Topological Edge and Surface States of Superfluid 3He and Chiral Superconductors

KITP Conference on Strong Correlations and Unconventional Superconductors

Speaker: J. A. Sauls
Department of Physics & Astronomy, Northwestern University, Evanston, IL 60208
September 24, 2014

Abstract: Broken symmetries in bulk condensed matter systems have implications for the spectrum of Fermionic excitations bound to surfaces and topological defects. The A-phase of superfluid 3He, described by the Anderson-Morel (AM) state, is the realization of a two-dimensional broken time-reversal topological superfluid. This state is also representative of spin-triplet, chiral superconductors discussed as possible ground states for the superconductors Sr2RuO4 and UPt3. I discuss the relationship between broken symmetries of the ground state and the topological nature of the Fermionic states confined near surfaces, domain walls and topological defects for the superfluid phases of 3He. The Fermionic spectrum of confined (2D) 3He-A are chiral edge states (Weyl Fermions). The negative energy states are related to the ground-state angular momentum, Lz = (N/2) ℏ, of superfluid 3He-A for N/2 Cooper pairs. The power law suppression of the angular momentum, Lz(T) ≃ (N /2) ℏ [1 - β T2] for 0 ≤ T ≪ Tc, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the Weyl branch of Fermions. I discuss the sensitivity of the edge current and ground-state angular momentum to topology, geometry and symmetry of the confining boundaries, and show that the edge current is protected by symmetry, not by topology of the bulk Hamiltonian. For local translationally invariant boundaries and axially symmetry the edge current accounts for the ground-state angular momentum, Lz = (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 can have a value ranging from Lz > (N/2) ℏ to Lz < -(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. The scaling of Lz, with (R2/R1)2 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.

This research was supported by NSF Grant: DMR-1106315.

Slides: [PDF] Video: [mov]

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