Surface States, Edge Currents and the Angular Momentum of Chiral p-wave Superfluids

Abstract

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 $\hslash /p_f\xi$. 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 $L_z(T)$ for $0\lesssim T\ll T_c$ 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, $L_z=(N/2)\hslash$, 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 $L_z>(N/2)\hslash$ to $L_z<-(N/2)\hslash$ 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 $L_z$, 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 \Hea, as well as direct observation of chiral edge currents.

11 pages, 9 figures

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• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Edge modes, edge currents, and gauge invariance in $p_x+i{p}_y$ superfluids and superconductors
• The Nonlinear Meissner Effect in Unconventional Superconductors
• On edge states in superconductor with time inversion symmetry breaking

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