Layered superconductor in a magnetic field: breakdown of the effective masses model

We theoretically study the upper critical magnetic fields at zero temperature in a quasi-two-dimensional (Q2D) superconductor in the parallel and perpendicular fields, $H_{c2}^{\parallel }(0)$ and $H_{c2}^{\perp }$(0), respectively. We find that $H_{c2}^{\parallel}(0) \approx 0.75 \ | d H_{c2}^{\parallel}/ dT|{T_c} T_c $andthat$H{c2}^{\perp}(0) \approx 0.59
| dH_{c2}^{\perp}/ d T|{T_c} T_c$,where$| d H{c2}^{\parallel}/ dT|{T_c}$and$| d H{c2}^{\perp}/ d T|_{T_c}$ are the corresponding Ginzburg-Landau slopes of the upper critical magnetic fields. Our results demonstrate the breakdown of the so-called effective mass model in Q2D case and may be partially responsible for the experimentally observed deviations from the effective mass model in a number of layered superconductors, including $Mg{B}_2$.