Intimate relations between electronic nematic, d-density wave and d-wave superconducting states

TL;DR

This paper explores the theoretical relationships and symmetries between electronic nematic, d-density wave, and d-wave superconducting states, revealing invariances and degeneracies that influence their competition.

Contribution

It identifies SO(4) invariance at the nematic to d-wave superconductor transition and shows nematic and ddw states are exactly degenerate under certain transformations.

Findings

SO(4) invariance at nematic to d-wave transition

Nematic and ddw states are degenerate under a unitary transformation

Competition between nematic and ddw states analyzed with degeneracy breaking

Abstract

This paper consists of two important theoretical observations on the interplay between l = 2 condensates; d-density wave (ddw), electronic nematic and d-wave superconducting states. (1) There is SO(4) invariance at a transition between the nematic and d-wave superconducting states. The nematic and d-wave pairing operators can be rotated into each other by pseudospin SU(2) generators, which are s-wave pairing and electron density operators. The difference between the current work and the previous O(4) symmetry at a transition between the ddw and d-wave superconducting states (Nayak 2000 Phys. Rev. B 62 R6135) is presented. (2) The nematic and ddw operators transform into each other under a unitary transformation. Thus, when a Hamiltonian is invariant under such a transformation, the two states are exactly degenerate. The competition between the nematic and ddw states in the presence of a degeneracy breaking term is discussed.