Coherent photogalvanic effect in fluctuating superconductors

We develop a theory of the coherent photogalvanic effect (CPGE) in low-dimensional superconductors in the fluctuating regime. It manifests itself in the appearance of a stationary electric current of Cooper pairs under the action of two coherent electromagnetic fields of light with frequencies lying in the sub-terahertz range. We derive the general formula for the electric current density, study the particular cases of linear and circular polarizations of the external light fields, and show that the current might have a nonmonotonous spectrum at certain polarization angles and turns out very sensitive to the proximity of the ambient temperature to the critical temperature of superconducting transition: Approaching the critical temperature, the peak in the spectrum becomes narrower, its frequency experiences a redshift, and the intensity of the peak drastically grows.

Figure 1

Geometry of incident fields: Panels (a) and (b) correspond to linear polarization of both the fields, whereas (c) and (d) correspond to the cases of circular polarization of one of the fields (see text for details).

Figure 2

Components of electric current densities, $j_x$ (solid) and $j_y$ (dashed), as functions of temperature. The green, gray, blue, and red curves correspond to Figs. 1, 1, 1, and 1 , respectively. Inset shows the dependence of $j_0$ on temperature. We used [34, 35] $T_c=10$ K, $n={10}^{14}{\mathrm{cm}}^{-2}$, $\tau =0.1$ ps, $m=0.5m_0$, where $m_0$ is free electron mass. We fixed $\omega =2\times {10}^{11}{\mathrm{s}}^{-1}$, ${\theta }_{\omega }={\theta }_{2\omega }=\pi /6$, $E_1=2$ V/cm, and $E_2=0.25$ V/cm.

Figure 3

Spectra of electric current density for different incident field geometries. The solid curves show $x$-projection of the current $j_x$ as functions of frequency, while the dashed curves show $j_y$ as functions of the same frequencies at two temperatures: 10.10 K (red) and 10.12 K (green) that are above the critical temperature $T_c=10$ K. Other parameters were taken the same as in Fig. 2.

Figure 4

Spectra of electric current densities corresponding to Figs. 1 and 1 for three different values of polarization angles (a) ${\theta }_{2\omega }$ and (b) ${\theta }_{\omega }$: $\pi /3$ (red), $7\pi /5$ (green), $9\pi /5$ (blue). We used $T=10.10$ K. Other parameters were taken the same as in Fig. 2.