CPM Seminar

Surface States, Edge Currents and the Chiral Ground State of Superfluid ³He

Jim Sauls

Department of Physics and Astronomy
Northwestern University

Broken symmetries in bulk condensed matter systems have implications for the spectrum of Fermionic excitations bound to surfaces and topological defects. Thin films of superfluid ³He are the realization of a two-dimensional broken time-reversal topological superfluid. The spectra of fermionic excitations, pairing correlations and edge currents of confined ³He-A is calculated to leading order in ℏ/p_fξ. Results for the energy- and momentum-resolved spectral functions, including the spectral current density are reported. The spectral functions reveal the subtle role of the chiral edge states (Weyl Fermion branch) in relation to the edge current and the angular momentum of a chiral p-wave superfluid, including the power law suppression of L_z(T)(N /2)ℏ[1-βT²] for 0≤T<<T_c in the fully gapped 2D chiral A-phase. The edge current and ground-state angular momentum are also 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(T)(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 unique signature of broken time-reversal symmetry of the ground state of superfluid ³He-A, as well as direct observation of chiral edge currents.