Ginzburg-Landau slopes of the anisotropic upper critical magnetic field and band parameters in the superconductor $\mathrm{(TMTSF)_2ClO_4}$

We theoretically determine the Ginzburg–Landau slopes of the anisotropic upper critical magnetic field in a quasi-one-dimensional superconductor and correct the previous works on this issue. By using the experimentally measured values of the Ginzburg–Landau slopes in the superconductor $\mathrm{(TMTSF)_2ClO_4}$, we determine band parameters of its electron spectrum. Our main result is that the so-called quantum dimensional crossover has to happen in this material in magnetic fields, $H = 3$–$8\,$T, which are much lower than the previously assumed. We discuss how this fact influences metallic and superconducting properties of the $\mathrm{(TMTSF)_2ClO_4}$.