Photogalvanic effect in hydrodynamic flows of nonreciprocal electron liquids

TL;DR

The paper investigates AC-driven nonlinear hydrodynamic electron transport in noncentrosymmetric conductors with broken time-reversal symmetry, showing that a DC current $I^{DC}$ arises quadratically with the drive in a nonreciprocal Hall-bar geometry. It develops a generalized Navier–Stokes framework with a nonreciprocal stress characterized by the dimensionless number $\mathcal{N}$ and a frequency-dependent vibrational number $\mathcal{R}$, yielding an explicit perturbative expression for $I^{DC}$ in terms of $\mathcal{N}$ and $\mathcal{R}$ and highlighting nonlocal, super-extensive behavior at low frequencies. The work also analyzes memory effects via hysteretic $I$–$V$ curves, explores the impact of weak disorder on the photogalvanic response, and studies transient relaxation to a steady-state current $I = I_0 f(\mathcal{N})$, providing concrete predictions for graphene-like hydrodynamic systems with intrinsic symmetry breaking. Overall, the results establish an intrinsic photogalvanic mechanism in hydrodynamic electron liquids and offer measurable signatures (dc rectification, hysteresis skewness, disorder dependencies, and transient dynamics) for experiments in TRS-broken, noncentrosymmetric materials.

Abstract

We study nonlinear hydrodynamic electron transport driven by an AC electric field. In noncentrosymmetric conductors with broken time-reversal (TR) symmetry the nonlinear flow of such liquids is nonreciprocal, giving rise to a DC current $I^{DC}$ that is quadratic in the amplitude of the AC electric field. This is the hydrodynamic analogue of the linear photogalvanic effect (PGE), which arises in bulk noncentrosymmetric materials with broken TR symmetry. The magnitude of $I^{DC}$ depends on both the properties of the electron fluid and the geometry of the flow, and may be characterized by two dimensionless parameters: the nonreciprocity number $\mathcal{N}$, and the frequency-dependent vibrational number $\mathcal{R}$. Due to nonlocality of hydrodynamic transport, at low frequencies of the AC drive, $I^{DC}$ is super-extensive. The AC component of the electric current is likewise strongly affected by nonreciprocity: the hysteretic current-voltage dependence becomes skewed, which can be interpreted in terms of nonreciprocity of the memory retention time.

Figures (8)

• Figure 1: Flow of an electron liquid in a Hall bar driven by a uniform AC electric field in the $\hat{\bm{x}}$ direction. For nonreciprocal liquids, a DC electric current appears that is quadratic in the amplitude of the AC electric field.
• Figure 2: Characteristic scaled velocity $u(y,\tau)/U_0$ profiles obtained by numerical solution of the time-dependent Stokes Eq. \ref{['ut0']} (with oscillating electric field) that we average over time and space to obtain the current denoted by the circle markers in panels (a) and (b) of figure \ref{['I_Re_num']}.
• Figure 3: Panel (a) continuous curve: Absolute value of scaled DC current \ref{['IavReN']} vs. the vibrational number $\mathcal{R}= \omega d^2/\nu$ for the nonreciprocal number $\mathcal{N} =0.1$. At low frequencies it reaches the value $\mathcal{N}/10$, as predicted by the first term in the series expansion in \ref{['IavRe']}. At high frequencies it decays as $\mathcal{R}^{-2}$ as predicted in the asymptotic expansion of Eq. \ref{['IavRe']}. Panel (b) continuous curve: Absolute value of scaled DC current \ref{['IavReN']} vs. the nonreciprocal number $\mathcal{N}$ for the experimentally relevant magnitude of the vibrational number $\mathcal{R} =12$. Circle markers denote scaled averaged current $|I|$ obtained by solving numerically the time-dependent Stokes Eq. \ref{['ut0']}. There is good agreement between the perturbative result \ref{['IavRe']} and the full numerical solution of the momentum equation \ref{['ut0']}. Panels (c): structure factors defined in (\ref{['Spm']}) and (\ref{['Sdis']}).
• Figure 4: Left panel: Current-voltage hysteresis loop evaluated at $\mathcal{R}=2$ which maximizes the loop area (i.e. maximum energy dissipation, cf. the $\mathcal{R}$ at the area maximum in the right panel). Right panel, continuous curve: Area between zeroth order current \ref{['I0ACb']} and voltage. The triangle markers denote the area formed between the current \ref{['I0ACb']} that includes first order corrections. The square markers denote the area between current and voltage by running numerical simulations of the full momentum equation \ref{['ut0']}. The frequency that maximizes the area of the loop, determines the characteristic 'memory' time $\tau_M \sim \frac{d^2}{2\nu}$, cf. Robin2023 and Kamsma2023PRL.
• Figure 5: Same as in figure \ref{['memory1']} but for $\mathcal{N} =1$. New features include an increased skewness of the hysteresis loop as $\mathcal{N}$ increases (compare left panel with its counterpart of Fig. \ref{['memory1']}). The hysteresis loop area also increases with $\mathcal{N}$. The approximate current (continuous line and triangle markers) starts to deteriorate.