Mesoscopic Effects in Disordered Superconductors nearHc2

A theory of disordered superconductors near the upper critical field $H_{c2\mathrm{}}^0$ is presented. It is shown that the magnetic field dependences of critical temperatures $T_c\left(H\right)$ in mesoscopic samples exhibit multiple reentrant superconductor–normal-metal transitions. In the framework of mean field theory $T_c$ of bulk samples remains finite at any $H$ and asymptotically approaches zero at large $H$. This means that at zero temperature the upper critical magnetic field does not exist. The role of quantum fluctuations of the phase of the order parameter is discussed.