Abstract
Bogliubov-de Gennes equations are solved self-consistently to investigate the properties of bound states in chiral p-wave superconductive disks. It shows that either an s-wave or the mixed d- and s-wave state with odd-frequency and spin-triplet symmetry is induced at the vortex core, depending both on the chirality of the pairing states and on the vortex topology. It is also found that the odd-frequency triplet even parity (OTE) bound state can be manipulated with a local non-magnetic potential. Interestingly, with an appropriate potential amplitude, the zero-energy OTE bound state can be stabilized at a distance from the vortex core and from the local potential. Possible existences of the Majorana fermion modes are expected if the particle-hole symmetry property is applied to the zero-energy OTE bound state. Moreover, skyrmion modes with an integer topological charge have been found to exist.
Highlights
The layered ruthenate superconductor Sr2RuO4 is the first perovskite compound showing superconductivity without cupper-oxide planes[1]
Possible existences of odd-frequency spin-triplet even parity (OTE) states in the chiral p-wave superconductor Sr2RuO4, e.g., the odd-frequency spin-triplet s-wave pairings at a vortex core has been discussed by several research groups[14,15,16,17,18]
We show that an odd-frequency spin-triplet s-wave core state exists for an anti-parallel vortex, in agreement with those reported in previous investigations[18]
Summary
We discuss first the properties of bound states around an axial vortex. For an antiparallel vortex with ν = −1 we obtain the results (not shown) that are in good agreement with those in ref. While the identical spatial profile between the odd-frequency triplet s-wave amplitude and the LDOS remains for the zero-energy mode, it disappears at finite energy levels for a parallel vortex with ν = 1 (Fig. 1). To identify the bound state that is responsible for the new DOS peak, spatial distributions for the local electron density and pairing amplitudes concerned are examined in an atomic length scale. An identical r-dependence of the local electron density with that of a mixed s- and p-wave triplet amplitude (Ts,p+ = 0.36Ts + 0.64Tp+) is expected in an atomic length scale when the mixed pairing amplitude is normalized by the maximum electron density at different quantized energy levels of the bound states. Possible existence of the Majorana mode remains expected if the p-wave component could be suppressed by embedding a non-magnetic quantum dot on the cycle where the zero-energy peak locates. When this happens the zero-energy LDOS signaled is a good indication of the Majorana excitation without an external magnetic topology defect
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