Energy gap tuning and gate-controlled topological phase transition in $\mathrm{In}\mathrm{As}/{\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{Sb}$ composite quantum wells

We report transport measurements of strained $\mathrm{InAs}/{\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{Sb}$ composite quantum wells (CQWs) in the quantum spin Hall phase, focusing on the control of the energy gap through structural parameters and an external electric field. For highly strained CQWs with $x=0.4$, we obtain a gap of 35 meV, an order of magnitude larger than that reported for binary InAs/GaSb CQWs. Using a dual-gate configuration, we demonstrate an electrical-field-driven topological phase transition, which manifests itself as a reentrant behavior of the energy gap. The sizable energy gap and high bulk resistivity obtained in both the topological and normal phases of a single device open the possibility of electrical switching of the edge transport.

Figure 1

(a) Band diagram of $\mathrm{InAs}/{\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{Sb}$ CQW with AlSb barriers. (b) Band dispersions of HH1 and E1 subbands calculated for samples A (left) and B (right), which have $x=0.2$ and 0.4 and $d_{\mathrm{InAs}}=8.5$ and 7.5 nm, respectively. The color of the lines denotes the orbital character, i.e., red and blue represent electronlike and heavy-hole–like characters, respectively.

Figure 2

(a), (b) $V_{\mathrm{FG}}$ dependence of ${\rho }_{xx}$ at different temperatures for (a) sample A and (b) sample B. (c) Temperature dependence of the peak resistivity ${\rho }_{xx}^{\mathrm{peak}}$. The solid lines are fits with a double-exponential function. The inset is an Arrhenius plot of the data in the high-temperature regime. The solid (broken) lines are fits with a double- (single-) exponential function. (d) Variation of the energy gap $\mathrm{\Delta }$ as a function of in-plane magnetic field $B_{\parallel }$ (sample A). The inset illustrates the band dispersion under finite $B_{\parallel }$.

Figure 3

Measured and calculated energy gap $\mathrm{\Delta }$ of $\mathrm{InAs}/{\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{Sb}$ CQWs in the inverted regime as a function of $d_{\mathrm{InAs}}$. The symbols represent measured $\mathrm{\Delta }$. The error in measured $\mathrm{\Delta }$ associated with the temperature dependence fitting [Eq. (1)] is less than 1%, smaller than the size of the symbols. Data reported in Ref. [22] for different $x$ and $d_{\mathrm{InGaSb}}$ are also plotted for comparison: $◃$, $x=0.32$ and $d_{\mathrm{InGaSb}}=4$ nm; $▵$, $x=0.2$ and $d_{\mathrm{InGaSb}}=4$ nm; $▿$, $x=0.25$ and $d_{\mathrm{InGaSb}}=4$ nm; $▹$, $x=0$ and $d_{\mathrm{GaSb}}=10$ nm. The solid and broken lines, enclosing the shaded areas, represent $\mathrm{\Delta }$ obtained from the self-consistent eight-band $\mathbf{k}·\mathbf{p}$ calculation assuming that the CQWs are pseudomorphically grown on a fully relaxed GaSb and AlSb layer, respectively.

Figure 4

(a) ${\rho }_{xx}$ as a function of $V_{\mathrm{FG}}$ for sample C ($x=0.4$, $d_{\mathrm{InAs}}=5.5$ nm), measured at various $V_{\mathrm{BG}}$'s. The inset shows an Arrhenius plot for representative $V_{\mathrm{BG}}$ values. (b) $\mathrm{\Delta }$ as a function of $\mathrm{\Delta }{V}_{\mathrm{BG}}$, the shift in $V_{\mathrm{BG}}$ from the topological transition at $V_{\mathrm{BG}}=1$ V. $\mathrm{\Delta }{V}_{\mathrm{BG}}>0$ ($\mathrm{\Delta }{V}_{\mathrm{BG}}<0$) corresponds to the topological (normal) insulator phase. The broken line represents $\mathrm{\Delta }$ obtained from the $\mathbf{k}·\mathbf{p}$ calculation. Note that $\mathrm{\Delta }$ for $\mathrm{\Delta }{V}_{\mathrm{BG}}<0$ represents the energy gap in the normal insulator phase.