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Current switching of valley polarization in twisted bilayer graphene

Xuzhe Ying, Mengxing Ye, and Leon Balents
Phys. Rev. B 103, 115436 – Published 23 March 2021
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  • INTRODUCTION
  • VALLEY POLARIZATION
  • CURRENT INDUCED VALLEY DENSITY…
  • SUMMARY AND DISCUSSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Twisted bilayer graphene (TBG) aligned with hexagonal boron nitride (h-BN) substrate can exhibit an anomalous Hall effect at 3/4 filling due to the spontaneous valley polarization in valley resolved moiré bands with opposite Chern number [Science 367, 900 (2020);  Science 365, 605 (2019)]. It was observed that a small DC current is able to switch the valley polarization and reverse the sign of the Hall conductance [Science 367, 900 (2020);  Science 365, 605 (2019)]. Here, we discuss the mechanism of the current switching of valley polarization near the transition temperature, where bulk dissipative transport dominates. We show that for a sample with rotational symmetry breaking, a DC current may generate an electron density difference between the two valleys (valley density difference). The current induced valley density difference in turn induces a first-order transition in the valley polarization. We emphasize that the intervalley scattering plays a central role since it is the channel for exchanging electrons between the two valleys. We further estimate the valley density difference in the TBG/h-BN system with a microscopic model and find a significant enhancement of the effect in the magic angle regime.

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    • Received 7 January 2021
    • Accepted 12 March 2021

    DOI:https://doi.org/10.1103/PhysRevB.103.115436

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Anomalous Hall effectPhase transitionsTransport phenomena
    1. Physical Systems
    Bilayer filmsGrapheneTwo-dimensional electron gas
    1. Techniques
    Boltzmann theoryNonequilibrium Green's function
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Xuzhe Ying1,2,3, Mengxing Ye3, and Leon Balents3

    • 1Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
    • 2School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
    • 3Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA

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    Issue

    Vol. 103, Iss. 11 — 15 March 2021

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    Images

    • Figure 1
      Figure 1

      Schematic of model with two valleys, with a Stoner-type interaction. The two valleys are time reversal related, so that they carry opposite Chern numbers.

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    • Figure 2
      Figure 2

      Hysteresis curve for valley polarization Φv upon tuning the valley density difference Δn0 at T<Tc. The coercive valley density difference is nc=−2α4r−rc3α43/2.

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    • Figure 3
      Figure 3

      (a) Brillouin zone (BZ) of single layer graphene with uniaxial strain; (b) moiré Brillouin zone without (left) and with (right) uniaxial strain. The C3z symmetry of the unstrained moiré BZ is explicitly broken by the strain field.

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    • Figure 4
      Figure 4

      Impurity scattering between two Fermi pockets.

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    • Figure 5
      Figure 5

      The valley density difference Δn0 as a function of the ratio of the inter- and intravalley scattering time τ′/τ. The density is normalized to the value of Eq. (15).

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    • Figure 6
      Figure 6

      The intervalley impurity scattering in twisted bilayer graphene. Layer 1 is strained, while layer 2 is not. The intralayer intervalley scattering (green arrows) are assumed to be isotropic. The interlayer intervalley scattering (red arrows) may be anisotropic, as in Eqs. (9) and (B14).

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    • Figure 7
      Figure 7

      The valley density difference generated by a DC current in TBG with a strain field. The density is normalized to 3t2/41+3t2/41hvFhe2ej. The dotted lines are obtained from a numerical calculation. The dashed lines correspond to the analytical expression of Eq. (19) for comparison. The parameters are chosen as θw=1.03∘, ϕ=17.20∘, vDq/m=0.1 and vDkF/m=0.005.

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    • Figure 8
      Figure 8

      The possible momentum transfers Δki (red) upon impurity scattering between states of K valley layer 1 and K′ valley layer 2. The green arrows labels the reciprocal lattice vectors G(2/3) of graphene layer 1.

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