Session A45: Helium 3 and Electron Hydrodynamics

Pair breaking at the surface of the unconventional superfluid

In unconventional p-wave superfluid ³He, Cooper pairs are subject to anisotropic pair breaking in the vicinity of surfaces and interfaces. This effect dominates when the superfluid is confined in a cavity of height comparable to the coherence length. The surface pair-breaking depends on the boundary condition for surface scattering of quasiparticles. We study superfluid ³He confined in a single nanofabricated 200 nm high cavity, using SQUID-NMR as a probe of superfluid order parameter, and pressure as a tuning parameter. The surface scattering is also tuned in situ, by adjustment of the surface boundary layer. We make an accurate determination of the suppression of the superfluid transition temperature, T_c. We also measure the gap suppression for different boundary conditions. With a solid ⁴He surface layer we find close to diffuse scattering, while by coating the surface with a superfluid ⁴He film we find close to perfect specular scattering, with the almost complete elimination of T_c and gap suppression. With a solid ³He layer on the surface, the observed T_c suppression is significantly stronger than that predicted by quasiclassical theory with diffuse scattering boundary conditions.   

Magnetically-active Boundaries in Topological Superfluid 3He-B

We calculate properties of the BW phase of superfluid Helium-3 near magnetically-active boundaries using quasiclassical theory. The quasiparticles acquire spin-dependent phase shift when scattering off such surfaces. This local breaking of the time-reversal symmetry by the boundary is sufficient to remove the topological protection of the surface zero-energy Majorana modes. We investigate how magnetic scattering affects the order parameter structure, surface density of states and helical surface spin currents. In He-B the spin and orbital degrees of freedom are connected by the broken relative spin-orbit rotational symmetry, and magnetic boundaries can provide a more flexible control of the surface bound states. In particular, we show that such boundaries strongly affect superfluid phases in confined geometry, such as slabs with thickness of several coherence length.   

Thermal Conductivity of 3He confined in a 1.1 micron sized channel.

We describe the results of experiments on the thermal conductivity of 3He confined to a nanofabricated channel of ~1.1 um height, fabricated in silicon that is anodically bonded to glass. The channel separates a 3He filled chamber of small volume containing a fork thermometer/heater from a separate chamber with a silver heat exchanger filled with 3He, which contains an identical fork thermometer. In the normal state of 3He at low pressure, an anticipated crossover from Fermi-liquid (inelastic scattering length varying as T^-2) to mean free-path-limited behavior (scattering length dominated by boundary scattering) is observed. In the superfluid, the presence of two-fluid flow near T_c is investigated and the supercooling and nucleation of the B phase from the A phase in the viciniy of the polycritical point is explored.   

The Polar-phase of Superfluid 3He Stabilized in Anisotropic Silica Aerogel

Silica aerogel can be used to introduce disorder into superfluid ³He, stablizing new phases and order parameter textures that do not occur in the pure superfluid^1,2,3. In particular, aerogel can be processed to have anisotropic disorder by either stretching or compressing the samples. Using NMR spectroscopy, we observe evidence for a new superfluid phase in ~20% compressed aerogel at low pressure. The magnetic susceptibility is consistent with a state where the atoms forming the Cooper pairs have aligned spin, an equal-spin pairing state. In addition, the frequency shift of this new phase is greater than the A-phase frequency shift in isotropic aerogel. Finally, there is a second-order phase transition into the B-phase at low temperature. These three observations indicate that the polar phase of superfluid ³He has been stabilized at low pressure by the anisotropic disorder of the aerogel.

[1] J. Pollanen et al, Nature Physics 8, 317-320 (2012).
[2] J.I.A. Li et al, Phys. Rev. Lett. 114, 105302 (2015).
[3] V.V. Dmitriev et al, Phys. Rev. Lett. 115, 165304 (2015).
  

Liquid Helium-3 as a Quantum Acoustic Metamaterial

Acoustic metamaterials exhibit interesting properties through manipulation of the density and bulk modulus. We propose liquid Helium-3 as a candidate for an acoustic metamaterial. We show this by exploiting properties of the collective sound modes, which with a specified forcing function can allow us to control the density response function. Furthermore, we will utilize the viscoelastic nature of liquid Helium-3, which introduces an anisotropy that is unique in liquids(Bedell, K., Pethick, C.J. J. Low Temp. Phys. 49, 213 (1982).). This provides us with an additional way to explore enhanced absorption and negative-index regions in Helium-3. We will explore this behavior at various temperature and density ranges.   

Low-energy Effective Field Theory of Superfluid 3He-B

The low-energy physics of a superfluid ³He-B is governed by Nambu-Goldstone bosons resulting from its characteristic symmetry breaking pattern. Here we construct an effective field theory at zero temperature consistent with all available symmetries in curved space, which are the U(1)_phase×SU(2)_spin×SO(3)_orbital gauge invariance and the nonrelativistic general coordinate invariance, up to the next-to-leading order in a derivative expansion. The obtained low-energy effective field theory is capable of predicting gyromagnetic responses of the superfluid 3He-B, such as a magnetization generated by a rotation and an orbital angular momentum generated by a magnetic field, in a model-independent and nonperturbative way. We furthermore show that the stress tensor exhibits a dissipationless Hall viscosity with coefficients uniquely fixed by the orbital angular momentum density, which manifests itself as an elliptical polarization of sound wave with an induced transverse component.   

Strong-Coupling Corrections to Collective-Mode Frequencies in Superfluid 3He-B

The frequencies of collective modes in superfluid ³He in principle provide sensitive probes of the quasiparticle interactions (Landau parameters and pairing interactions), but the interpretaqtion of experiemntal results for these frequencies has always been uncertain due to unknown corrections from non-trivial strong-coupling effects (those not subsumed in the magnitude of the order parameter). We will report perturbative calculations of corrections to to the frequency of the J^C = 2⁺ mode of ³He-B using the weak-coupling-plus model of Rainer and Serene.[1]

References:
[1] J.W. Serene and D. Rainer, Phys. Rep. 101, 221 (1983)   

Probing the dynamics of 3He adsorbed on MCM-41 with NMR

A one dimensional quantum gas can be realized by confining ³He atoms in certain 1D nano-channels. Previously, researchers examined the dynamics of ³He atoms adsorbed on the surface of the pores of mesaporous materials such as MCM-41 and FSM due to their unique cylindrical pore shapes. Interesting 1D signatures were disclosed through nuclear susceptibility and nuclear relaxometry measurements. However to explore the behavior of a neutral Tomonaga-Luttinger liquid as predicted by theory, the sample has to be cooled down to much lower temperatures. In this preliminary experimental study, we measured the nuclear susceptibility, the spin-lattice relaxation times (T₁) and spin-spin relaxation times (T₂) of a single layer ³He adsorbed in MCM-41 over a broad temperature range of 0.03-2.5 K. Our results show both quantum solid and 1D Fermi gas behavior of the ³He.
  

Bounds on hydrodynamic data from many-body quantum chaos

Is the hydrodynamics of an interacting many-body system fundamentally limited by basic principles of quantum mechanics? Starting with the conjecture that viscosity is at least as large as entropy density (as measured in fundamental units), there has been a long search for a precise answer to this question. I point out a simple relationship between hydrodynamics and many-body quantum chaos in a broad class of experimentally realizable systems. Consistency with the quantum butterfly effect leads to upper bounds on the speed of sound and diffusion constants of hydrodynamics. These bounds link two very different theories of quantum many-body dynamics, clarify the relationship between classical hydrodynamics and quantum information loss, and provide a simple way to constrain theories of thermalization and quantum chaos in experiments.   

Many-body chaos in a conformal gauge theory

The onset of many-body quantum chaos in fermionic systems can be diagnosed from the growth of initally anticommuting fermion field operators. We compute such anti-commutators of fermion field operators in (2 + 1)d U (1) gauge theory with N_f flavors of fermions to leading order in 1/N_f . For large enough N_f , this is an interacting conformal field theory and describes the low energy properties of the Dirac spin liquid. The anticommutator grows exponentially in time with a rate defined by the Lyapunov exponent λ_L and grows ballistically in space at a speed identified as the “butterfly velocity” v_B. The scaling with temperature is fixed by conformal invariance. We briefly comment on the growth of local current operators and the breakdown of the large N_f expansion.   

Many-Body Chaos in the Quantum Lifshitz Model

We compute the parameters characterizing many-body quantum chaos in the 2+1D Quantum Lifshitz model with N flavors, specifically the Lyapunov exponent and butterfly velocity as a function of temperature, diffusion constant, and interaction strength. The quartic term added to break integrability gives logarithmic (in temperature) corrections to the naive expression for the Lyapunov exponent. Despite z=2 scaling, an effective temperature-dependent velocity is generated and chaos spreads ballistically.   

Microscopic Models for Electron Hydrodynamics

A novel regime of transport whereby electrons behave like a viscous fluid has been the subject of intense study over the past few years. By using various kinetic and hydrodynamic models, we will study the conditions under which such a regime can be obtained and the experimental signatures one should look for. We will show in particular that the viscous Hall effect is a very useful probe of hydrodynamic effects and that the interplay of restricted geometries and applied magnetic fields leads to extremely rich physics.   

title{Hydrodynamic behavior driven by surface boundary state in Weyl semimetals} \author{D. Schmeltzer} \affiliation{Physics Department, City College of the City University of New York, New York, New York 10031, USA} % \begin{abstract We derive a theory for the Weyl semimetal with a boundary

Hydrodynamic behavior driven by surface boundary state in Weyl semimetals   

Screening properties of quasielectrons in Laughlin states

I review recent work on how to construct a matrix product state representation of quasielectron excitations of Laughlin QH wave functions. These, which are obtained, either by using composite fermions, or conformal field theory, have a known defect - the the positions of the quasielectrons depend on the presence of other quasiparticles even when these are far removed. This poses a serious problem since the braiding phases of the quasiparticles are not correct which signifies that the states do not have correct topological properties. This failure is analyzed in detail and is shown to arise because of an incomplete screening which causes the plasma analogy. We discuss various ways to overcome the problems by adding screening operators.   

Superballistic flow of viscous electron fluid through graphene constrictions

Electron–electron (e–e) collisions can impact transport in a variety of surprising and sometimes counterintuitive ways. Despite strong interest, experiments on the subject proved challenging because of the simultaneous presence of different scattering mechanisms that suppress or obscure consequences of e–e scattering. Only recently, sufficiently clean electron systems with transport dominated by e–e collisions have become available [1]. In this talk, we will discuss electron transport through graphene constrictions and show that their conductance below 150 K increases with increasing temperature [2], in contrast to the metallic character of graphene. Notably, the measured conductance exceeds the maximum conductance possible for free electrons. This anomalous behavior is attributed to collective movement of interacting electrons, which ‘shields’ individual carriers from momentum loss at sample boundaries. The measurements allow us to identify the conductance contribution arising due to electron viscosity and determine its temperature dependence.

[1] D. A. Bandurin, et. al., Science 351, 1055 (2016).
[2] R. Krishna Kumar, et. al., Nature Physics in press, (2017).