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

摘要

To understand the role of electronic nematic order in the interplay betweens- and d-wave particle-particle or particle-hole condensate states, relationsbetween various s- and d-wave order parameters are studied. We find that thenematic operator transforms two independent six-dimensional vectors. The d-wavesuperconducting, d-density wave, and antiferromagnetic orders are organizedinto one vector, and the s-wave superconducting, charge density wave, andspin-triplet d-density wave orders into the other vector. Each vector acts as asuperspin and transforms under the action of SO(6) where charge, spin, eta- andpi-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 all15 generators. Our findings imply that nematic order does not affect thecompetition among the order parameters within the same superspin, while itstrongly interferes the interplay between two order parameters that belong todifferent superspins. For example, nematicity allows a linear coupling betweend- and s-wave superconducting order parameters which modifies thesuperconducting transition temperature. A generalized Ginzburg-Landau theoryand further physical implications are discussed.