Semenov, A. V., Devyatov, I. A., Korneev, A. A., Smirnov, K. V., Goltsman, G. N., & Melnikov, A. P. (2012). Derivation of expression for thermodynamic potential of “dirty” superconductor. Rus. J. Radio Electron., (4).
Abstract: We derive a formula for thermodynamic potential of dirty superconductor which express it via isotropic quasiclassical Green functions of Usadel theory. Our result allows unify description of dynamic processes and fluctuations in superconducting nano-electronic devices.
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Sergeev, A., Karasik, B. S., Ptitsina, N. G., Chulkova, G. M., Il'in, K. S., & Gershenzon, E. M. (1999). Electron–phonon interaction in disordered conductors. Phys. Rev. B Condens. Matter, 263-264, 190–192.
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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Sergeev, A., & Mitin, V. (2000). Electron-phonon interaction in disordered conductors: Static and vibrating scattering potentials. Phys. Rev. B., 61(9), 6041–6047.
Abstract: Employing the Keldysh diagram technique, we calculate the electron-phonon energy relaxation rate in a conductor with the vibrating and static δ-correlated random electron-scattering potentials. If the scattering potential is completely dragged by phonons, this model yields the Schmid’s result for the inelastic electron-scattering rate τ−1e−ph. At low temperatures the effective interaction decreases due to disorder, and τ−1e−ph∝T4l (l is the electron mean-free path). In the presense of the static potential, quantum interference of numerous scattering processes drastically changes the effective electron-phonon interaction. In particular, at low temperatures the interaction increases, and τ−1e−ph∝T2/l. Along with an enhancement of the interaction, which is observed in disordered metallic films and semiconducting structures at low temperatures, the suggested model allows us to explain the strong sensitivity of the electron relaxation rate to the microscopic quality of a particular film.
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Ptitsina, N. G., Chulkova, G. M., Il’in, K. S., Sergeev, A. V., Pochinkov, F. S., Gershenzon, E. M., et al. (1997). Electron-phonon interaction in disordered metal films: The resistivity and electron dephasing rate. Phys. Rev. B, 56(16), 10089–10096.
Abstract: The temperature dependence of the resistance of films of Al, Be, and NbC with small values of the electron mean free path l=1.5–10nm has been measured at 4.2–300 K. The resistance of all the films contains a T2 contribution that is proportional to the residual resistance; this contribution has been attributed to the interference between the elastic electron scattering and the electron-phonon scattering. Fitting the data to the theory of the electron-phonon-impurity interference (M. Yu. Reiser and A. V. Sergeev, Zh. Eksp. Teor. Fiz. 92, 224 (1987) [Sov. Phys. JETP 65, 1291 (1987)]), we obtain constants of interaction of the electrons with transverse phonons, and estimate the contribution of this interaction to the electron dephasing rate in thin films of Au, Al, Be, Nb, and NbC. Our estimates are in a good agreement with the experimental data on the inelastic electron-phonon scattering in these films. This indicates that the interaction of electrons with transverse phonons controls the electron-phonon relaxation rate in thin-metal films over a broad temperature range.
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Kardakova, A., Finkel, M., Morozov, D., Kovalyuk, V., An, P., Dunscombe, C., et al. (2013). The electron-phonon relaxation time in thin superconducting titanium nitride films. Appl. Phys. Lett., 103(25), 252602 (1 to 4).
Abstract: We report on the direct measurement of the electron-phonon relaxation time, τeph, in disordered TiN films. Measured values of τeph are from 5.5 ns to 88 ns in the 4.2 to 1.7 K temperature range and consistent with a T−3 temperature dependence. The electronic density of states at the Fermi level N0 is estimated from measured material parameters. The presented results confirm that thin TiN films are promising candidate-materials for ultrasensitive superconducting detectors.
The work was supported by the Ministry of Education and Science of the Russian Federation, Contract No. 14.B25.31.0007 and by the RFBR Grant No. 13-02-91159.
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