Spin Polarization of Half-Quantum Vortex in Systems with Equal Spin Pairing

Abstract

We present a variational analysis for a half-quantum vortex (HQV) in the equal-spin-pairing superfluid state which, under suitable conditions, is believed to be realized in Sr2RuO4 and 3 He-A. Our approach is based on a description of the HQV in terms of a BCS-like wave function with a spin-dependent boost. We predict a novel feature: the HQV, if stable, should be accompanied by a non-zero spin polarization. Such a spin polarization would exist in addition to the one induced by the Zeeman coupling to the external field and hence may serve as an indicator in experimental search for HQV. When3 He is liquified and cooled into the millidegree regime it enters a new phase which has been proved to possess a spin triplet paired condensate. There also exists by now a growing body of experimental evidence that Sr 2 RuO 4 below 1.5 K is a spin triplet superconductor [1]. This implies the possibility of many interesting phenomena not expected in systems with spin singlet pairing. One of them is the existence of half-quantum vortices (HQV's) in the equal-spin-pairing (ESP) state of the spin triplet condensate [2,3].The pairing symmetry for 3 He is well established and the so-called A phase is confidently believed to realize an ESP spin triplet state [4,5]. While there is, to the best of our knowledge, no unambiguous observation of HQV in 3 He-A [6], there is a strong theoretical argument in favor of their existence at least under some assumptions on the geometry of the experiment. On the contrary, the pairing state of Sr 2 RuO 4 is currently poorly understood and the observation (or not) of HQV, along with other experimental information, would facilitate identification of the underlying pairing symmetry. In addition, there is a significant interest in HQV for topological quantum computing [13].It should be noted right away that the identification of the superconducting phase of Sr 2 RuO 4 with an ESP state does not by itself guarantee thermodynamic stability of HQV in this compound. Even under the assumption of negligible spin-orbit coupling, the kinetic energy of unscreened spin currents which accompany HQV disfavors its formation vis-à-vis the formation of a regular vortex where electromagnetic currents are screened over the length of the penetration depth. Such an unfavorable energy balance can be avoided by limiting the sample size to a few microns [7]. This however further complicates the experimental detection of HQV in Sr 2 RuO 4 .One of the most direct ways for detection of HQV is to look for spin currents which circulate around it. The usual techniques for spin current detection are based on the accumulation of spin and their straightforward application to this situation seems to be difficult. One can however use a fact that spin currents generate electric field. A very rough conservative estimate shows that for a ring of size 1µ the quadrupole electric field generated by the spin currents of HQV will create a potential difference of 1nV across the ring -quite small, but not beyond the capabilities of current exper...

Little-Parks oscillations with half-quantum fluxoid features in Sr2RuO4 microrings

“…For this, small samples are necessary in order to reduce the spin-current energy of the HQF state, as pointed out by Chung et al [25]. The role of the Zeeman field to lower the kinetic energy of a HQF state is discussed by Vakaryuk and Leggett [26]. Accordingly, a transition from IQF to HQF is expected to occur with increasing in-plane field, with free-energy minima for the HQF states appearing in the middle of neighboring IQF states [ Fig.…”

Multiple half-quantum vortices in rotating superfluid3He

“…A HQV is also expected to be present in BEC of alkali atoms [6][7][8] and spin-triplet superconductors [9][10][11], among other physical systems. In spite of extensive theoretical [12][13][14] and experimental [15,16] research on HQV in superfluid 3 He since then, its existence is yet to be experimentally confirmed.…”

“…A HQV is also expected to be present in BEC of alkali atoms [6][7][8] and spin-triplet superconductors [9][10][11], among other physical systems. In spite of extensive theoretical [12][13][14] and experimental [15,16] research on HQV in superfluid 3 He since then, its existence is yet to be experimentally confirmed.Recently, we investigated a rotating superfluid 3 He in a slab geometry under a strong magnetic field [17], in which we have shown that a HQV is energetically stable compared to a singular vortex (SV) in the A 2 -phase side (i.e., lower temperature side) in the vicinity of the A 1 -A 2 phase boundary. In this part of the phase diagram, a HQV will nucleate first as the angular velocity of the rotation is increased from zero.…”

Stability of topological defects in chiral superconductors: London theory

“…(1), may contain terms describing kinetic energies of charge and spin currents 20 , spin-orbit interaction energy 21 , effects of kinematic spin polarization 22 etc. In London theory the free energy of a superconductor is approximated by the kinetic energy of supercurrents described by superfluid velocity v s .…”