Surface States, Edge Currents and the Angular Momentum of Chiral p-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 h̄/p f ξ . Results for the energyand momentumresolved 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 0 . T ≪ Tc in the fully gapped 2D 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)h̄, of a cylindrical disk of chiral superfluid with N/2 fermion pairs. Non-specular scattering can dramatically suppress the edge current. In the limit of perfect retro-reflection the edge states form a flat band of zero modes that are non-chiral and generate no edge current. For a chiral superfluid film confined in a cylindrical toroidal geometry the ground-state angular momentum is, in general, non-extensive, and can have a value ranging from Lz > (N/2)h̄ to Lz <−(N/2)h̄ depending on the ratio of the inner and outer radii and the degree of back scattering on the inner and outer surfaces. Non-extensive 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.