Quantum criticality of fermion velocities and critical temperature nearby a putative quantum phase transition in the $d$-wave superconductors

TL;DR

This paper investigates quantum critical behaviors near a putative quantum phase transition in d-wave superconductors, revealing how fermion velocities and critical temperatures are renormalized and exhibit critical phenomena influenced by quantum fluctuations.

Contribution

It introduces a renormalization group analysis of fermion velocities and critical temperatures near a quantum phase transition in d-wave superconductors, highlighting the effects of quantum fluctuations and interactions.

Findings

Fermion velocities are driven to finite anisotropic fixed points by quantum fluctuations.

Critical temperatures can be enhanced or suppressed due to fermion velocity renormalization.

Quantum fluctuations and interactions significantly influence quantum critical behaviors.

Abstract

Quantum critical behaviors induced by a putative quantum phase transition are vigilantly investigated, which separates a $d$-wave superconducting state and $d$-wave superconducting+$X$ state below the superconducting dome of the $d-$wave superconductors with tuning the non-thermal doping variable. Within the framework of renormalization group approach, we start with a phenomenological effective theory originated from the Landau-Ginzburg-Wilson theory and practice one-loop calculations to construct a set of coupled flows of all interaction parameters. After extracting related physical information from these coupled evolutions, we address that both fermion velocities and critical temperatures exhibit critical behaviors, which are robust enough against the initial conditions due to strong quantum fluctuations. At first, the evolution of Yukawa coupling between $X$-state order parameter and nodal fermions in tandem with quantum fluctuations heavily renormalize fermion velocities and generally drive them into certain finite anisotropic fixed point at the lowest-energy limit, whose concrete value relies upon the very quantum phase transition. In addition, these unique properties of fermion velocities largely reshape the fate of superfluid density, giving rise to either an enhancement or a dip of critical temperature. Moreover, we find that fermion-fermion interactions bring non-ignorable quantitative corrections to quantum critical behaviors despite they are subordinate to quantum fluctuations of order parameters.