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Thermal and Quantum Melting Phase Diagrams for a Magnetic-Field-Induced Wigner Solid

Meng K. Ma, K. A. Villegas Rosales, H. Deng, Y. J. Chung, L. N. Pfeiffer, K. W. West, K. W. Baldwin, R. Winkler, and M. Shayegan
Phys. Rev. Lett. 125, 036601 – Published 14 July 2020
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    Abstract

    A sufficiently large perpendicular magnetic field quenches the kinetic (Fermi) energy of an interacting two-dimensional (2D) system of fermions, making them susceptible to the formation of a Wigner solid (WS) phase in which the charged carriers organize themselves in a periodic array in order to minimize their Coulomb repulsion energy. In low-disorder 2D electron systems confined to modulation-doped GaAs heterostructures, signatures of a magnetic-field-induced WS appear at low temperatures and very small Landau level filling factors (ν≃1/5). In dilute GaAs 2D hole systems, on the other hand, thanks to the larger hole effective mass and the ensuing Landau level mixing, the WS forms at relatively higher fillings (ν≃1/3). Here we report our measurements of the fundamental temperature vs filling phase diagram for the 2D holes’ WS-liquid thermal melting. Moreover, via changing the 2D hole density, we also probe their Landau level mixing vs filling WS-liquid quantum melting phase diagram. We find our data to be in good agreement with the results of very recent calculations, although intriguing subtleties remain.

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    • Received 6 January 2020
    • Accepted 12 June 2020

    DOI:https://doi.org/10.1103/PhysRevLett.125.036601

    © 2020 American Physical Society

    Physics Subject Headings (PhySH)

    1. Physical Systems
    2-dimensional systemsWigner crystal
    1. Techniques
    Dilution refrigerator
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Meng K. Ma1, K. A. Villegas Rosales1, H. Deng1, Y. J. Chung1, L. N. Pfeiffer1, K. W. West1, K. W. Baldwin1, R. Winkler2, and M. Shayegan1

    • 1Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
    • 2Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA

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    Vol. 125, Iss. 3 — 17 July 2020

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    Images

    • Figure 1
      Figure 1

      Temperature dependence of the longitudinal resistivity ρxx vs magnetic field B at p=3.8. The y scale for the grey trace is expanded by a factor of 10. The inset shows the Arrhenius plots of ρxx at ν=0.30, 0.37, 2/5, and 1/3.

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    • Figure 2
      Figure 2

      Left inset: Schematic of the measurement setup. Top and bottom yellow plates represent front and back gates and the middle blue plate the 2DHS layer. An ac excitation voltage Vac is applied to the bottom gate which generates an electric field E0, and subsequently a penetrating electric field EP as a function of the screening efficiency of the 2DHS. A current IP in response to EP is then measured. Trace in the main figure shows IP, normalized to its maximum value, vs B. Horizontal line marks the maximum of IP when the 2DHS screening is minimum. Right inset: IP vs temperature traces for ν ranging from 0.120 to 0.370.

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    • Figure 3
      Figure 3

      WS thermal melting phase diagram. The yellow and white regions indicate the solid and liquid phases, respectively. The grey line connecting the measured data points is a guide to the eye.

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    • Figure 4
      Figure 4

      WS quantum melting phase diagram, with the Landau level mixing parameter κ and ν for the axes. The grey solid squares connected by the guide-to-the-eye lines are from theoretical calculations [45]. The yellow and white regions indicate the predicted WS and liquid phases. The color-coded circles represent experimental data points deduced from measurements at six different densities, as listed in the inset box. The closed and open circles indicate WS and liquid phases, respectively. The half-filled circles are used to imply a close competition between the WS and the liquid phase.

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    • Figure 5
      Figure 5

      Magnetoresistivity data for a 2DHS with p=7.9 at 30 and 60 mK. The y scale for the grey trace is expanded by a factor of 50 to show the numerous observed FQHSs, attesting to the high quality of the 2DHS.

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