Chiral Correction to the Spin Fluctuation Feedback in two-dimensional p-wave Superconductors

– We consider the stability of the superconducting phase for spin-triplet p-wave pairing in a quasi-two-dimensional system. We show that in the absence of spin-orbit coupling there is a chiral contribution to spin fluctuation feedback which is related to spin quantum Hall effect in a chiral superconducting phase. We show that this mechanism supports the stability of a chiral p-wave state. Cooper pairing in the spin-triplet (odd-parity) channel has been for a long time the privilege of the superfluid He only [1]. In the mid-eighties superconductors have been discovered which were considered good candidates for spin-triplet pairing appeared, the so-called heavy Fermion superconductors, e.g. UPt3 and UBe13 [2] More recently, several new compounds such as UGe2 and Sr2RuO4 have been added to the list of potential spin-triplet superconductors. In particular, in the case the ruthenate we have to date overwhelming experimental evidence of spin-triplet pairing in a state which resembles the A-phase of He from point of view of broken symmetries [3]. Spin-triplet pairing provides even in case of reduced rotation symmetry (crystal field) still a large number of degrees of freedom, which leads in many cases to long lists of potential superconducting phases [4]. An interesting situation occurs in a two-dimensional system, where the weak-coupling approach leads to several spin-triplet pairing states that possess the same condensation energy in the presence of complete spin-rotation symmetry. Systems of this kind are Sr2RuO4 which has a quasi-two-dimensional (2D) electron band structure [3, 5] and thin films of He (whereby we avoid the discussion of the Berezinsky-Kosterlitz-Thouless transition which would occur in a film, see [6]). In both cases the state realized has the structure of a “chiral p-wave” state, with an orbital angular momentum pointing out of the plane, px ± ipy. This chirality has been discussed in connection with a variety of possible effects, such as the zero-field Hall effect [7, 8], modified vortex core states [9] or the spin quantum Hall effect (SQHE) [10–12]. In this letter we will show that chirality may also be an essential part to stabilization of the chiral p-wave state through a spin-induced feedback effect.