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Bardeen J, Mattis DC. Theory of the anomalous skin effect in normal and superconducting metals. Phys Rev. 1958;111(2):412–7.
Abstract: Chambers' expression for the current density in a normal metal in which the electric field varies over a mean free path is derived from a quantum approach in which use is made of the density matrix in the presence of scattering centers but in the absence of the field. An approximate expression used for the latter is shown to reduce to one derived by Kohn and Luttinger for the case of weak scattering. A general space-and time-varying electromagnetic interaction is treated by first-order perturbation theory. The method is applied to superconductors, and a general expression derived for the kernel of the Pippard integral for fields of arbitrary frequency. The expressions derived can also be used to discuss absorption of electromagnetic radiation in thin superconducting films.
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Sergeev A, Karasik BS, Ptitsina NG, Chulkova GM, Il'in KS, Gershenzon EM. Electron–phonon interaction in disordered conductors. Phys Rev B Condens Matter. 1999;263-264:190–2.
Abstract: The electron–phonon interaction is strongly modified in conductors with a small value of the electron mean free path (impure metals, thin films). As a result, the temperature dependencies of both the inelastic electron scattering rate and resistivity differ significantly from those for pure bulk materials. Recent complex measurements have shown that modified dependencies are well described at K by the electron interaction with transverse phonons. At helium temperatures, available data are conflicting, and cannot be described by an universal model.
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Bardeen J, Cooper LN, Schrieffer JR. Microscopic theory of superconductivity. Phys Rev. 1957;106:162–4.
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Bulaevskii LN, Graf MJ, Batista CD, Kogan VG. Vortex-induced dissipation in narrow current-biased thin-film superconducting strips. Phys Rev B. 2011;83(14):9.
Abstract: A vortex crossing a thin-film superconducting strip from one edge to the other, perpendicular to the bias current, is the dominant mechanism of dissipation for films of thickness d on the order of the coherence length ξ and of width w much narrower than the Pearl length Λâ‰<ab>wâ‰<ab>ξ. At high bias currents I*<I<Ic the heat released by the crossing of a single vortex suffices to create a belt-like normal-state region across the strip, resulting in a detectable voltage pulse. Here Ic is the critical current at which the energy barrier vanishes for a single vortex crossing. The belt forms along the vortex path and causes a transition of the entire strip into the normal state. We estimate I* to be roughly Ic/3. Furthermore, we argue that such “hot†vortex crossings are the origin of dark counts in photon detectors, which operate in the regime of metastable superconductivity at currents between I* and Ic. We estimate the rate of vortex crossings and compare it with recent experimental data for dark counts. For currents below I*, that is, in the stable superconducting but resistive regime, we estimate the amplitude and duration of voltage pulses induced by a single vortex crossing.
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Bulaevskii LN, Graf MJ, Kogan VG. Vortex-assisted photon counts and their magnetic field dependence in single-photon superconducting detectors. Phys Rev B. 2012;85(1):9.
Abstract: We argue that photon counts in a superconducting nanowire single-photon detector (SNSPD) are caused by the transition from a current-biased metastable superconducting state to the normal state. Such a transition is triggered by vortices crossing the thin and narrow superconducting strip from one edge to another due to the Lorentz force. Detector counts in SNSPDs may be caused by three processes: (a) a single incident photon with sufficient energy to break enough Cooper pairs to create a normal-state belt across the entire width of the strip (direct photon count), (b) thermally induced single-vortex crossing in the absence of photons (dark count), which at high-bias currents releases the energy sufficient to trigger the transition to the normal state in a belt across the whole width of the strip, and (c) a single incident photon of insufficient energy to create a normal-state belt but initiating a subsequent single-vortex crossing, which provides the rest of the energy needed to create the normal-state belt (vortex-assisted single-photon count). We derive the current dependence of the rate of vortex-assisted photon counts. The resulting photon count rate has a plateau at high currents close to the critical current and drops as a power law with high exponent at lower currents. While the magnetic field perpendicular to the film plane does not affect the formation of hot spots by photons, it causes the rate of vortex crossings (with or without photons) to increase. We show that by applying a magnetic field one may characterize the energy barrier for vortex crossings and identify the origin of dark counts and vortex-assisted photon counts.
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