Gate-tunable electronic transport in $p$-type GaSb quantum wells

Gate-tunable electronic transport in $p$ -type GaSb quantum wells

Matija Karalic, Christopher Mittag, Michael Hug, Thomas Tschirky, Werner Wegscheider, Klaus Ensslin, Thomas Ihn, Kenji Shibata, and R. Winkler

Phys. Rev. B 99, 115435 – Published 26 March 2019

Abstract

We investigate two-dimensional hole transport in GaSb quantum wells at cryogenic temperatures using gate-tunable devices. Measurements probing the valence band structure of GaSb unveil a significant spin splitting of the ground subband induced by spin-orbit coupling. We characterize the carrier densities, effective masses, and quantum scattering times of these spin-split subbands and find that the results are in agreement with band structure calculations. Additionally, we study the weak antilocalization correction to the conductivity present around zero magnetic field and obtain information on the phase coherence. These results establish GaSb quantum wells as a platform for two-dimensional hole physics and lay the foundations for future experiments in this system.

Received 30 January 2019

DOI:https://doi.org/10.1103/PhysRevB.99.115435

Physics Subject Headings (PhySH)

Quantum transport Spin-orbit coupling Weak antilocalization

Quantum wells

Shubnikov-de Haas effect

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Matija Karalic^*, Christopher Mittag, Michael Hug, Thomas Tschirky, Werner Wegscheider, Klaus Ensslin, and Thomas Ihn

Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland

Kenji Shibata

Tohoku Institute of Technology, Sendai 982-8577, Japan

R. Winkler

Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA

^*makarali@phys.ethz.ch

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Vol. 99, Iss. 11 — 15 March 2019

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Images

Figure 1
(a) Composition of the heterostructure hosting the GaSb QW. The dashed line marks the position of Si dopants. (b) Schematic representation of the measured device and its orientation with respect to the crystallographic axes. (c) Longitudinal resistivity $ρ_{x x}$ as a function of top gate voltage $V_{tg}$ and magnetic field $B$ . (d) Hall density $p_{tot}$ derived from the transverse resistivity $ρ_{x y}$ as a function of $V_{tg}$ in the range $| B | \leq 2 T$ . The dashed line is a guide to the eye indicating the linear $p_{tot} (V_{tg})$ dependence.
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Figure 2
(a) Examples of SdH oscillations in $ρ_{x x}$ at several values of $V_{tg}$ , as marked in Fig. 1. (b) Power spectra $S$ obtained by Fourier transforming the traces from (a). Up to three frequencies, $f_{1}, f_{2}$ , and $f_{1} + f_{2}$ , are visible, as indicated. The presence of frequencies around zero is an artifact linked to incomplete background subtraction. (c) Self-consistent $k \cdot p$ band structure calculations $E (k_{∥})$ associated with the traces from (a). The total density is chosen to be the same as in (a) for each respective trace. The spin-split ground subband (solid) is labeled with $| g 〉$ ; the spin-split first excited subband (dashed) is labeled with $| e 〉$ . The horizontal lines mark the position of the Fermi energy. (d) Collection of power spectra as in (b) in the whole $V_{tg}$ range, presented as a color map. The dotted line follows the Hall density $p_{tot}$ from Fig. 1. (e) Calculated evolution of the densities $p_{i}$ of the spin-split ground subbands with total density. Note that in the calculation a small fraction of the total density resides in the first excited subband so that $p_{1} + p_{2} < p_{tot}$ .
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Figure 3
(a) Temperature dependence of the relative SdH oscillation amplitude $Δ ρ_{x x} / {\bar{ρ}}_{x x}$ at $V_{tg} = 1.75 V$ after subtracting the slowly varying background ${\bar{ρ}}_{x x}$ ( $Δ ρ_{x x} = ρ_{x x} - {\bar{ρ}}_{x x}$ ). (b) Effective mass $m^{*}$ and quantum scattering time $τ_{q}$ found from (a) with Eq. (1) for many minima and maxima, up to $B = 6 T$ . The dashed lines mark the weighted averages of $m^{*}$ and $τ_{q}$ (see inset). (c) Decay of the power spectrum at $V_{tg} = - 0.75 V$ with temperature $T$ . The magnetic field range used for the Fourier transform is $2 T \leq B \leq 9 T$ , and the frequencies of interest are annotated as before. (d) Peak heights at frequencies $f_{1}, f_{2}$ as a function of $T$ together with the associated fits (method II in the text). The extracted $m^{*}$ and $τ_{q}$ are inserted. The magnetic field ranges used for the Fourier transform are $2 T \leq B \leq 6 T$ and $3 T \leq B \leq 9 T$ in the case of $f_{1}$ and $f_{2}$ , respectively.
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Figure 4
(a) Examples of the WAL correction to the longitudinal conductivity $σ_{x x}$ at several values of $V_{tg}$ . The measured traces are shown as is, i.e., prior to any background subtraction, together with their respective fits according to Eq. (2) in the range $| B | \leq 20 mT$ . (b) Phase coherence length $l_{ϕ}$ found from the WAL correction as a function of $V_{tg}$ at base temperature. In the shaded region, no reliable determination of $l_{ϕ}$ is possible. (c) Temperature dependence of $l_{ϕ}$ at $V_{tg} = 1.75$ and $- 0.75 V$ . Also depicted are fits with a power law dependence $T^{γ}$ .
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