Record-quality GaAs two-dimensional hole systems

Yoon Jang Chung, C. Wang, S. K. Singh, A. Gupta, K. W. Baldwin, K. W. West, M. Shayegan, L. N. Pfeiffer, and R. Winkler

Phys. Rev. Materials 6, 034005 – Published 14 March 2022

Abstract

The complex band structure, large spin-orbit induced band splitting, and heavy effective mass of two-dimensional (2D) hole systems hosted in GaAs quantum wells render them rich platforms to study many-body physics and ballistic transport phenomena. Here we report ultra-high-quality (001) GaAs 2D hole systems, fabricated using molecular beam epitaxy and modulation doping, with mobility values as high as $5.8 \times 10^{6} {cm}^{2}$ /(V s) at a hole density of $p = 1.3 \times 10^{11}$ / ${cm}^{2}$ , implying a mean free path of $≃ 27 μ m$ . In the low-temperature magnetoresistance trace of this sample, we observe high-order fractional quantum Hall states up to the Landau level filling $ν = 12 / 25$ near $ν = 1 / 2$ . Furthermore, we see a deep minimum develop at $ν = 1 / 5$ in the magnetoresistance of a sample with a much lower hole density of $p = 4.0 \times 10^{10}$ / ${cm}^{2}$ where we measure a mobility of $3.6 \times 10^{6} {cm}^{2}$ /(V s). These improvements in sample quality were achieved by the reduction of residual impurities both in the GaAs channel and in the AlGaAs barrier material, as well as optimization in the design of the sample structure.

Received 30 December 2021
Accepted 23 February 2022

DOI:https://doi.org/10.1103/PhysRevMaterials.6.034005

Physics Subject Headings (PhySH)

Fractional quantum Hall effect Landau levels Magnetotransport

2-dimensional systems

Molecular beam epitaxy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yoon Jang Chung^*, C. Wang, S. K. Singh, A. Gupta , K. W. Baldwin, K. W. West, M. Shayegan , and L. N. Pfeiffer

Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA

R. Winkler

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

^*Corresponding author: edwinyc@princeton.edu

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Vol. 6, Iss. 3 — March 2022

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Images

Figure 1
(a) Two-dimensional hole density in GaAs QWs flanked by ${Al}_{x} {Ga}_{1 - x} As$ barriers with varying alloy fraction ( $x$ ). Symbols with different colors show data from a series of samples grown with spacer layer thicknesses $s = 168$ nm (black squares), 336 nm (red circles), and 672 nm (blue triangle). The solid lines are guides to the eye highlighting a linear dependence of hole density on $x$ for a given spacer layer thickness. (b) Schematic diagram of the structure used for the samples shown in (a). After a GaAs buffer layer, a superlattice (SL) of alternating ${Al}_{x} {Ga}_{1 - x} As$ (10 nm)/GaAs (1 nm) layers are grown on the substrate prior to defining the main region that hosts the 2DHS. All samples are $δ$ doped with C symmetrically on both sides of the QW. The cap layer has a bulk C doping density of $\sim 4 \times 10^{17}$ / ${cm}^{3}$ . The structure of the high-mobility, stepped-barrier samples used for the 2DHSs discussed in Fig. 2 for (c) $p ≃ 4.0 \times 10^{10}$ / ${cm}^{2}$ and (d) $p ≃ 1.3 \times 10^{11}$ / ${cm}^{2}$ .
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Figure 2
Mobility, measured at a temperature of 0.3 K, of the high-quality 2DHSs hosted in GaAs QWs with varying well width. The data in (a) are for a series of samples with density $p ≃ 4.0 \times 10^{10}$ / ${cm}^{2}$ and in (b) for samples with $p ≃ 1.3 \times 10^{11}$ / ${cm}^{2}$ . The density variation is within $\pm 5$ % for both sets, and the mobility for every data point is deduced from the measured density and resistance of each sample. The closed black squares denote experimentally measured mobility values and the open blue circles denote the calculated density-of-states effective masses for the ground-state subband. The light-blue band indicates the QW width range where, according to calculations, the population of the second subband is expected to begin. (c)–(e) and (f)–(h) show the calculated energy-band dispersions along the [110] and [100] directions at various QW widths for samples with $p = 4.0 \times 10^{10}$ and $1.3 \times 10^{11}$ / ${cm}^{2}$ , respectively. In each panel, the black and red curves represent the first and second subbands, while the Fermi energy ( $E_{F}$ ) is marked by a solid blue line. The solid and dashed lines denote the dispersions along [110] and [100], respectively. The self-consistently calculated hole charge distribution functions (shaded red) and QW potential (black lines) for each of the cases of (c)–(h) are also shown at the bottom of each panel.
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Figure 3
Representative magnetoresistance traces for high-quality 2DHSs with (a) QW width $w = 30$ nm and $p = 4.0 \times 10^{10}$ / ${cm}^{2}$ and (b) $w = 20$ nm and $p = 1.3 \times 10^{11}$ / ${cm}^{2}$ . All traces were taken at $T = 0.3$ K in the van der Pauw geometry. The inset of each figure enlarges the region near $ν = 1 / 2$ . The magnetic field positions of some integer and fractional quantum Hall states are marked.
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Figure 4
Representative magnetoresistance trace of the record-quality 2DHS with $p = 1.3 \times 10^{11}$ / ${cm}^{2}$ and $w = 30$ nm taken at $T ≃ 30$ mK. (a) shows the data over the entire magnetic field range, while (b) and (c) enlarge regions near the Landau level fillings $ν = 3 / 2$ and 1/2, respectively. The magnetic field positions of several quantum Hall states, as well as $ν = 3 / 2$ and 1/2, are marked in each trace.
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