Quantum-resistance states of superconducting Pb films

We found that the $I-V$ curves of a Pb film in a parallel magnetic field may consist of several linear current branches, characterized by a set of quantized resistances proportional to $n-\alpha$, where $n$ is an integer and $\alpha$ is a field-dependent constant parameter between 0 and ½. The film thickness $t$ and the parallel magnetic field $H_{\parallel }$ required for observing these quantum-resistance states are $\xi <t<\mathrm{}3\mathrm{}\xi$ and $H_{c2\mathrm{}}<H_{\parallel }<H_{c3\mathrm{}}$, respectively. A simple phenomenological model based on the assumption that the film has a superconducting-normal-superconducting layer structure has been presented with the interpretation of the quantum resistances in terms of the momentum quantization of bound quasiparticles. Our data indicate that if the interpretation based on the bound quasiparticles is correct, then the quantum resistances we have observed are those with $\hslash k_{\mathrm{ZF}}\ll {\left(2m\Delta \right)}^{\frac{1}{2}}$, where $k_{\mathrm{ZF}}$ is the component of the Fermi momentum perpendicular to the film surface.