 0.04 Te, respectively [7].The present work reports on a major progress in this situation. We use CdTe-Cd 0.5 Zn 0.5 Te (001) strainedlayer superlattices (SLS) as virtual ...

Approaching Quantization in Macroscopic Quantum Spin Hall Devices through Gate Training

“…This method of band gap engineering is explained in more detail in Ref. [23]. Each QW exhibits a Cd 0.7 Hg 0.3 Te top barrier of 16 to 18 nm.…”

Realistic picture of helical edge states in HgTe quantum wells

“…The latter significantly enhances the band gap in QSHI state (up to 55 meV) and suppresses the side maxima in the valence subband. Figure 4 presents the band structure of compressively strained HgTe QWs of 7.5 nm width, realized experimentally Leubner et al 36 . Under these conditions, the QW is characterized by QSHI state with a direct band gap, opened between the H 1 and H 2 subbands.…”

“…Such buffer results in a tensile strain in the HgTe epilayers ( = −0.3%). Recently, Leubner et al 36 have discovered the way to change the strain in HgTe QWs from tensile ( < 0) to compressive (up to = 1.4%). The latter significantly enhances the band gap in QSHI state (up to 55 meV) and suppresses the side maxima in the valence subband.…”

Interplay of Dirac Nodes and Volkov-Pankratov Surface States in Compressively Strained HgTe

“…1b). While there is no commercially available substrate with a lattice constant slightly below that of HgTe, compressive strain is experimentally still accessible through a superlattice virtual substrate [14] as sketched in Fig. 1b.…”