Nonreciprocal charge transport in two-dimensional noncentrosymmetric superconductors

Nonreciprocal charge transport phenomena are studied theoretically for two-dimensional noncentrosymmetric superconductors under an external magnetic field $B$. Rashba superconductors, surface superconductivity on the surface of three-dimensional topological insulators, and transition metal dichalcogenides (TMD) are representative systems, and the current-voltage $I$-$V$ characteristics, i.e., $V=V(I)$, for each of them is analyzed. $V(I)$ can be expanded with respect to the current $I$ as $V(I)= \sum_{j=1,\infty} a_j(B,T) I^j$, and the $(B,T)$-dependence of $a_j$ depends on the mechanism of the charge transport. Above the mean field transition temperature $T_0$, the fluctuation of the superconducting order parameter gives the additional conductivity, i.e., paraconductivity. Extending the analysis to the nonlinear response, we obtain the nonreciprocal charge transport expressed by $a_2(B,T) = a_1(T) \gamma(T) B$, where $\gamma$ converges to a finite value at $T=T_0$. Below $T_0$, the vortex motion is relevant to the voltage drop, and the dependence of $a_j$ on $B,T$ is different depending on the system and mechanisms. For the superconductors under the in-plane magnetic field, the Kosterlitz-Thouless (KT) transition occurs at $T_{\rm KT}$. In this case $\gamma$ has the characteristic temperature dependences such as $\gamma \sim (T-T_{\rm KT})^{-3/2}$ near $T_{\rm KT}$. On the other hand, for TMD with out-plane magnetic field, the KT transition is gone, and there are two possible mechanisms for the nonreciprocal response. One is the anisotropy of the damping constant for the motion of the vortex. In this case, $a_1(B) \sim B$ and $a_2(B) \sim B^2$. The other one is the ratchet potential acting on the vortex motion, which gives $a_1(B) \sim B$ and $a_2(B) \sim B$. Based on these results, we propose the experiments to identify the mechanism of the nonreciprocal charge transport.