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 3 He, described by the Anderson-Morel (AM) state with ψ ∼ (x + i y), is predicted to be the ground state at all pressures in dimensionally confined superfluid 3 He [1]. In the limit D ≪ 10ξ 0 the AM state is the realization of a two-dimensional (2D) broken time-reversal topological superfluid. Edge States and the Ground State of a Topological Superfluid with Broken Time-Reversal Symmetry James A. Sauls, Northwestern University, DMR occupied unoccupie d Stripe Phase Figure 2. Fermionic excitations, pairing correlations and edge currents confined near the boundary of a chiral p-wave superfluid are reported in [2]. The spectral functions reveal the subtle role of the chiral edge states (Weyl Fermion branch) in relation to the edge current. Occupation of the negative energy states shown in Fig. 2 implies an edge current and ground state angular momentum of (N/2) ħ [2]. Figure 1: Phase diagram for confined superfluid 3 He for specular boundary conditions. For film thicknesses with 9 << D/ξ 0 << 13 a one- dimensional stripe phase with crystalline order in the plane of the film was predicted. Ref. [1]. The A- phase (AM state) is stable for dimensions D ≪ 10ξ 0. Figure 3. The signature temperature dependence of the angular momentum of dimensionally confined 3 He (both 2D and 3D) is the power law suppression of L z (T) ≈ (N/2) ħ [1 - cT 2 ] for 0 ≲ T ≪ Tc. The T 2 suppression of L z (T) reflects the reduction in the edge current resulting from thermal excitations of the Weyl Fermion branch with a linear dispersion in edge momentum near the Fermi energy. By contrast the superfluid density decreases exponentially at low temperature due to the gap in the bulk quasiparticle spectrum. 1. Crystalline Order in Superfluid 3 He Films, Physical. Review Letters 98, (2007), A. Vorontsov & J. A. Sauls. 2. Surface states, edge currents, and the angular momentum of chiral p-wave superfluids, J. A. Sauls, Phys. Rev. B 84, (2011) 1. Crystalline Order in Superfluid 3 He Films, Physical. Review Letters 98, (2007), A. Vorontsov & J. A. Sauls. 2. Surface states, edge currents, and the angular momentum of chiral p-wave superfluids, J. A. Sauls, Phys. Rev. B 84, (2011) Weyl Fermion Dispersion Relation L z (T) is ``soft’’ (2D or 3D) due to thermally Excited Weyl Fermions 2D ρ s (T)

In collaboration with the Ultra-Low Temperature group at Northwestern headed by Prof. Bill Halperin, the PI developed a theory for the ESP phases observed in superfluid 3 He infused into homogeneous anisotropic aerogels [Ref. 1]. The theory is based on the limit of homogeneous anisotropy (Cooper pair size ξ 0 >> ξ a aerogel correlation length) in which the medium scatters quasiparticles preferentially parallel (or perpendicular) to the uniaxial symmetry axis of the anisotropic aerogel, i.e. ℓ|| ℓ ⊥ ). Anisotropic scattering leads to a splitting of the zero-field transition Identification of the Chiral Phases of Superfluid 3 He Uniaxial Anisotropic Silica Aerogels James A. Sauls, Northwestern University, DMR Phase ESP-1 is identified as the Chiral ABM phase with the axis of chirality along the strain axis, i.e. ℓ|| z, This phase spontaneously breaks time-reversal symmetry as well as 2D parity. For the field aligned to the strain axis (z) the nuclear dipole energy and Zeeman energies are minimized and lead to a maximally positive NMR frequency shift. The NMR line is sharp and the Larkin-Imry-Ma (LIM) effect is suppressed by the anisotropy energy. The test of this theory would be the observation of a negative NMR frequency shift for the static field aligned along the strain axis. Phase ESP-1 is identified as the Chiral ABM phase with the axis of chirality along the strain axis, i.e. ℓ|| z, This phase spontaneously breaks time-reversal symmetry as well as 2D parity. For the field aligned to the strain axis (z) the nuclear dipole energy and Zeeman energies are minimized and lead to a maximally positive NMR frequency shift. The NMR line is sharp and the Larkin-Imry-Ma (LIM) effect is suppressed by the anisotropy energy. The test of this theory would be the observation of a negative NMR frequency shift for the static field aligned along the strain axis. 1. New Chiral Phases of Superfluid 3 He Stabilized by Anisotropic Silica Aerogel, J. Pollanen et al., Nature Phys. 8, 317 (2012).New Chiral Phases of Superfluid 3 He Stabilized by Anisotropic Silica Aerogel, J. Pollanen et al., Nature Phys. 8, 317 (2012) 2. Equal Spin Pairing Phases of Superfluid 3 He in Uniaxially Strained Aerogel, J. A. Sauls, Phys. Rev. B, submitted (2012). 1. New Chiral Phases of Superfluid 3 He Stabilized by Anisotropic Silica Aerogel, J. Pollanen et al., Nature Phys. 8, 317 (2012).New Chiral Phases of Superfluid 3 He Stabilized by Anisotropic Silica Aerogel, J. Pollanen et al., Nature Phys. 8, 317 (2012) 2. Equal Spin Pairing Phases of Superfluid 3 He in Uniaxially Strained Aerogel, J. A. Sauls, Phys. Rev. B, submitted (2012). T c2 T c1 Phase ESP-2 is tentatively identified as an ESP phase with a complex order parameter characterized as an axi-polar phase in which the polar order parameter develops in the presence of a pre-established ABM phase and evolves for T < T c2 to with α+2β=π. This phase exhibits a complex NMR spectrum since there are multiple local minima of the dipole energy as shown below. Phase ESP-2 is tentatively identified as an ESP phase with a complex order parameter characterized as an axi-polar phase in which the polar order parameter develops in the presence of a pre-established ABM phase and evolves for T < T c2 to with α+2β=π. This phase exhibits a complex NMR spectrum since there are multiple local minima of the dipole energy as shown below.

✓ The PI is on the Executive Committee of the Divsion of Condensed Matter Physics (DCMP) of the American Physical Society. DCMP represents the broad range of sub-fields of condensed matter physics. The executive committee has responsibility for organizing the March meeting of the APS and to help increase broader public awareness of significant developments in physics, publicize exciting new discoveries, and to help to educate the public on the importance of basic research for our society. QFS2009: International Symposium on Quantum Fluids and Solids. August 5-11, Northwestern University, Evanston, Illinois ✓ Northwestern University was host to the International Symposium on Quantum Fluids and Solids, QFS2009 [website]. The PI chaired the program committee for 50 invited speakers, 200 poster presentations and 245 participants. The conference brought together distinguished scientists and young researchers from Brazil, Canada, Europe, Israel, Japan, Korea, Russia, Ukraine and the USA.website ✓ The PI has been a member of the Aspen Center for Physics (ACP) for over 20 years. The ACP sponsors workshops in all areas of theoretical physics and is devoted to support of research and the dissemination of physics and related science. The PI is co-organizer of the summer 2013 program on ``Multi-component Many-Body Systems’’ with Egor Babaev (U.Mass), Leo Radzihovsky (U. Colorado) and Asle Sudbø (Trondheim). The PI served as chair of the Heinz Pagels Memorial Public Lecture Series that brings distinguished scientists to engage the broader public on ideas and discoveries in physics. Excitations, Topological Defects and Quantum Transport in Superconductors and Superfluid 3 He in Confined Geometries James A. Sauls, Northwestern University, DMR Multi-component superconducting phases of UPt 3 [PRB 62, (2000)] Multi-component superconducting phases of UPt 3 [PRB 62, (2000)] Aspen Center for Physics Summer Program, August - September 2013 ACP summer lecturer