Research ArticleCONDENSED MATTER PHYSICS

High-frequency rectification via chiral Bloch electrons

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Science Advances  27 Mar 2020:
Vol. 6, no. 13, eaay2497
DOI: 10.1126/sciadv.aay2497
  • Fig. 1 Schematic figure of a rectifier based on a 2D material.

    In this setup, we detect the rectified DC current transverse to the incident electric field, which is advantageous in reducing noise. The antenna is attached to both sides to collect bigger power from radiation and enhance the sensitivity.

  • Fig. 2 Second-order response by skew scattering on a honeycomb lattice.

    (A) Schematics of skew scattering. When a self-rotating wave packet (red) is scattered by an inversion-symmetric potential (black), its motion is deflected like the Magnus effect. Two wave packets moving in the opposite directions produces zero net current. However, if the two self-rotate in different directions, then skew scattering produces net current in the perpendicular direction. (B) Electric field and rectified current on a honeycomb lattice. The left and right panels in (A) to (D) correspond to χyxx and χyyy, respectively. (C) Fermi surface displacement at frequency ω (green). The oscillating electric field E(ω) forces the Fermi surface to swing back and forth from its equilibrium position (red). Owing to the Fermi surface anisotropy, each valley yields finite velocity V along the kx direction after time averaging. This velocity is canceled with the two valleys, and there is no DC current generated as a linear response. (D) Stationary Fermi surface displacement. The electric field and skew scattering produce the stationary Fermi surface displacement (blue) from the equilibrium state (red) as a second-order response. Finite rectified current is observed when the contributions from the two valleys do not cancel.

  • Fig. 3 Second-order response for graphene heterostructures and multilayers.

    (A and B) Second-order DC response for monolayer and (C and D) bilayer graphene. The second-order conductivity χ is shown in (A) and (C), and the reduced voltage responsivity ηV is shown in (B) and (D). The carrier density n is changed from 0.5 × 1012 cm−2 (red) to 5 × 1012 cm−2 (purple). We use the values v = 0.94 × 106 m/s, Δ = 15 meV, and τ = 1.13 ps for the monolayer case; and Δ = 50 meV and τ = 0.96 ps for the bilayer case, from transport, infrared spectroscopy, and scanning tunneling microscopy/spectroscopy measurements (37, 4751). For the bilayer case, λ = (2m)−1 is determined by the effective mass m ≈ 0.033 me (me, electron mass) and v ≈ 1 × 105 m/s (52, 53). See also the Supplementary Materials for details.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/13/eaay2497/DC1

    Section S1. Semiclassical Boltzmann theory

    Section S2. Current response

    Section S3. Graphene-based models with trigonal lattice structures

    Section S4. Estimate of parameters

    Section S5. Surface state of a topological insulator

    Fig. S1. Monolayer and bilayer graphene models.

    Fig. S2. Carrier density dependence of the material properties.

    Fig. S3. Frequency dependence of the response.

    Fig. S4. Frequency and temperature dependence of the response.

    Fig. S5. Frequency and temperature dependence of the response with a logarithmic scale for the frequency axis.

    References (5462)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Semiclassical Boltzmann theory
    • Section S2. Current response
    • Section S3. Graphene-based models with trigonal lattice structures
    • Section S4. Estimate of parameters
    • Section S5. Surface state of a topological insulator
    • Fig. S1. Monolayer and bilayer graphene models.
    • Fig. S2. Carrier density dependence of the material properties.
    • Fig. S3. Frequency dependence of the response.
    • Fig. S4. Frequency and temperature dependence of the response.
    • Fig. S5. Frequency and temperature dependence of the response with a logarithmic scale for the frequency axis.
    • References (5462)

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