Competition between superconductivity and nematic order in high-$T_c$ superconductor

TL;DR

This paper studies how gapless fermions influence the competition between superconductivity and nematic order in high-$T_c$ superconductors, revealing that fermions can decouple these orders at critical points, leading to continuous phase transitions.

Contribution

It demonstrates that including fermionic degrees of freedom fundamentally alters the interaction between superconducting and nematic orders, enabling their coexistence at quantum critical points.

Findings

Fermions decouple superconductivity and nematic order at criticality.

Phase transitions become continuous with fermionic effects.

Gapless fermions are crucial for accurate theoretical modeling.

Abstract

We investigate the competition between d-wave superconductivity and nematic order in high-$T_c$ superconductor, and examine the role played by gapless fermionic degrees of freedom. Apart from the competitive interaction with the superconducting order parameter, the nematic order parameter couples strongly to gapless nodal quasiparticles. The interplay of these two kinds of interactions is analyzed by means of renormalization group method. In case the fermionic degree of freedom are entirely neglected, the competitive interaction between two bosonic order parameters is strongly relevant, and can lead to runaway behavior. However, these properties are fundamentally changed once the dynamics of fermions are taken into account. At the nematic quantum critical point where an extreme fermion velocity anisotropy occurs, the superconducting and nematic order parameters are decoupled from each other. Consequently, the phase transitions are continuous, and d-wave superconductivity can coexist with nematic order homogeneously. These results indicate that the gapless fermions can play an important role and should be carefully included in the theoretical description of competing orders.