Non-analytical angular dependence of the upper critical magnetic field in a quasi-one-dimensional superconductor

We have derived the so-called gap equation, which determines the upper critical magnetic field, perpendicular to conducting chains of a quasi-one-dimensional superconductor. By analyzing this equation at low temperatures, we have found that the calculated angular dependence of the upper critical magnetic field is qualitatively different than that in the so-called effective mass model. In particular, our theory predicts a non-analytical angular dependence of the upper critical magnetic field, $H_{c2}(0) - H_{c2}(\alpha) \sim \alpha^{3/2}$, when magnetic field is close to some special crystallographic axis and makes an angle $\alpha$ with it. We discuss possible experiments on the superconductor (DMET)$_2$I$_3$ to discover this non-analytical dependence.