## CMT139

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

**Author(s):**
J. A. Sauls
- Address: Department of Physics & Astronomy, Northwestern University, Evanston, IL 60208
- Date: September 25, 2011
**Journal:**
Phys. Rev. B 84, 214509 (2011)
[DOI]
**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
ℏ/p_{f} ξ. 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 ≲ T ≪ 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) ℏ, 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) ℏ to L_{z} < -(N/2) ℏ
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
^{3}He-A, as well as direct observation of chiral edge currents.

- Comment: 11 pages, 9 figures, with a historical review of the angular momentum paradox in
^{3}He-A

**Eprint:**
[arXiv]
[PDF]