We utilize an exact variational numerical procedure to calculate the ground state properties of a polaron in the presence of a Rashba-like spin orbit interaction. Our results corroborate with previous work performed with the Momentum Average approxim
ation and with weak coupling perturbation theory. We find that spin orbit coupling increases the effective mass in the regime with weak electron phonon coupling, and decreases the effective mass in the intermediate and strong electron phonon coupling regime. Analytical strong coupling perturbation theory results confirm our numerical results in the small polaron regime. A large amount of spin orbit coupling can lead to a significant lowering of the polaron effective mass.
A single band optical sum rule derived by Kubo can reveal a novel kind of superconducting state. It relies, however, on a knowledge of the single band contribution from zero to infinite frequency. A number of experiments over the past five years have
used this sum rule; their data has been interpreted in support of kinetic energy-driven superconductivity. However, because of the presence of unwanted interband optical spectral weight, they necessarily have to truncate their sum at a finite frequency. This work examines theoretical models where the impact of this truncation can be examined first in the normal state, and then in the superconducting state. The latter case is particularly important as previous considerations attributed the observed anomalous temperature dependence as an artifact of a non-infinite cutoff frequency. We find that this is in fact not the case, and that the sign of the corrections from the use of a non-infinite cutoff is such that the observed temperature dependence is even more anomalous when proper account is taken of the cutoff. On the other hand, in these same models, we find that the strong observed temperature dependence in the normal state can be attributed to the effect of a non-infinite cutoff frequency.
