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Valley Hall effect and nonlocal resistance in locally gapped graphene

Thomas Aktor, Jose H. Garcia, Stephan Roche, Antti-Pekka Jauho, and Stephen R. Power
Phys. Rev. B 103, 115406 – Published 4 March 2021
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    Abstract

    We report on the emergence of bulk, valley-polarized currents in graphene-based devices, driven by spatially varying regions of broken sublattice symmetry, and revealed by nonlocal resistance (RNL) fingerprints. By using a combination of quantum transport formalisms, giving access to bulk properties as well as multiterminal device responses, the presence of a nonuniform local band gap is shown to give rise to valley-dependent scattering and a finite Fermi-surface contribution to the valley Hall conductivity, related to characteristics of RNL. These features are robust against disorder and provide a plausible interpretation of controversial experiments in graphene/hexagonal boron nitride superlattices. Our findings suggest both an alternative mechanism for the generation of valley Hall effect in graphene and a route towards valley-dependent electron optics, by materials and device engineering.

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    • Received 18 September 2019
    • Accepted 18 February 2021

    DOI:https://doi.org/10.1103/PhysRevB.103.115406

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Band gapElectronic structureMesoscopicsTransport phenomenaValleytronics
    1. Physical Systems
    Dirac semimetalGrapheneNanostructures
    1. Techniques
    Landauer formulaTight-binding model
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Thomas Aktor1, Jose H. Garcia2, Stephan Roche2,3, Antti-Pekka Jauho1, and Stephen R. Power4,*

    • 1Center for Nanostructured Graphene, DTU Physics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
    • 2Catalan Institute of Nanoscience and Nanotechnology, CSIC and The Barcelona Institute of Science and Technology, Campus UAB, Bellaterra, 08193 Barcelona (Cerdanyola del Vallès), Spain
    • 3Institució Catalana de Recerca i Estudis Avançats, 08070 Barcelona, Spain
    • 4School of Physics, Trinity College Dublin, Dublin 2, Ireland

    • *stephen.power@tcd.ie

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    Issue

    Vol. 103, Iss. 11 — 15 March 2021

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    Images

    • Figure 1
      Figure 1

      (a) Incoming, scattered, and transmitted waves for scattering from a mass dot. (b) A and B sublattice sites in the dot have different onsite potentials. (c) K and K′ valleys in the low-energy spectrum of graphene. (d) Valley polarization of scattered currents: the peak indicates a strong K′ polarization in the +y direction. (e) Total (bold) and individual valley angular scattering profiles in the far-field limit at Ẽ=0.12 [purple dot in (d)].

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    • Figure 2
      Figure 2

      (a) Total and (b), (c) individual valley current flows near a mass dot at low energy. Electrons from different valleys flow in opposite directions around the dot. (d) Similar valley-splitting behavior for a disordered mass region. (e) Phase space map for the average valley polarization ξavg for different Ẽ and Δ̃ values, with the dotted line denoting the band edge.

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    • Figure 3
      Figure 3

      (a) Valley Hall conductivity σxyv, and (b) σxyv normalized by its peak value, for three different supercell sizes. (c), (d) σxyv for WC=5R and uniform mass distributions, together with their Fermi-surface contribution (shaded). Dashed vertical lines show the band edges in mass regions.

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    • Figure 4
      Figure 4

      (a) Six-terminal device for RNL simulations. (b) RNL with and without mass dots, showing a robust positive trend in the presence of dots. (c) Transmission along one edge (TAL) and diagonally across the device (TDI). (d) Map of local current flow (arrows) and valley polarization (color) for the energy shown in orange in (b) and (c). RNL is mediated by valley-polarized currents in the device.

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