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 such as ${\mathrm{MoS}}_2$ are representative systems, and the current-voltage $I-V$ characteristics, i.e., $V=V\left(I\right)$, for each of them is analyzed. $V\left(I\right)$ can be expanded with respect to the current $I$ as $V\left(I\right)={\sum }_{j=1,\infty }{a}_j(B,T)I^j$, and the $(B,T)$ dependence of $a_j$ depends on the mechanism of the charge transport. Our analysis is based on the time-dependent Ginzburg-Landau theory, which contains up to third-order terms in the momentum of the order parameter. Above the mean field superconducting transition temperature $T_0$, the fluctuation of the superconducting order parameter gives the additional conductivity, i.e., paraconductivity. With the extension of paraconductivity to the nonlinear response, we obtain the nonreciprocal charge transport. On the other hand, below $T_0$, the vortices determine the Kosterlitz-Thouless transition and also the resistivity. The nonreciprocal resistivity is analyzed from the dynamics of vortices in this temperature region. Based on these results, we propose the experiments to identify the mechanism of the nonreciprocal transport with the realistic estimates for the order of magnitude of the coefficients $a_j(B,T)$ for each case.

• Received 16 May 2018
• Revised 31 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.054510