Ratchet effect in lateral plasmonic crystal: Giant enhancement due to interference of "bright" and "dark" modes

TL;DR

This work develops a non-perturbative theory of the ratchet effect in a tunable lateral plasmonic crystal formed by a dual-grating gate. By solving exactly for the static gate-induced potential while treating the THz radiation perturbatively within a hydrodynamic framework, it reveals that interference between bright and dark plasmon modes can dramatically enhance the dc photocurrent, with enhancements scaling as roughly (ω_0^2 Δ^2)/(γ^2). The analysis identifies distinct operational regimes—weak coupling, resonant, and super-resonant—where the photocurrent exhibits Drude and plasmonic peaks, Fano-like line shapes, and a dense forest of peaks in the strong coupling limit, all tunable by gate voltages. The results provide a comprehensive mechanism for gate-controlled, high-efficiency THz detectors and frequency-selective current sources based on plasmonic ratchets, consistent with recent experimental observations in LPCs.

Abstract

We develop a theory of the ratchet effect in a lateral plasmonic crystal (LPC) formed by a two dimensional electron gas under a periodic dual-grating gate. The system is driven by terahertz radiation, and the spatial asymmetry required for the generation of dc photocurrent is introduced by a phase shift between the radiation's near-field modulation and the static electron density profile. In contrast to the commonly used perturbative "minimal model" of the ratchet effect, which assumes weak density modulation, we solve the problem exactly with respect to the static gate-induced potential while treating the radiation field perturbatively. This approach reveals a dramatic enhancement of the plasmonic contribution to the ratchet current due to the interference of "bright" and "dark" plasmon modes, which are excited on an equal footing in the asymmetric LPC. Specifically, we predict a parametric growth of the plasmonic peak as compared with the Drude peak with increasing coupling, and the appearance of a dense super-resonant structure when the spacing between plasmonic sub-bands becomes larger than the damping rate. Hence, the dc response exhibits both resonant and super-resonant regimes observed in recent experiments on the radiation transmission through the LPC. The interplay of bright and dark modes, together with their interference, provides a powerful mechanism for controlling the magnitude and sign of the photocurrent by gate voltages and the radiation frequency.

Figures (14)

• Figure 1: (updated from Ref. Gorbenko2024) Dependence of the frequencies $\omega_n^{\rm bright}$ (red lines) and $\omega_n^{\rm dark}$ (grey lines) in the units of $\omega_1=2\pi s_1/L$ on the ratio $s_2/s_1$ for $L_1 = L_2.$ Panel (a) shows interval $0.1<s_2/s_1<1,$ Panel (b) shows interval $0<s_2/s_1<0.1.$ As seen from the panel (b), spectrum of resonances becomes infinitely dense in the limit $s_2 \to 0$ because distance between neighboring levels turns to zero: $\Delta \omega \sim s_2/L_2 \to 0$.
• Figure 2: (updated from Ref. Gorbenko2024) Spectrum of the ideal (i.e. with $\gamma=0$) LPC for $s_2 = 0.3~ s_1, ~L_1=L_2.$ Bright and dark modes are shown at $K=0$ by thick red points and open circles, respectively.
• Figure 3: Plot of dc current, $J$ on frequency $\omega/\omega_0$ for the resonant case $\gamma/\omega_0 = 0.05$ and different values of $\Delta$: $\Delta=0.1,~ \Delta=0.3$ and $\Delta=0.5$.
• Figure 4: Plot of exact and approximate expressions for dc current at resonant frequency: $J(\omega = \omega_b)$ (red curve, $\omega_b$ is given by Eq.\ref{['Eq_wb_split']} and $J$ by Eq.\ref{['Eq_J']}), $J_{\rm weak}^{\rm max}$ (dashed blue curve, see Eq. \ref{['Eq_J_weak_res']}) and linear-in-$\Delta$ approximation $J_{\rm weak}^0$ (dashed green curve, see Eq. \ref{['Eq_Jweak']}). Plots are made for the resonant case $\gamma/\omega_0 = 0.01$. To simplify plot we replaced exact numerical values with approximations: $3^{3/4}/4 \approx 0.6$, $3^{1/4} \approx 1.3$.
• Figure 5: Schematic plot of the ratio of the amplitude at the resonant frequency to the Drude peak on $\gamma/\omega_0$ for weak coupling, $\Delta \ll 1.$ For small $\gamma/\omega_0<\Delta^2$ bright and dark modes are distinguishable. For $\Delta^2 < \gamma/\omega_0$ dark and bright modes are merged into single plasmonic resonance. (Here we limit ourselves with regime $\gamma \ll \omega _0$.)