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Valley-Tunable Even-Denominator Fractional Quantum Hall State in the Lowest Landau Level of an Anisotropic System

Md. Shafayat Hossain, Meng K. Ma, Y. J. Chung, S. K. Singh, A. Gupta, K. W. West, K. W. Baldwin, L. N. Pfeiffer, R. Winkler, and M. Shayegan
Phys. Rev. Lett. 130, 126301 – Published 20 March 2023
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    Abstract

    Fractional quantum Hall states (FQHSs) at even-denominator Landau level filling factors (ν) are of prime interest as they are predicted to host exotic, topological states of matter. We report here the observation of a FQHS at ν=1/2 in a two-dimensional electron system of exceptionally high quality, confined to a wide AlAs quantum well, where the electrons can occupy multiple conduction-band valleys with an anisotropic effective mass. The anisotropy and multivalley degree of freedom offer an unprecedented tunability of the ν=1/2 FQHS as we can control both the valley occupancy via the application of in-plane strain, and the ratio between the strengths of the short- and long-range Coulomb interaction by tilting the sample in the magnetic field to change the electron charge distribution. Thanks to this tunability, we observe phase transitions from a compressible Fermi liquid to an incompressible FQHS and then to an insulating phase as a function of tilt angle. We find that this evolution and the energy gap of the ν=1/2 FQHS depend strongly on valley occupancy.

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    • Received 6 October 2022
    • Accepted 22 February 2023

    DOI:https://doi.org/10.1103/PhysRevLett.130.126301

    © 2023 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Fractional quantum Hall effectLandau levelsMagnetotransport
    1. Physical Systems
    Quantum wells
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Md. Shafayat Hossain1, Meng K. Ma1, Y. J. Chung1, S. K. Singh1, A. Gupta1, K. W. West1, K. W. Baldwin1, L. N. Pfeiffer1, R. Winkler2, and M. Shayegan1

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

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    Vol. 130, Iss. 12 — 24 March 2023

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    • Figure 1
      Figure 1

      Observation of FQHS at ν=1/2 in an X-valley occupied AlAs 2DES when subjected to a tilted magnetic field; θ denotes the angle between B⊥ and total B.

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    • Figure 2
      Figure 2

      Sample description and valley tuning. (a) First Brillouin zone of bulk AlAs, showing anisotropic conduction band valleys. (b) Sample geometry, showing the orientation of the two occupied valleys (X and Y) and the measured resistances (R[100] and R[010]). Electrical contacts to the sample are denoted by 1–8. For R[100], we pass current from contact 8 to 2 and measure the voltage between contacts 6 and 4. For R[010], the current is passed from 8 to 6 and we measure the voltage between 2 and 4. (c) Experimental setup for applying in-plane strain (ϵ). (d) Resistance of the sample at B=0 and T≃0.03  K, measured as a function of ϵ. (e) Direction of tilted magnetic field with respect to the crystallographic directions.

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    • Figure 3
      Figure 3

      Tilt evolution of magnetoresistance data near ν=1/2 for different valley occupancies, all traces taken at T≃0.03  K, and the tilt angles are indicated in each panel. The direction of B|| is along [100], i.e., along R[100]. (a) and (b) contain data for cases when the electrons occupy only X or only Y valley, respectively. In both (a) and (b), with increasing θ, the 2DES at ν=1/2 undergoes transitions from a compressible phase to an incompressible FQHS, and then finally to an insulating phase. However, the transitions happen at relatively smaller θ for case (a) where the electrons occupy the X valley. Insets in each panel show the calculated charge distribution for the corresponding B|| that is experienced by the electrons at ν=1/2 [52].

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    • Figure 4
      Figure 4

      Strength of the ν=1/2 FQHS, as defined in the inset to (a), plotted against B|| for different valley occupancies. (a), (b) Data for the hard and easy axis directions (see text). (c),(d) Extraction of the pseudo activation gap (Δ1/2) of the ν=1/2 FQHS from T dependence of R[100] (black) and R[010] (red) for the two valleys.

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