Electric and Magnetic Tuning Between the Trivial and Topological Phases in InAs/GaSb Double Quantum Wells

Among the theoretically predicted two-dimensional topological insulators, $\mathrm{InAs}/\mathrm{GaSb}$ double quantum wells (DQWs) have a unique double-layered structure with electron and hole gases separated in two layers, which enables tuning of the band alignment via electric and magnetic fields. However, the rich trivial-topological phase diagram has yet to be experimentally explored. We present an in situ and continuous tuning between the trivial and topological insulating phases in $\mathrm{InAs}/\mathrm{GaSb}$ DQWs through electrical dual gating. Furthermore, we show that an in-plane magnetic field shifts the electron and hole bands relatively to each other in momentum space, functioning as a powerful tool to discriminate between the topologically distinct states.

Figure 1

(a) Schematic of the $\mathrm{InAs}/\mathrm{GaSb}$ DQWs structure. $E1$ and $H1$ mark the bottom of the conduction band and the top of the valence band, respectively, showing an inverted band alignment. (b) Phase diagram as a function of the applied electric field ($E_z$) and the Fermi level position ($E_F$), which can both be tuned by dual gating using the top gate and back gate. The vertical white line, along which the electron (red) and hole (blue) bands touch, separates the normal and inverted band alignment regimes. (c) Sketch of the phase diagram as a function of back gate voltage ($V_{\mathrm{BG}}$) and top gate voltage ($V_{\mathrm{TG}}$). The labeled points in (b) are indicated accordingly in (c). The red and blue lines mark constant electron and hole densities, respectively. The yellow dashed lines indicate constant band overlap for the inverted case or constant band separation for the normal case. The black dashed line represents charge neutrality. The white regions above and below point $E$ correspond to the hybridization gap and the normal gap, respectively.

Figure 2

(a) Four terminal longitudinal resistance ($R_{\mathrm{xx}}$) as a function of $V_{\mathrm{BG}}$ and $V_{\mathrm{TG}}$ for device No. 1 measured at 300 mK, showing the phase diagram of the $\mathrm{InAs}/\mathrm{GaSb}$ DQWs. Lines $L$ and $R$ cross the two different gapped regions (resistance peaks), labeled as I and II. Colored dots indicate the positions in gate space where longitudinal resistance and Hall traces are taken, as shown in Figs. 3 and 3. The two green lines indicate the two less pronounced resistance peaks (see text). Inset shows the optical image of the Hall bar. The scale bar represents $20\mu \mathrm{m}$. (b),(c) Resistance along lines $L$ and $R$, respectively.

Figure 3

(a),(b) Hall resistance as a function of the perpendicular magnetic field for five out of seventeen measured points along lines $L$ and $R$ in Fig. 2, respectively. The colors of the traces here correspond to the colored dots in Fig. 2. (c),(d) Carrier densities and longitudinal resistance for the seventeen uniformly distributed positions along lines $L$ and $R$ in Fig. 2, respectively. Black squares represent the electron densities ($n_{\mathrm{SdH}}$) obtained from SdH. Red dots are the total densities ($n_{\text{Hall}}$) extracted from the Hall slope. Zero magnetic field resistances ($R_{\mathrm{xx}}$) are shown by the green circles. In (c), the blue open triangles show the difference between the electron density and the total density ($n_{\text{SdH}}\text{−}{n}_{\text{Hall}}$), i.e., the hole density. At the left side of the resistance peak, the blue solid triangles and the red solid triangles represent the hole density ($p_{\text{fit}}$) and the electron density ($n_{\text{fit}}$) obtained from the fit of the bended Hall traces with a two-carrier model, respectively. In (d), the hole density near the gapped region II deduced from fitting is shown by the blue solid triangles.

Figure 4

Longitudinal resistance as a function of $V_{\mathrm{BG}}$ and $V_{\mathrm{TG}}$ at a perpendicular magnetic field of 2 T for device No. 1. In a fixed perpendicular magnetic field, Landau levels will cross the Fermi level when the carrier density is tuned by gates. The parallel lines correspond to SdH oscillations and each line represents a contour of constant carrier density. The red curve denotes a constant density line for electrons, where the Fermi level is fixed relative to the bottom of the electron band and only the hole band moves. The two green lines separate the regions with a single type and two types of carriers.

Figure 5

(a),(b) In-plane magnetic field ($B_y$) dependence of the longitudinal resistance for device No. 2, along the same lines $L$ and $R$ in Fig. 2. (c),(d) The same as (a),(b) but for $B_x$. The resistance for line $L$ drops as $B_x$ or $B_y$ increases, while for line $R$, it stays constant. Insets in (a)–(d) show the band structure along $k_x$. As the relative shift of the bands in momentum is perpendicular to the in-plane magnetic field, the hybridization gap closes more quickly in $B_y$ (perpendicular to the transport direction) than in $B_x$ (parallel to the transport direction).