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Electromotive entrainment of charge and heat currents in graphene

E. Kirkinis, A. Levchenko, A. V. Andreev

Abstract

We develop a hydrodynamic theory of charge and heat currents induced by traveling waves, such as surface acoustic waves, in graphene devices near charge neutrality. The currents depend on the intrinsic conductivity and viscosity of the electron liquid, the disorder strength, and the geometry of the device. We obtain analytic expressions for the heat and charge currents to second order in the wave amplitude for Hall-bar devices. At charge neutrality and in the absence of DC bias, the heat content is entrained by the wave in the absence of net charge transfer. At the same time, device conductance is enhanced by the wave. Away from charge neutrality, the transport charge current induced by the wave arises in the absence of a DC bias.

Electromotive entrainment of charge and heat currents in graphene

Abstract

We develop a hydrodynamic theory of charge and heat currents induced by traveling waves, such as surface acoustic waves, in graphene devices near charge neutrality. The currents depend on the intrinsic conductivity and viscosity of the electron liquid, the disorder strength, and the geometry of the device. We obtain analytic expressions for the heat and charge currents to second order in the wave amplitude for Hall-bar devices. At charge neutrality and in the absence of DC bias, the heat content is entrained by the wave in the absence of net charge transfer. At the same time, device conductance is enhanced by the wave. Away from charge neutrality, the transport charge current induced by the wave arises in the absence of a DC bias.
Paper Structure (12 sections, 49 equations, 4 figures)

This paper contains 12 sections, 49 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Wave-induced currents in graphene Hall-bar devices
  3. Clean systems with uniform density
  4. Weakly disordered systems
  5. Summary
  6. Velocity fields induced by the traveling wave EMF
  7. Structure factors
  8. Density and entropy perturbations
  9. Clean case currents
  10. Nonisothermal case asymptotics
  11. Weak disorder
  12. Self-consistency and validity of approximations

Figures (4)

  • Figure 1: A Hall-bar configuration subjected to a traveling-wave EMF, $e\delta\mathcal{E}\cos(kx - \omega t)$, superposed on a uniform field $\bar{\mathcal{E}}$ in the $\hat{\mathbf{x}}$ direction, induces (at charge neutrality) a traveling-wave density perturbation $\delta n \cos(kx - \omega t)$, which is itself superposed on a uniform background density $\bar{n}$. This, in turn, gives rise to a DC electric current that enhances the conductivity and entrains both the electron liquid and its heat content.
  • Figure 2: The wave-induced conductivity enhancement, $\delta\sigma$ defined in Eq. (\ref{['dsigma']}), is plotted as a function of the dimensionless parameters $kd$ and $\delta/d$. The overall conductivity scale is normalized to the unit $\delta\sigma_0 \equiv \sigma^2 \delta\mathcal{E}^2 d^2 / (6 \eta c^2)$.
  • Figure 3: Disorder-averaged wave-induced conductivity enhancement, normalized by the long-wavelength limit conductivity (\ref{['dsigma']}). Here, $k_{\text{dis}}$ denotes the disorder wavenumber, $k$ the excitation wavenumber, and $d$ the half-width of the Hall bar. As the disorder strength increases, $k_{\text{dis}} d > 1$, the conductivity enhancement induced by the wave is progressively suppressed.
  • Figure 4: Structure factor functions $\mathscr{G}(kd)$ and $g(kd)$; see their asymptotic forms in Eqs. (\ref{['ReGas']})–(\ref{['gas']}).