Finite conductivity in mesoscopic Hall bars of inverted InAs/GaSb quantum wells

We have studied experimentally the low-temperature conductivity of mesoscopic size InAs/GaSb quantum well Hall bar devices in the inverted regime. Using a pair of electrostatic gates we move the Fermi level into the electron-hole hybridization state, observing a mini gap and Van Hove singularity at its edge. Temperature dependence of the conductivity in the gap shows a residual conductivity, which can be consistently explained by the contributions from the free as well as the hybridized carriers in the presence of impurity scattering, as proposed by Naveh and Laikhtman, [Europhys. Lett. 55, 545 (2001)]. Experimental implications for the stability of proposed quantum spin Hall helical edge states will be discussed.

Figure 1

(Color online) (a) Shows structure and energy spectrum of inverted CQW with $\text{E}1<\text{H}1$. Separation of the bands, $E_{go}$, as well as Fermi energy $E_F$ can be tuned with front and back gates. When $E_F>\text{H}1$, only electrons are present in the well and representative magnetotransport data at $T=0.3\text{K}$ is shown in (b) for $10\times 20\mu {\text{m}}^2$ (sample B) and in (c) for $0.7\times 1.5\mu {\text{m}}^2$ (sample A) Hall bar (scanning electron microscopy image in the inset) where $R_{xx}$ exhibits strong fluctuations. (d) Fluctuations in conductivity (sample A) are on the order of $e^2/h$, indicating mesoscopic regime.

Figure 2

(Color online) The figure shows $R_{xx}$ vs $V_{front}$ in sample A for $V_{back}$ from 10 to $-10\text{V}$, in 1 V steps, $B=0\text{T}$, $T=0.3\text{K}$; and in sample B (dashed) for $V_{back}=-10\text{V}$. Inset (a) at the anticrossing point, where $n\sim p$, a hybridization gap $\Delta$ opens. For $E_F$ in the gap, $R_{xx}$ exhibits resonance peaks, which decrease for increasing $V_{back}$. (b) Resonance peaks vary lineary with $n^{-1}$ for $n\lesssim 5\times {10}^{11}{\text{cm}}^{-2}$ as proposed in Ref. 11.

Figure 3

(Color online) (a) The figure shows $R_{xx}$ vs $V_{front}$ in sample A for $V_{back}$ from $-9$ to $-11\text{V}$, in 0.5 V steps, $B=0\text{T}$, $T=20\text{mK}$. Resistance dips occur at singularities in DOS near gap edges shown in (b). From relative position of dips and peaks in $V_{front}$ we determine $\Delta \approx 3.6\text{meV}$. Dips weaken with in-plane magnetic field in (c), due to induced anisotropy in the dispersion in (d).

Figure 4

(Color online) (a) The figure shows temperature dependence of resonance peaks in sample A for $V_{back}=-10\text{V}$ for $T$ from 0.3 to 40 K consecutively in roughly 2 K steps. (b) Resonance peaks shown vs $T^{-1}$ saturate for $T<2\text{K}$, for six different $k_{cross}$.