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Inelastic scattering rates in d-wave superconductors

Jens Paaske, D.V. Khveshcheko

Published Aug 28, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.17615/83tk-b854

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In the vortex state of a ddd-wave superconductor, massless Dirac quasiparticles are scattered from magnetic vortices via a combination of two basic mechanisms: effective potential scattering due to the superflow swirling about the vortices, and Aharonov-Bohm scattering due to the Berry phase acquired by a quasiparticle upon circling a vortex. In this paper, we study the superflow contribution by calculating the differential cross section for a quasiparticle scattering from the effective noncentral potential of a single vortex. We solve the massless Dirac equation in polar coordinates and obtain the cross section via a partial wave analysis. We also present a more transparent Born-limit calculation, and in this approximation we provide an analytic expression for the differential cross section. The Berry phase contribution to the quasiparticle scattering is considered in a separate paper.
Forward scattering and backscattering play an exceptional role in the physics of two-dimensional interacting fermions. In a Fermi liquid, both give rise to a nonanalytic ${\ensuremath{\omega}}^{2}ln(\ensuremath{\omega})$ form of the fermionic scattering rate at second order in the interaction. Here we argue that higher powers of $ln(\ensuremath{\omega})$ appear in the backscattering contribution at higher orders. We show that these terms come from ``planar'' processes, which are effectively one-dimensional. This is explicitly demonstrated by extending a Fermi liquid to the limit of $N\ensuremath{\gg}1$ fermionic flavors, when only planar processes survive. We sum the leading logarithms for the case of a two-dimensional Fermi liquid near a nematic transition, and we obtain an expression for the scattering rate at T=0T=0T=0 to all orders in the interaction. For a repulsive interaction, the resulting rate is logarithmically suppressed, and the result is valid down to $\ensuremath{\omega}=0$. For an attractive interaction, the ground state is an sss-wave superconductor with a gap ${\mathrm{\ensuremath{\Delta}}}_{0}$. We show that in this case the scattering rate increases as $\ensuremath{\omega}$ is reduced toward ${\mathrm{\ensuremath{\Delta}}}_{0}$. At $\ensuremath{\omega}\ensuremath{\ge}{\mathrm{\ensuremath{\Delta}}}_{0}$, the behavior of the scattering rate is rather unconventional as many pairing channels compete near a nematic critical point, and the sss-wave wins only by a narrow margin. We take superconductivity into consideration and obtain the scattering rate also at smaller $\ensuremath{\omega}\ensuremath{\simeq}{\mathrm{\ensuremath{\Delta}}}_{0}$.
Abstract We have calculated changes in the phonon self‐energy originating from d‐wave superconductivity in the two‐dimensional Hubbard model (U → ∞ limit). Strong local correlations have been incorporated within the mean‐field approximation for auxiliary boson fields. Due to the presence of correlated quasiparticles at the Fermi surface, changes in phonon‐energy shifts and linewidths strongly depend on the concentration of holes. In particular, pronounced effects have been derived for low frequency q = 0 phonons at low doping, where superconductivity starts to set in.
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