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

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 ${\mathrm{CdTe}\text{−}\mathrm{Cd}}_{0.5}{\mathrm{Zn}}_{0.5}\mathrm{Te}$ strained-layer superlattices on GaAs as virtual substrates with adjustable lattice constant to control the strain of the QW. We present magnetotransport 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.

Figure 1

(a) HRXRD $2\theta -\omega$ scan (black) and simulation (orange) of the (004) reflection of a SLS with superlattice period $p=109\AA$. The (004) reflection from the GaAs substrate is labeled $S$, the SLS Bragg and higher-order peaks are labeled with 0 and $\pm 1,\pm 2,\pm 3,\dots$, respectively. (b) Sketch of a single SLS period: one monolayer ${\mathrm{Cd}}_{0.5}{\mathrm{Zn}}_{0.5}\mathrm{Te}$ alternating with an adjustable thickness $d_{\mathrm{CT}}$ of CdTe. (c) Dots: effective lattice constant $a_{\mathrm{SLS}}$ of a set of SLS with varying product of CdTe growth time and Te beam equivalent pressure $t_{\mathrm{CT}}\times {\phi }_{\mathrm{Te}}$. The line is a fit to Eq. (1). Dashed lines indicate the lattice constants used for samples $A$ ($ϵ=-0.3\%$), $B$ ($ϵ=+0.4\%$), and $C$ ($ϵ=+1.4\%$).

Figure 2

(a) HRXRD $2\theta -\omega$ scan of the (004) reflection of samples $A$ (top), $B$ (center), and $C$ (bottom). Reflections are labeled as in Fig. 1. Arrows indicate the strain-induced shift of the ${\mathrm{Cd}}_{0.7}{\mathrm{Hg}}_{0.3}\mathrm{Te}$ QW barrier reflections (unlabeled). The diffracted intensity of the QW (“$Q$”) is only visible in sample $C$. Black lines are simulated diffraction profiles, which are slightly offset downwards for clarity. (b) Calculated band structures of samples $A$, $B$, and $C$ (from top to bottom). Numbers in brackets denote crystal directions. Dashed lines indicate the energetic overlap $E_{\mathrm{ov}}$ of VB and CB for sample $A$ and the band gap $E_G$ of samples $B$ and $C$.

Figure 3

(a) Hall resistance $R_{xy}$ as a function of magnetic field for samples $A$ (red) and $B$ (blue) at carrier densities $n\approx +2$ and $-4\times 10^{11}{\mathrm{cm}}^{-2}$, labeled $n$ and $p$, respectively. Measurement at $-2\times 10^{11}{\mathrm{cm}}^{-2}$ (labeled $c$) was only possible for sample $A$. Dashed lines are obtained by fitting $R_{xy}$ and $R_{xx}$ simultaneously to a two-carrier Drude model. (b) Derivative of the Hall resistance of sample $A$ as a function of magnetic field $B$ for gate voltages from $-0.6\mathrm{V}$ (magenta) to $+1.0\mathrm{V}$ (black). (c) Crosses: net carrier density estimated from $R_{xy}$ at higher fields, as a function of gate voltage $U_G$. Filled (empty) circles: density of electrons (holes) obtained from two-carrier fit. The double arrow highlights $n$-type carrier density $n_e^{*}$ at the onset of two-carrier conductance.

Figure 4

(a) Minimum conductance $G_{\min }$ of samples $A$, $B$, and $C$ as function of temperature. Empty and filled dots correspond to values measured on large and small Hall bars. Inset gives the Hall bar dimensions—note the different scales. Dashed rectangles and black areas indicate the gated regions, while the probed edge current paths are indicated by orange lines. (b) Arrhenius plot of $G_{\min }$ of samples $B$ and $C$ at $T>10\mathrm{K}$. Lines are fit of the large Hall bar data to Eq. (2).