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Decoupled heat and charge rectification as a many-body effect in quantum wires

Conor Stevenson and Bernd Braunecker
Phys. Rev. B 103, 115413 – Published 8 March 2021
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  • INTRODUCTION
  • PHYSICS BEHIND RECTIFICATION
  • MODEL AND CURRENTS
  • NONINTERACTING ELECTRONS
  • INTERACTING ELECTRONS
  • RECTIFICATION EFFICIENCY
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We show that for a quantum wire with a local asymmetric scattering potential the principal channels for charge and heat rectification decouple and renormalize differently under electron interactions, with heat rectification generally being more relevant. The polarization of the rectification results from quantum interference and is tunable through external gating. Furthermore, for spin-polarized or helical electrons and sufficiently strong interactions a regime can be obtained in which heat transport is strongly rectified but charge rectification is very weak.

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    • Received 10 February 2020
    • Revised 14 December 2020
    • Accepted 17 February 2021

    DOI:https://doi.org/10.1103/PhysRevB.103.115413

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Heat transferQuantum interference effectsQuantum transportThermoelectric effects
    1. Physical Systems
    DiodesQuantum wires
    1. Techniques
    Luttinger liquid model
    Condensed Matter, Materials & Applied PhysicsGeneral Physics

    Authors & Affiliations

    Conor Stevenson and Bernd Braunecker

    • SUPA, School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, United Kingdom

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    Issue

    Vol. 103, Iss. 11 — 15 March 2021

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    • Figure 1
      Figure 1

      (a) Scheme of the voltage V driven quantum wire with a spatially asymmetric potential U(x). Rectification arises from dressing U(x) by backscattered charges together with renormalization through interactions. (b) The wire as a thermodynamic system with right (left) moving modes R (L) in equilibrium with the reservoir on their left (right). The reservoirs are fully absorbing for incoming particles. Backscattering by U(x) (curved arrows) connects the R and L subsystems and causes the transport asymmetry under V.

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    • Figure 2
      Figure 2

      Sensitivity of sin(α) in Eq. (9) to the shape of U(x), given here by the sum of two Lorentzians, as indicated in the figure with parameters δx=2x0 and kF=0.4/x0 in generic units x0,u1. The inset shows U(x) for the ratios u2/u1 marked by the circle (solid line) and square (dashed line).

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    • Figure 3
      Figure 3

      Heat rectification as a function of voltage for U corresponding to the red square in Fig. 2 (with u1/EF=0.7 and EF setting the order of the bandwidth). Interactions with γ<2 enhance the noninteracting γ=2. For γ<1 (possible only for spin polarized electrons) a maximum enhancement is reached near V=V*, where Eq. (9) crosses over to strong-coupling scaling and Q̇Rr decreases again to zero (expected trend shown by the dotted line). The inset shows the corresponding efficiency Q̇Rr/P, with P being the dissipated power. While the scaling is exact, only the order of magnitude is known for the amplitudes, and we have set C′=1.

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