Hidden quasi one-dimensional superconductivity in Sr$_2$RuO$_4$

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Abstract

Using an asymptotically exact weak coupling analysis of a multi-orbital Hubbard model of the electronic structure of \SRO, we show that the interplay between spin and charge fluctuations leads unequivocally to triplet pairing which originates in the quasi-one dimensional bands. The resulting superconducting state spontaneously breaks time-reversal symmetry and is of the form $\Delta \sim p_x + i p_y \hat{z}$ with sharp gap minima and a d-vector that is only {\it weakly} pinned. The supercondutor is topologically {\it trivial} and hence lacks robust chiral Majorana fermion modes along the boundary. The absence of topologically protected edge modes could explain the surprising absence of experimentally detectable edge currents in this system.

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Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect

N Read, Dmitry Green (1999)

We analyze pairing of fermions in two dimensions for fully-gapped cases with broken parity (P) and time-reversal (T), especially cases in which the gap function is an orbital angular momentum ($l$) eigenstate, in particular $l=-1$ (p-wave, spinless or spin-triplet) and $l=-2$ (d-wave, spin-singlet). For $l\neq0$, these fall into two phases, weak and strong pairing, which may be distinguished topologically. In the cases with conserved spin, we derive explicitly the Hall conductivity for spin as the corresponding topological invariant. For the spinless p-wave case, the weak-pairing phase has a pair wavefunction that is asympototically the same as that in the Moore-Read (Pfaffian) quantum Hall state, and we argue that its other properties (edge states, quasihole and toroidal ground states) are also the same, indicating that nonabelian statistics is a {\em generic} property of such a paired phase. The strong-pairing phase is an abelian state, and the transition between the two phases involves a bulk Majorana fermion, the mass of which changes sign at the transition. For the d-wave case, we argue that the Haldane-Rezayi state is not the generic behavior of a phase but describes the asymptotics at the critical point between weak and strong pairing, and has gapless fermion excitations in the bulk. In this case the weak-pairing phase is an abelian phase which has been considered previously. In the p-wave case with an unbroken U(1) symmetry, which can be applied to the double layer quantum Hall problem, the weak-pairing phase has the properties of the 331 state, and with nonzero tunneling there is a transition to the Moore-Read phase. The effects of disorder on noninteracting quasiparticles are considered.

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Generalized Bardeen-Cooper-Schrieffer States and the Proposed Low-Temperature Phase of LiquidHe3

P W Anderson, P Morel (1961)

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Orbital dependent superconductivity in Sr_2RuO_4

, , (2009)

We show that for superconducting Sr_2RuO_4 any unconventional pairing in the part of the Fermi surface with Ru 4d-xy orbital character is weakly coupled to that with Ru 4d-xz, 4d-yz orbital character. This naturally gives rise to two disparate energy scales in the superconducting state which leads to novel low temperature properties in a variety of thermodynamic and transport properties and which would also account for the large residual density of states seen in specific heat and NQR measurements.