The collision frequency in two unconventional superconductors

Abstract

The collision frequency (also known as the inverse scattering lifetime) can be self-consistently calculated from the imaginary part of the zero-temperature elastic scattering cross-section in unconventional superconductors. We find these types of studies helpful to describe a hidden self-consistent damping due to incoherent fermions in two physical spaces: The Phase Space of the Nonequilibrium Statistical Mechanics, and the Configuration Space of Nonrelativistic Quantum Mechanics. The direct relation of the collision frequency with those well-known Physical Spaces is addressed in a singular way this time. Since the use of collisions for different elastic scattering regimes, is a well-developed formalism using retarded, and advanced Green functions in Many Body Physics; in order to describe our findings, we define and characterize a Reduced Phase Space for collision frequencies in the triplet strontium ruthenate compound and the singlet doped with strontium lanthanum cuprate ceramic. Both compounds display different nodal behavior of the superconducting order parameter. In this work, their zero gap behavior is numerically scanned and used to give some illustrative examples. Finally, it intuitively explores the geometrical nonlocality of the collision frequency of this type of hidden self-consistency in the Boltzmann equation, when the zero superconducting gap value drives the physics below the transition temperature, and incoherent fermions quasiparticles govern several nonequilibrium phenomena since the macroscopic behavior remarkably changes with the strontium atomic potential strength, and the concentration inherent to both compounds.