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 with ψ∼ (x + i y), is predicted to be the ground state at all pressures in dimensionally confined superfluid 3He [1]. In the limit D 10≪ ξ0 the AM state is the realization of a two-dimensional (2D) broken time-reversal topological superfluid.

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 with ψ∼ (x + i y), is predicted to be the ground state at all pressures in dimensionally confined superfluid 3He [1]. In the limit D 10≪ ξ0 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 1106315

occupied

occupied

unoccupiedunoccupied

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 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 3He for specular boundary conditions. For film thicknesses with 9 << D/ξ0 << 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 10≪ ξ0.

Figure 1: Phase diagram for confined superfluid 3He for specular boundary conditions. For film thicknesses with 9 << D/ξ0 << 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 10≪ ξ0.

Figure 3. The signature temperature dependence of the angular momentum of dimensionally confined 3He (both 2D and 3D) is the power law suppression of Lz(T) ≈ (N/2) ħ [1 - cT2] for 0 T Tc. The T≲ ≪ 2 suppression of Lz(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.

Figure 3. The signature temperature dependence of the angular momentum of dimensionally confined 3He (both 2D and 3D) is the power law suppression of Lz(T) ≈ (N/2) ħ [1 - cT2] for 0 T Tc. The T≲ ≪ 2 suppression of Lz(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 3He Films, Physical. Review Letters 98, 045301 (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, 214509 (2011)1. Crystalline Order in Superfluid 3He Films, Physical. Review Letters 98, 045301 (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, 214509 (2011)

Weyl Fermion Dispersion RelationWeyl Fermion Dispersion Relation

LLzz(T) is ``soft’’ (2D (T) is ``soft’’ (2D or 3D) due to or 3D) due to thermally Excited thermally Excited Weyl FermionsWeyl Fermions

LLzz(T) is ``soft’’ (2D (T) is ``soft’’ (2D or 3D) due to or 3D) due to thermally Excited thermally Excited Weyl FermionsWeyl Fermions

2D2Dρρss(T)(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 3He infused into homogeneous anisotropic aerogels

[Ref. 1]. The theory is based on the limit of homogeneous anisotropy (Cooper

pair size ξ0 >> ξa 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⊥ (ℓ|| > ℓ⊥). Anisotropic

scattering leads to a splitting of the zero-field transition

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 3He infused into homogeneous anisotropic aerogels

[Ref. 1]. The theory is based on the limit of homogeneous anisotropy (Cooper

pair size ξ0 >> ξa 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⊥ (ℓ|| > ℓ⊥). Anisotropic

scattering leads to a splitting of the zero-field transition

Identification of the Chiral Phases of Superfluid 3He Uniaxial Anisotropic Silica Aerogels

James A. Sauls, Northwestern University, DMR 1106315

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).2. Equal Spin Pairing Phases of Superfluid 3He 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).2. Equal Spin Pairing Phases of Superfluid 3He in Uniaxially Strained Aerogel, J. A. Sauls, Phys. Rev. B, submitted (2012).

Tc2

Tc2 T

c1T

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 < Tc2 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 < Tc2 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, 2009 - Northwestern University, Evanston, Illinois

QFS2009: International Symposium on Quantum Fluids and Solids. August 5-11, 2009 - 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.

✓ 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 3He in Confined Geometries

James A. Sauls, Northwestern University, DMR 1106315

Multi-component superconducting phases of UPt3 [PRB 62, 14393 (2000)]

Multi-component superconducting phases of UPt3 [PRB 62, 14393 (2000)]

Aspen Center for Physics Summer Program, August - September 2013

Aspen Center for Physics Summer Program, August - September 2013

ACP summer lecturerACP summer lecturer