The relaxation rates of thermal and hot quasiparticles when scatter with each other are calculated. The transition probabilities at low temperatures express in terms of Bogoliubov coefficients, singlet and triplet scattering amplitudes and dimensionless Landau parameters. Comparison of the theoretical and experimental results gives the values of two Landaus parameters .
The relaxation rates of thermal and hot quasiparticles when scatter with each other are calculated. The transition probabilities at low temperatures express in terms of Bogoliubov coefficients, singlet and triplet scattering amplitudes and dimensionless Landau parameters. Comparison of the theoretical and experimental results gives the values of two Landaus parameters .
Motivated by recent pump-probe experiments we consider the processes by which "hot" quasiparticles produced near the antinodes of a d-wave superconductor can relax. We show that in a large region of momentum space processes which break Cooper pairs are forbidden by energy and momentum conservation. Equilibration then occurs by scattering with thermal quasiparticles: Umklapp scattering is exponentially suppressed at low temperatures, but small-angle scattering leads to power-law behavior. By solving the Boltzmann equation analytically we make detailed predictions for the temperature and intensity dependence of these processes, which we compare with experiment.
Motivated by the strong, low temperature damping of nodal quasiparticles observed in some cuprate superconductors, we study quantum phase transitions in d(x(2)-y(2)) superconductors with a spin-singlet, zero momentum, fermion bilinear order parameter. We present a complete, group-theoretic classification of such transitions into seven distinct cases (including cases with nematic order) and analyze fluctuations by the renormalization group. We find that only two, the transitions to d(x(2)-y(2))+is and d(x(2)-y(2))+id(xy) pairing, possess stable fixed points with universal damping of nodal quasiparticles; the latter leaves the gapped quasiparticles along (1,0), (0,1) essentially undamped.
We derive the Boltzmann equation describing long-wavelength low-frequency transport and relaxation processes in a superfluid Fermi liquid close to the transition temperature Tc. In the superfluid, the quasiparticle number is not conserved and therefore one has to take into account the decay of one quasiparticle into three and the inverse process, as well as the two-quasiparticle scattering process. We calculate the collision term in the Boltzmann equation to first order in the superfluid gap $\ensuremath{\Delta}$ and show that it is related rather simply to the corresponding normal-state collision term. As applications of the Boltzmann equation, we solve it exactly to calculate the shear viscosity, and the intrinsic spin relaxation rate. The shear viscosity drops as $\ensuremath{\Delta}\ensuremath{\propto}{({T}_{c}\ensuremath{-}T)}^{\frac{1}{2}}$ for temperatures just below Tc, and we determine the coefficient of $\ensuremath{\Delta}$ as a function of the normal-state collision probability. Leggett and Takagi's characteristic spin-relaxation time is shown to be equal to the relaxation time of a normal-state quasiparticle at the Fermi energy at Tc. The results provide one with a useful consistency check on experimental measurements which is independent of any assumption about the normal-state collision probability.
The inelastic scattering rates of quasiparticles in a two-dimensional d-wave superconductor, which arise from interactions with either acoustic phonons or other quasiparticles, are calculated within second order perturbation theory. We discover a strong enhancement of scattering with collinear momenta, brought about by the special kinematics of the two-dimensional fermions with Dirac-like spectrum near the nodes of the d-wave order parameter. In the case of a local instantaneous interparticle potential we find that either an RPA-type resummation of the perturbation series or an inclusion of non-linear corrections to the Dirac spectrum is called for in order to obtain a finite scattering rate in the limit ω/T→0. In either way, we find drastic changes in the scattering rate, as compared to the naively expected cubic temperature dependence.
Superconducting materials are useful for a wide range of applications, ranging from particle detectors to quantum computing. The presence of excitations (quasiparticles) in the superconductor can be a resource in some devices and a disturbance in others - in kinetic inductance detectors, the generation of quasiparticles by an incoming photon can be read out and used to calculate the energy of the photon, while the tunnelling of quasiparticles is a cause of decoherence in quantum computing. While early research mostly focused on superconductors close to the critical temperature, temperatures that are far below the critical temperatures are often used for current applications. At these low temperatures, the energy exchange between quasiparticles and phonons becomes slow, and even small disturbances may drive the energy distribution of the quasiparticles out of thermal equilibrium. In fact, experiments usually show a residual number of quasiparticles even at milikelvin temperatures, for which the thermal density of quasiparticles would be negligible. This thesis consists of two parts: In the first part, I model the energy distribution of quasiparticles in superconducting resonators: Quasiparticles absorb energy by absorbing photons and release it as phonons, which drives the superconductor out of thermal equilibrium. I solve a set of rate equations, both numerical and analytical, to calculate the energy distribution of the quasiparticles. For parameters typically used in kinetic inductance detectors made of aluminum, the microwave signal used to read out the resonator dominates the energy distribution of the quasiparticles, while their density is determined by other processes. At not too low temperatures, quasiparticles are mainly produced by thermal phonons, and my calculations reproduce recently measured quality factors of resonators at temperatures above 250 mK without free parameters. I show that even a very small number of photons of higher energy, which I ascribe to noise from the microwave generator, would dominate the quasiparticle density at lower temperatures. Under this assumption, my calculations also reproduce the quality factors at lower temperatures. In the second part of this thesis, I investigate the effects of spatial fluctuations of the superconducting energy gap on the dynamics of quasiparticles. Recently, it has been proposed that such fluctuations may lead to the localization of quasiparticles in states below the energy gap, which could cause a finite quasiparticle density even at very low temperatures. Using the Keldysh-Usadel formalism, I derive rates for the different processes (recombination/(de-) localization/generation) of quasiparticles in such systems. Using these rate equations I derive new upper limits for the quasiparticle density that could result from these localized states. These upper limits show that localization caused by weak magnetic impurities in typical aluminum systems does not lead to a relevant quasiparticle density. This contradicts previous theories, which only consider the recombination between two localized quasiparticles without examining their dynamics in detail.
Recent numerical calculation of the intrinsic thermal Hall conductivity of nodal d-wave superconductors in the mixed state revealed a rapid increase of this quantity above an onset temperature. Interestingly, this defines a measurable energy scale in an otherwise gapless state. Using the mathematics of magnetic coherent states, in this paper such energy scale is related to a dynamical process associated with the Andreev scattering of an electron wave packet moving along the constant energy contours in the momentum space. This energy scale is then used to obtain an improved scaling collapse of numerically calculated thermal Hall conductivity in a tight-binding model as a function of temperature, magnetic field, and the d-wave pairing amplitude at various band fillings. The results indicate that the mentioned onset temperature is associated with the ability of the quasiparticle wave packet to complete its semiclassical orbit before it is appreciably scattered by the superconducting condensate.