Experimental signatures of the inverted phase in InAs/GaSb coupled quantum wells

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Experimental signatures of the inverted phase in InAs/GaSb coupled quantum wells

Matija Karalic, Susanne Mueller, Christopher Mittag, Kiryl Pakrouski, QuanSheng Wu, Alexey A. Soluyanov, Matthias Troyer, Thomas Tschirky, Werner Wegscheider, Klaus Ensslin, and Thomas Ihn

Phys. Rev. B 94, 241402(R) – Published 12 December 2016

Abstract

Transport measurements are performed on InAs/GaSb double quantum wells at zero and finite magnetic fields applied parallel and perpendicular to the quantum wells. We investigate a sample in the inverted regime where electrons and holes coexist, and compare it with another sample in the noninverted semiconducting regime. The activated behavior in conjunction with a strong suppression of the resistance peak at the charge neutrality point in a parallel magnetic field attest to the topological hybridization gap between electron and hole bands in the inverted sample. We observe an unconventional Landau level spectrum with energy gaps modulated by the magnetic field applied perpendicular to the quantum wells. This is caused by a strong spin-orbit interaction provided jointly by the InAs and the GaSb quantum wells.

Received 11 June 2016
Revised 31 October 2016

DOI:https://doi.org/10.1103/PhysRevB.94.241402

Physics Subject Headings (PhySH)

Quantum Hall effect Spin-orbit coupling

Quantum wells Topological insulators

Transport techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Matija Karalic^1,*, Susanne Mueller¹, Christopher Mittag¹, Kiryl Pakrouski², QuanSheng Wu², Alexey A. Soluyanov^2,3, Matthias Troyer^2,4,5, Thomas Tschirky¹, Werner Wegscheider¹, Klaus Ensslin¹, and Thomas Ihn¹

¹Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
²Theoretische Physik and Station Q Zurich, ETH Zurich, 8093 Zurich, Switzerland
³Department of Physics, St. Petersburg State University, St. Petersburg 199034, Russia
⁴Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
⁵Microsoft Research Station Q, Santa Barbara, California 93106, USA

^*makarali@phys.ethz.ch

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Issue

Vol. 94, Iss. 24 — 15 December 2016

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Images

Figure 1
(a) Longitudinal resistivity $ρ_{xx}$ of the TI sample as a function of top-gate voltage $V_{tg}$ , or equivalently, total density $n_{tot}$ , at different in-plane magnetic fields $B_{∥}$ at $T = 130$ mK. The inset shows the position of the Fermi energy $E_{F}$ at the points indicated by the arrows. (b) $ρ_{xx}$ as a function of $V_{tg}$ at different temperatures at zero magnetic field. The data were collected in a different cooldown compared to (a), resulting in a slight shift along the $V_{tg}$ axis. (c) $ρ_{xx}$ as a function of $V_{tg}$ and perpendicular magnetic field $B_{⊥}$ at $T = 130$ mK. The numbers indicate filling factors $ν$ , where we assign positive $ν$ to electron and negative $ν$ to hole Landau levels. The highlighted region is reproduced in Fig. 2. (d) Transverse resistivity $ρ_{xy}$ as a function of $B_{⊥}$ for $|B_{⊥}| \leq 1$ T for different $V_{tg}$ at $T = 130$ mK.
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Figure 2
Zoom-in of Fig. 1, where each row is normalized according to $ρ_{xx} / ρ_{xx} (B_{⊥} = 0)$ . The numbers on the outside indicate filling factors $ν$ . The dashed lines are guides to the eye, marking the evolution of selected filling factors as a function of $V_{tg}$ and $B_{⊥}$ . Along the dotted (dashed-dotted) line, even (odd) filling factors are enhanced and odd (even) filling factors are suppressed. The activation energy $Δ$ at the positions of the symbols is found by fitting the temperature dependence of the minima of the longitudinal conductivity $σ_{xx} = ρ_{xx} / (ρ_{xx}^{2} + ρ_{xy}^{2})$ with an exponential function of the form $σ_{0} e^{- Δ / (2 k_{B} T)}$ [24]. The unit of $Δ$ is $μ eV$ .
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Figure 3
(a) Longitudinal resistivity $ρ_{xx}$ of the NI sample as a function of top-gate voltage $V_{tg}$ , or equivalently, total density $n_{tot}$ , at zero in-plane magnetic field $B_{∥}$ and at $B_{∥} = 0$ at $T = 155$ mK. The inset shows the position of the Fermi energy $E_{F}$ in the trivial gap. (b) $ρ_{xx}$ as a function of $V_{tg}$ at different temperatures at zero magnetic field. The data were collected in a different cooldown compared to (a). (c) $ρ_{xx}$ as a function of $V_{tg}$ and perpendicular magnetic field $B_{⊥}$ at $T = 130$ mK. The numbers indicate filling factors $ν$ , where we assign positive $ν$ to electron and negative $ν$ to hole Landau levels. The horizontal stripe visible around $B_{⊥} = 7$ T is due to the sample being unstable. (d) Comparison of $ρ_{xx}$ at $B_{⊥} = 5$ , 5.5, and 6 T for NI and TI samples. The horizontal axis is the total density $n_{tot}$ . The dotted lines follow the movement of the denoted filling factors.
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Figure 4
(a) Landau level spectrum calculated numerically for the TI sample at $V_{tg} = - 4$ V, inverted regime. States dominated by electrons or holes of certain spin and mixed states are shown in corresponding colors. The vertical dashed lines indicate the magnetic fields for $ν = 2$ , 3, and 4 where the Fermi energy jumps to the next unoccupied Landau level. The inset depicts the dispersion $Y - Γ - X$ and the position of the Fermi energy at $B_{⊥} = 0$ . (b) As in (a), but at $V_{tg} = - 10$ V, noninverted regime. The spectrum calculated for the NI sample is qualitatively the same.
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