Role of electronic nematicity in the interplay between s- and d-wave broken-symmetry states

TL;DR

This paper explores how electronic nematic order influences the interaction between s- and d-wave symmetry states, revealing that nematicity affects inter-superspin couplings but not within the same superspin, impacting superconducting properties.

Contribution

It introduces a theoretical framework showing nematic order's selective interference with order parameters organized into superspins, and discusses its effects on superconducting transition temperatures.

Findings

Nematic order commutes with all SO(6) generators, not part of the group.

Nematicity enables linear coupling between s- and d-wave superconducting orders.

Nematic order influences the interplay between different superspins, affecting phase competition.

Abstract

To understand the role of electronic nematic order in the interplay between s- and d-wave particle-particle or particle-hole condensate states, relations between various s- and d-wave order parameters are studied. We find that the nematic operator transforms two independent six-dimensional vectors. The d-wave superconducting, d-density wave, and antiferromagnetic orders are organized into one vector, and the s-wave superconducting, charge density wave, and spin-triplet d-density wave orders into the other vector. Each vector acts as a superspin and transforms under the action of SO(6) where charge, spin, eta- and pi-pairing, spin-triplet nematic operators satisfy the SO(6) Lie algebra. Electronic nematic order is not a part of the SO(6) group. It commutes with all 15 generators. Our findings imply that nematic order does not affect the competition among the order parameters within the same superspin, while it strongly interferes the interplay between two order parameters that belong to different superspins. For example, nematicity allows a linear coupling between d- and s-wave superconducting order parameters which modifies the superconducting transition temperature. A generalized Ginzburg-Landau theory and further physical implications are discussed.