  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.
