Velocity renormalization of nodal quasiparticles in d-wave superconductors

TL;DR

This paper investigates how the velocities of nodal quasiparticles in d-wave superconductors are renormalized near quantum critical points, revealing potential velocity ratio behaviors and the effects of different disorders on system stability.

Contribution

It provides a renormalization-group analysis of velocity renormalization and disorder effects in high-$T_c$ cuprate superconductors near quantum critical points, highlighting stability conditions.

Findings

Velocity ratio can vanish, approach unity, or diverge at quantum critical points.

Random mass and gauge potential are irrelevant, maintaining fixed points.

Random chemical potential is marginal, causing fixed point instability.

Abstract

Gapless nodal quasiparticles emerge at a low-energy regime of high-$T_c$ cuprate superconductors due to the $d_{x^2 - y^2}$ gap symmetry. We study the unusual renormalizations of the Fermi velocity $v_F$ and gap velocity $v_{\Delta}$ of these quasiparticles close to various quantum critical points in a superconducting dome. Special attention is paid to the behavior of the velocity ratio, $v_{\Delta}/v_F$, since it determines a number of observable quantities. We perform a renormalization-group analysis and show that the velocity ratio may vanish, approach unity, or diverge at different quantum critical points. The corresponding superfluid densities and critical temperatures are suppressed, slightly increased, or significantly enhanced. The effects of three types of static disorders, namely, random mass, random gauge potential, and random chemical potential, on the stability of the system are also addressed. An analogous analysis reveals that both random mass and random gauge potential are irrelevant. This implies that these fixed points of the velocity ratio are stable, and hence observable effects ignited by them are unchanged. However, the random chemical potential is marginal. As a result, these fixed points are broken, and thus, the instabilities of quantum phase transitions are triggered.