Nonreciprocal Terahertz Second-Harmonic Generation in Superconducting NbN under Supercurrent Injection

Abstract

Giant second-harmonic generation in the terahertz (THz) frequency range is observed in a thin film of an $s$-wave superconductor NbN, where the time-reversal ($\mathcal{T}$) and space-inversion ($\mathcal{P}$) symmetries are simultaneously broken by supercurrent injection. We demonstrate that the phase of the second-harmonic signal flips when the direction of supercurrent is inverted; i.e., the signal is ascribed to the nonreciprocal response that occurs under broken $\mathcal{P}$ and $\mathcal{T}$ symmetries. The temperature dependence of the SH signal exhibits a sharp resonance, which is accounted for by the vortex motion driven by the THz electric field in an anharmonic pinning potential. The maximum conversion ratio ${\ensuremath{\eta}}_{\mathrm{SHG}}$ reaches $\ensuremath{\approx}{10}^{\ensuremath{-}2}$ in a thin film NbN with the thickness of 25 nm after the field cooling with a very small magnetic field of $\ensuremath{\approx}1\text{ }\text{ }\mathrm{Oe}$, for a relatively weak incident THz electric field of $2.8\text{ }\text{ }\mathrm{kV}/\mathrm{cm}$ at 0.48 THz.