Orbital angular momentum in a nonchiral topological superconductor

Abstract

We investigate the bulk orbital angular momentum in a two-dimensional time-reversal broken topological superconductor with the Rashba spin-orbit interaction, the Zeeman interaction, and the s-wave pairing potential. Prior to the topological phase transition, we find the crossover from s wave to p wave. For the large spin-orbit interaction, even in the topological phase, L z /N does not reach −1/2, which is the intrinsic value in chiral pwave superconductors. Here L z and N are the bulk orbital angular momentum and the total number of electrons at zero temperature, respectively. Finally, we discuss the effects of nonmagnetic impurities.

Ground-state angular momentum, spectral asymmetry, and topology in chiral superfluids and superconductors

“…The connection between angular momentum and spectral flow is, however, absent for example in the artificial p-wave model studied in Ref. [32] by Shitade and Nagai. They found that in the artificial p-wave model, achieved through the interplay of the s-wave proximity effect, the Rashba effect, and Zeeman field, angular momentum changes continuously even when the gap remains open and no states cross the zero energy.…”

Manifestation of chirality in the vortex lattice in a two-dimensional topological superconductor

“…Moreover, it is not immediately obvious how to map out chirality-based order parameters 15,52 from the sole order parameter in the model that is of s-wave pairing symmetry. The chiral nature of 2D s-wave TSC states and the role that the angular momentum carried by Cooper pairs plays in determining various properties of the system are to be explored in further detail in a future publication.…”

“…5 Although the Fermi surface has a certain chirality (spin winding), in principle the two intrinsic chiralities are always present in a 2D s-wave TSC state. 15 It is known that in a spin-triplet chiral p-wave superconductor, vortices in the p x + ip y and p x − ip y states, which are degenerate at zero field, are not equivalent.…”

“…Although orbital angular momentum is not a good quantum number in the presence of SO coupling, it has been found in Ref. 15 that when α is small enough, the average angular momentum carried by a Cooper pair can be close to − in non-Abelian states dominated by p x − ip y , as in chiral p-wave superconductors.…”

“…Moreover, we only have the superconducting order parameter stemming from spin-singlet s-wave pairing, and the enlargement of the vortex core for h = t and the enhancement around the vortex centre for h = −t are happening within the same s-wave order parameter. Both underlying chiralities ±1 are always present and mixed except for α ≪ t, 15 and it is not clear as to whether there is a way to define a unique order parameter for each of the two chi- ralities separately. It is apparent nonetheless that some extra order is induced in the h = −t system inside the vortex core, increasing the superconducting order somewhat.…”