Magneto-induced topological phase transition in inverted InAs/GaSb bilayers

We report a magneto-induced topological phase transition in inverted InAs/GaSb bilayers from a quantum spin Hall insulator to a normal insulator. We utilize a dual-gated Corbino device in which the degree of band inversion, or equivalently the electron and hole densities, can be continuously tuned. We observe a topological phase transition around the magnetic field where a band crossing occurs, accompanied by a bulk-gap closure characterized by a bulk conductance peak (BCP). In another set of experiments, we study the transition under a tilted magnetic field (tilt angle θ). We observe the characteristic magnetoconductance around BCP as a function of θ, which dramatically depends on the density of the bilayers. In a relatively deep inversion (hence a higher density) regime, where the electron-hole hybridization dominates the excitonic interaction, the BCP grows with θ. On the contrary, in a shallowly inverted (a lower density) regime, where the excitonic interaction dominates the hybridization, the BCP is suppressed indicating a smooth crossover without a gap closure. This suggests the existence of a low-density, correlated insulator with spontaneous symmetry breaking near the critical point. Our highly controllable electron-hole system offers an ideal platform to study interacting topological states as proposed by recent theories.

Figure 1

(a) Energy dispersion of type-II InAs/GaSb QWs with an inverted band structure based on a noninteracting model. The dashed lines describe the dispersion without hybridization, where $E1$ and $H1$ denote the electron and hole bands, respectively. (b) LL spectra for the inverted case in (a). Two unhybridized LLs divide the region in the vicinity of the inversion transition into four regimes with different Chern numbers labeled (i)–(iv). Corresponding schematics of the band structures are plotted below: (i) a QSHI state with an inverted band order with the Chern number $C$ = 0; (ii) a QH state with only the lowest electron LL occupied ($C$ = 1); (iii) a QH state with only the lowest hole LL occupied ($C$ = −1); (iv) a QH state with no occupation in LLs ($C$ = 0), namely, a normal insulator, where the blue (red) lines denote the electron (hole) LLs and the black lines represent the chemical potentials. (c) Energy dispersion and (d) LL spectra for a noninverted case.

Figure 2

(a) Bulk conductivity as a function of $V_{\text{f}}$ and $B_{\perp }$ at $V_{\text{b}}$ = 0 V. The conductivity is measured from a dual-gated Corbino device. The red dashed-line box marks a bulk conductance peak around 12 T. The blue (red) dashed line denotes the IQH state with Chern number $C$ = 1 ($C$ = −1) as described in Fig. 1. The magnetoconductance trace is plotted in (b) where the Fermi energy is pinned at the CNP ($V_{\text{f}}$ = −0.75 V, yellow line in the contour plot). (c) The temperature dependence of the bulk conductance peak near the transition point at the CNP. (d) The energy gap vs perpendicular magnetic field acquired by the Arrhenius analysis from the data in (c). The energy gap Δ shows a minimum around 13 T accompanied by the opening of a small gap Δ*.

Figure 3

The magneto-induced phase transitions under different band inversions. Two respective bulk conductivity maps are plotted at (b) $V_{\text{b}}$ = −1.5 V and (e) $V_{\text{b}}$ = 3 V. Corresponding conductance traces (horizontal linecuts) extracted with the Fermi energy pinned at the CNP are shown (a) at $V_{\text{f}}$ = −0.6 V ($n$ = $p$ ∼ 1.24 × ${10}^{11}{\text{cm}}^{-2}$) and (d) at $V_{\text{f}}$ = −1 V ($n$ = $p$ ∼ 2.48 × ${10}^{11}{\mathrm{cm}}^{-2}$), respectively. Vertical line cuts are plotted to present bulk conductance at the transition point (c) at $B_{\perp }$ = 10.8 T and (f) at $B_{\perp }$ = 16.3 T.

Figure 4

The in-plane magnetic field dependence (a) at $V_{\mathrm{b}}=2$ V (deeply inverted regime), and (c) at $V_{\mathrm{b}}=-1.5$ V (shallowly inverted regime). The corresponding peak conductance is extracted with $B_{\perp }$ fixed (b) at 14.4 T ($V_{\mathrm{b}}=2$ V) and (d) at 10.8 T ($V_{\mathrm{b}}=-1.5$ V).