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

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.Comment: 4 pages, 1 figures, updated to the published versio

Nematic domains and resistivity in an itinerant metamagnet coupled to a lattice

The nature of the emergent phase near a putative quantum critical point in the bilayer ruthenate Sr$_3$Ru$_2$O$_7$ has been a recent subject of intensive research. It has been suggested that this phase may possess electronic nematic order(ENO). In this work, we investigate the possibility of nematic domain formation in the emergent phase, using a phenomenological model of electrons with ENO and its coupling to lattice degrees of freedom. The resistivity due to the scattering off the domain walls is shown to closely follow the ENO parameter. Our results provide qualitative explanations for the dependence of the resistivity on external magnetic fields in Sr$_3$Ru$_2$O$_7$.Comment: 4 pages, 4 figures, published versio

Meta-nematic transitions in a bilayer system: Application to the bilayer ruthenate

It was suggested that the two consecutive metamagnetic transitions and the large residual resistivity discovered in Sr$_3$Ru$_2$O$_7$ can be understood via the nematic order and its domains in a single layer system. However, a recently reported anisotropy between two longitudinal resistivities induced by tilting the magnetic field away from the c-axis cannot be explained within the single layer nematic picture. To fill the gap in our understanding within the nematic order scenario, we investigate the effects of bilayer coupling and in-plane magnetic field on the electronic nematic phases in a bilayer system. We propose that the in-plane magnetic field in the bilayer system modifies the energetics of the domain formation, since it breaks the degeneracy of two different nematic orientations. Thus the system reveals a pure nematic phase with a resistivity anisotropy in the presence of an in-plane magnetic field. In addition to the nematic phase, the bilayer coupling opens a novel route to a hidden nematic phase that preserves the x-y symmetry of the Fermi surfaces.Comment: 8 pages, 6 figure