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We theoretically study the upper critical magnetic fields at zero temperaturein a quasi-two-dimensional (Q2D) superconductor in the parallel andperpendicular fields, $H_{c2}^{\parallel}(0)$ and $H_{c2}^{\perp}$(0),respectively. We find that $H_{c2}^{\parallel}(0) \approx 0.75 \ | dH_{c2}^{\parallel}/ dT|_{T_c} T_c $ and that $H_{c2}^{\perp}(0) \approx 0.59 \| dH_{c2}^{\perp}/ d T|_{T_c} T_c$, where $| d H_{c2}^{\parallel}/ dT|_{T_c}$and $| d H_{c2}^{\perp}/ d T|_{T_c}$ are the corresponding Ginzburg-Landauslopes of the upper critical magnetic fields. Our results demonstrate thebreakdown of the so-called effective mass model in Q2D case and may bepartially responsible for the experimentally observed deviations from theeffective mass model in a number of layered superconductors, including $MgB_2$.

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