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Nonreciprocal current induced by dissipation in time-reversal symmetric systems

Takahiro Anan, Sota Kitamura, Takahiro Morimoto

Abstract

We study nonreciprocal current response in noncentrosymmetric crystals under time-reversal symmetry. We show that the nonreciprocal current appears in a dissipative system through interband processes. The nonreciprocal current is inversely proportional to the lifetime $τ$ and has a close relationship to the geometric quantity called the shift vector. The current mechanism is suitable for minigap systems where the energy gap and relaxation strength are comparable. We present a numerical simulation of the nonreciprocal current in the one-dimensional Rice--Mele model.

Nonreciprocal current induced by dissipation in time-reversal symmetric systems

Abstract

We study nonreciprocal current response in noncentrosymmetric crystals under time-reversal symmetry. We show that the nonreciprocal current appears in a dissipative system through interband processes. The nonreciprocal current is inversely proportional to the lifetime and has a close relationship to the geometric quantity called the shift vector. The current mechanism is suitable for minigap systems where the energy gap and relaxation strength are comparable. We present a numerical simulation of the nonreciprocal current in the one-dimensional Rice--Mele model.

Paper Structure

This paper contains 19 sections, 53 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Results
  3. Model calculation
  4. Discussion
  5. Derivation of the DC response
  6. Derivation of the DC response from the AC response
  7. No divergence in the static limit
  8. $O(\omega^0)$ terms
  9. $O(\omega^1)$ terms
  10. $O(\omega^2)$ terms
  11. derivation of injection current and shift current
  12. derivation of the Drude terms and the BCD terms
  13. Case $a=b\neq c$
  14. Case $a\neq b=c$
  15. Case $a=c\neq b$
  16. ...and 4 more sections

Figures (3)

  • Figure 1: Schematic picture of nonreciprocal current induced by dissipation. (a) Intraband scattering and relaxation process within relaxation-time approximation. (b) Interband scattering and relaxation process in photocurrent or dissipation-induced nonreciprocal current. (c) Nonreciprocal current induced by dissipation. With finite dissipation, Bloch electrons can be excited to upper bands with application of an electric field, which produces nonreciprocal current in inversion symmetry broken systems.
  • Figure 2: Nonreciprocal current $\sigma^{xxx}$ of the Rice--Mele model. (a) Color plot of $\sigma^{xxx}$ as a function of chemical potential $\mu$ and relaxation rate $\Gamma$. Dashed line indicates the half gap $\Delta=\sqrt{m^2+\delta t^2}$. The inset in (a) shows the band structure of the Rice--Mele model. (b) $\sigma^{xxx}$ as a function of $\mu$ for different values of $\beta$. We set the parameters as $m=0.1t_0,\delta t=0.1t_0$.
  • Figure 3: Nonreciprocal current $\sigma^{xxx}$ of the Rice--Mele model as a function of relaxation rate $\Gamma$. The nonreciprocal current is plotted for different values of the inverse temperature $\beta$. (a) Nonreciprocal current in the insulating case with $\mu=0$. (b) Nonreciprocal current in the metallic case with $\mu=0.15t_0$.