Surface states, edge currents, and the angular momentum of chiralp-wave superfluids

The spectra of fermionic excitations, pairing correlations, and edge currents confined near the boundary of a chiral p-wave superfluid are calculated to leading order in /pfξ. Results for the energy- and momentum-resolved spectral functions, including the spectral current density, of a chiral p-wave superfluid near a confining boundary are reported. The spectral functions reveal the subtle role of the chiral edge states in relation to the edge current and the angular momentum of a chiral p-wave superfluid, including the rapid suppression of Lz(T) for 0TTc in the fully gapped two-dimensional chiral superfluid. The edge current and ground-state angular momentum are shown to be sensitive to boundary conditions, and as a consequence the topology and geometry of the confining boundaries. For perfect specular boundaries, the edge current accounts for the ground-state angular momentum, Lz=(N/2), of a cylindrical disk of a chiral superfluid with $N/2$ fermion pairs. Nonspecular scattering can dramatically suppress the edge current. In the limit of perfect retroreflection, the edge states form a flat band of zero modes that are nonchiral and generate no edge current. For a chiral superfluid film confined in a cylindrical toroidal geometry, the ground-state angular momentum is, in general, nonextensive, and can have a value ranging from Lz>(N/2) to Lz<-(N/2) depending on the ratio of the inner and outer radii and the degree of backscattering on the inner and outer surfaces. Nonextensive scaling of Lz, and the reversal of the ground-state angular momentum for a toroidal geometry, would provide a signature of broken time-reversal symmetry of the ground state of superfluid ³He-A, as well as direct observation of chiral edge currents.