Philip B. Allen

Theory of Superconducting Tc

Publisher Summary This chapter discusses that Bardeen–Cooper–Schrieffer (BCS) theory is a remarkably complete theory of the superconducting state, and it raises the possibility to understand and predict numerical values of the superconducting transition temperature Tc. The Migdal theory of electron–phonon effects in the normal state and the Eliashberg theory, which generalizes BCS theory to incorporate Migdal theory in the normal limit, provide a rigorous basis for understanding Tc , and prediction of Tc is still largely an unsolved problem. The chapter reviews Migdal–Eliashberg (ME) theory with two aims: first, to make the theory accessible to a wider audience and second to examine the assumptions of the theory to clarify the degree of rigor in each of its parts and in its more recent additions. It has been assumed that the lattice vibrational spectrum and the electronic spectrum of a material are given, the former presumably by neutron scatterers and the latter by band theorists. It is assumed that the required electron–phonon coupling can be computed.

Diffusons, locons and propagons: Character of atomie yibrations in amorphous Si

Abstract Numerical studies of amorphous Si show that the lowest 4% of vibrational modes are piane wave like (‘propagons’) and the highest 3% of modes are localized (‘locons’). The rest are neither piane wave like nor localized. We cali them ‘diffusons’. Since diffusons are by far the most numerous, we try to characterize them by calculating such properties as the wave-vector and polarization (which do not seem to be useful), ‘phase auotient’ (a measure of the change of vibrational phase between first-neighbour atoms), spadal polarization memory and diffusivity. Localized states are characterized by finding decay lengths, inverse participation ratios and coordination numbers of the participating atoms.

Electron transport through a circular constriction

We calculate the conductance of a circular constriction of radius a in an insulating diaphragm which separates two conducting half spaces characterized by the mean free path l. Using the Boltzmann equation we obtain an answer for all values of the ratio

Anomalous nuclear quantum effects in ice

l/a.

Theory of Sound Attenuation in Glasses: The Role of Thermal Vibrations

Our exact result interpolates between the Maxwell conductance in diffusive

Anharmonic Decay of Vibrational States in Amorphous Silicon.

(l\ensuremath{\ll}a)

Evolutionary method for predicting surface reconstructions with variable stoichiometry

and the Sharvin conductance in ballistic

Improved Callaway model for lattice thermal conductivity

(l\ensuremath{\gg}a)

Self-Trapped Exciton and Franck-Condon Spectra Predicted in LaMnO 3

transport regimes. Following Wexlers work, our main advance is to find the explicit form of the Greens function for the linearized Boltzmann operator. The formula for the conductance deviates by less than

Effect of soft phonons on superconductivity: A re-evaluation and a positive case for Nb3Sn

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