Splitting of the Fermi Contour of Quasi-2D Electrons in Parallel Magnetic Fields

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Splitting of the Fermi Contour of Quasi-2D Electrons in Parallel Magnetic Fields

M. A. Mueed, D. Kamburov, M. Shayegan, L. N. Pfeiffer, K. W. West, K. W. Baldwin, and R. Winkler

Phys. Rev. Lett. 114, 236404 – Published 11 June 2015

Abstract

In a quasi-two-dimensional electron system with nonzero layer thickness, a parallel magnetic field can couple to the out-of-plane electron motion and lead to a severe distortion and eventual splitting of the Fermi contour. Here we directly and quantitatively probe this evolution through commensurability and Shubnikov–de Haas measurements on electrons confined to a 40-nm-wide GaAs (001) quantum well. We are able to observe the Fermi contour splitting phenomenon, in good agreement with the results of semiclassical calculations. Experimentally, we also observe intriguing features, suggesting magnetic-breakdown-type behavior when the Fermi contour splits.

Received 2 February 2015

DOI:https://doi.org/10.1103/PhysRevLett.114.236404

Authors & Affiliations

M. A. Mueed¹, D. Kamburov¹, M. Shayegan¹, L. N. Pfeiffer¹, K. W. West¹, K. W. Baldwin¹, and R. Winkler^2,3

¹Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
²Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
³Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA

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Vol. 114, Iss. 23 — 12 June 2015

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Images

Figure 1
(a)–(e) Calculated Fermi contours for a 2DES with density $n = 1.75 \times 10^{11} {cm}^{- 2}$ confined to a 40-nm-wide GaAs QW. $B_{∥}$ is applied along [110]. Insets show the corresponding charge distributions in light blue. Inset of (e) also shows the charge distribution from the $k [\bar{1} 10] > 0$ (the shaded pink region) and $k [\bar{1} 10] < 0$ (the shaded yellow region) states.
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Figure 2
(a) Sample schematics. The electron-beam resist grating covering the surface of each Hall bar arm is shown as blue stripes. Part of the [110] arm is left unpatterned as a reference region. (b) $B_{∥}$ -induced magnetoresistance for $R_{ref}$ . A–E mark the $B_{∥}$ values that correspond approximately to the calculations of Fig. 1.
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Figure 3
(a) SdH oscillations measured in the reference region of the Hall bar as $B_{∥}$ increases; traces are shifted vertically for clarity. (b) FT spectra of the SdH oscillations. The dotted and solid black lines show the expected positions of the spin-unresolved and spin-resolved FT peaks at $B_{∥} = 0$ , respectively. The FT signal to the left of the vertical lines indicated by $\div 10$ and $\div 50$ is affected by the Hamming window used in the Fourier analysis and is shown suppressed. (c) Summary of the FT peak positions normalized to $f_{SdH}^{o}$ , the frequency at $B_{∥} = 0$ . Closed squares represent the measured frequencies. The frequencies predicted by the calculations for the spin subbands are shown as green and red lines. A–E mark the $B_{∥}$ values from Fig. 1 calculations.
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Figure 4
(a) COs along [110] from the patterned region. Vertical lines mark the expected positions of the COs’ resistance minima. The corresponding trace from the unpatterned reference region clearly shows no COs. (b),(c) COs from the patterned regions of the $L$ -shaped Hall bar along [110] and $[\bar{1} 10]$ for different values of $B_{∥}$ . In order to do Fourier analysis, we extract the oscillatory part of these traces as a function of $1 / B_{⊥}$ by subtracting the background resistance. Examples of this process are shown as top three traces in (b). Traces are shifted vertically for clarity. (d),(e) Normalized FT spectra of the CO data shown in (a) and (b), respectively. The vertical dotted lines mark $f_{CO}^{0}$ (see text).
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Figure 5
Summary of the Fermi wave vectors ( $k_{F}$ ) deduced from the positions of the CO FT spectra for the two Hall bar arms. Blue and red symbols represent the experimental data for $k_{F} ⊥ B_{∥}$ and $k_{F} ∥ B_{∥}$ , respectively. A–E mark the $B_{∥}$ values from the calculations of Fig. 1.
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