Hall Viscosity Research Articles

Odd Viscosity Suppresses Intermittency in Direct Turbulent Cascades.

Intermittency refers to the broken self-similarity of turbulent flows caused by anomalous spatiotemporal fluctuations. In this Letter, we ask how intermittency is affected by a nondissipative viscosity, known as odd viscosity (also Hall viscosity or gyroviscosity), which appears in parity-breaking fluids such as magnetized polyatomic gases, electron fluids under magnetic field, and spinning colloids or grains. Using a combination of Navier-Stokes simulations and theory, we show that intermittency is suppressed by odd viscosity at small scales. This effect is caused by parity-breaking waves, induced by odd viscosity, that break the multiple scale invariances of the Navier-Stokes equations. Building on this insight, we construct a two-channel helical shell model that reproduces the basic phenomenology of turbulent odd-viscous fluids including the suppression of anomalous scaling. Our findings illustrate how a fully developed direct cascade that is entirely self-similar can emerge below a tunable length scale, paving the way for designing turbulent flows with adjustable levels of intermittency.

Microscopic Model for Fractional Quantum Hall Nematics.

Geometric fluctuations of the density mode in a fractional quantum Hall (FQH) state can give rise to a nematic FQH phase, a topological state with a spontaneously broken rotational symmetry. While experiments on FQH states in the second Landau level have reported signatures of putative FQH nematics in anisotropic transport, a realistic model for this state has been lacking. We show that the standard model of particles in the lowest Landau level interacting via the Coulomb potential realizes the FQH nematic transition, which is reached by a progressive reduction of the strength of the shortest-range Haldane pseudopotential. Using exact diagonalization and variational wave functions, we demonstrate that the FQH nematic transition occurs when the system's neutral gap closes in the long-wavelength limit while the charge gap remains open. We confirm the symmetry-breaking nature of the transition by demonstrating the existence of a "circular moat" potential in the manifold of states with broken rotational symmetry, while its geometric character is revealed through the strong fluctuations of the nematic susceptibility and Hall viscosity.

Analysis of hyperbolic magneto-hydrodynamic [HMHD] wave propagation through neutrino-coupled plasma

By using the Hyperbolic Magneto Hydrodynamic model, we investigated the propagation dynamics of a neutrino-coupled plasma system, with the influence of Hall current, rotation, viscosity and finite electrical resistivity. The general dispersion relation is obtained from the perturbed equations for both the Jean’s and neutrino beam instability. The effect of different parameters has been discussed in both parallel and perpendicular modes of wave propagation. The Jean’s instability condition is modified due to the presence of Hall current, Magnetic field and neutrino in both modes of propagation. The growth rate of the neutrino beam is affected by Hall current, viscosity magnetic field and rotation in both propagating modes. We also show the effect of different parameters on the growth rate of a neutrino-coupled plasma system through a graphical presentation.

Phonon Hall Viscosity of Ionic Crystals.

When time-reversal symmetry is broken, the low-energy description of acoustic lattice dynamics allows for a dissipationless component of the viscosity tensor, the phonon Hall viscosity, which captures how phonon chirality grows with the wave vector. In this work, we show that, in ionic crystals, a phonon Hall viscosity contribution is produced by the Lorentz forces on moving ions. We calculate typical values of the Lorentz force contribution to the Hall viscosity using a simple square lattice toy model, and we compare it with literature estimates of the strengths of other Hall-viscosity mechanisms.

Optical N-plasmon: topological hydrodynamic excitations in graphene from repulsive Hall viscosity

Edge states occurring in Chern and quantum spin-Hall phases are signatures of the topological electronic band structure in two-dimensional (2D) materials. Recently, a new topological electromagnetic phase of graphene characterized by the optical N-invariant was proposed. Optical N-invariant arises from repulsive Hall viscosity in hydrodynamic many-body electron systems, distinct from the Chern and Z 2 invariants. In this paper, we introduce the topologically protected edge excitation—optical N-plasmon of interacting many-body electron systems in the topological optical N-phase. These optical N-plasmons are signatures of the topological plasmonic band structure in 2D materials. We demonstrate that optical N-plasmons exhibit unique dispersion relations, stability against various boundary conditions, and edge profiles when compared with the topologically trivial edge magneto plasmons. Based on the optical N-plasmon, we design an ultra sub-wavelength broadband topological hydrodynamic circulator, which is a chiral quantum radio-frequency circuit component crucial for information routing and interfacing quantum–classical computing systems. Furthermore, we reveal that optical N-plasmons can be effectively tuned by the neighboring dielectric environment without breaking the topological properties. Our work provides a smoking gun signature of topological electromagnetic phases occurring in 2D materials arising from repulsive Hall viscosity.

Two-dimensional electron hydrodynamics in a random array of impenetrable obstacles: Magnetoresistivity, Hall viscosity, and the Landauer dipole

Two-dimensional electron hydrodynamics in a random array of impenetrable obstacles: Magnetoresistivity, Hall viscosity, and the Landauer dipole

Adiabatic deformations of quantum Hall droplets

We consider area-preserving deformations of the plane, acting on electronic wave functions through “quantomorphisms” that change both the underlying metric and the confining potential. We show that adiabatic sequences of such transformations produce Berry phases that can be written in closed form in terms of the many-body current and density, even in the presence of interactions. For a large class of deformations that generalize squeezing and shearing, the leading piece of the phase is a super-extensive Aharonov-Bohm term (\propto N^2∝N2 for NN electrons) in the thermodynamic limit. Its gauge-invariant subleading partner only measures the current, whose dominant contribution to the phase stems from a jump at the edge in the limit of strong magnetic fields. This results in a finite Berry curvature per unit area, reminiscent of the Hall viscosity. We show that the latter is in fact included in our formalism, bypassing its standard derivation on a torus and suggesting realistic experimental setups for its observation in quantum simulators.

Hall viscosity and hydrodynamic inverse Nernst effect in graphene

Motivated by Hall viscosity measurements in graphene sheets, we study hydrodynamic transport of electrons in a channel of finite width in external electric and magnetic fields. We consider electric charge densities varying from close to the Dirac point up to the Fermi-liquid regime. We find two competing contributions to the hydrodynamic Hall and inverse Nernst signals that originate from the Hall viscous and Lorentz forces. This competition leads to a nonlinear dependence of the full signals on the magnetic field and even a cancellation at different critical field values for both signals. In particular, the hydrodynamic inverse Nernst signal in the Fermi-liquid regime is dominated by the Hall viscous contribution. We further show that a finite channel width leads to a suppression of the Lorenz ratio, while the magnetic field enhances this ratio. All of these effects are predicted in parameter regimes accessible in experiments.

Coulomb drag of viscous electron fluids: Drag viscosity and negative drag conductivity

We show that Coulomb drag in bilayer systems in the regime of electron hydrodynamics leads to additional viscosity terms in the hydrodynamic equations, the drag, and drag-Hall viscosities, besides the well-known kinematic and Hall viscosities. These additional viscosity terms arise from a change of the stress tensor due to the interlayer Coulomb interactions. All four viscosity terms are tunable by varying the applied magnetic field and the electron densities in the two layers. At certain ratios between the electron densities in the two layers, the drag viscosity dramatically changes the longitudinal transport resulting in a negative drag conductivity.

Resolving Hall and dissipative viscosity ambiguities via boundary effects

We examine the physical implications of the viscous redundancy of two-dimensional anisotropic fluids, where different components of the viscosity tensor lead to identical effects in the bulk of a system [Rao and Bradlyn, Phys. Rev. X $\textbf{10}$, 021005 (2020)]. We first re-introduce the redundancy, show how it reflects a lack of knowledge of microscopic information of a system, and give microscopic examples. Next, we show that fluid flow in systems with a boundary can distinguish between otherwise redundant viscosity coefficients. In particular, we show how the dispersion and damping of gravity-dominated surface waves can be used to resolve the redundancies between both dissipative and Hall viscosities, and discuss how these results apply to recent experiments in chiral active fluids with nonvanishing Hall viscosity. Our results highlight the importance of divergenceless, magnetization-like contributions to the stress (which we dub ``contact terms''). Finally, we apply our results to the hydrodynamics of quantum Hall fluids, and show that the extra contribution to the action that renders the bulk Wen-Zee action gauge invariant in systems with a boundary can be reinterpreted in terms of the bulk viscous redundancy.

Generalized topological bulk-edge correspondence in bulk-Hermitian continuous systems with non-Hermitian boundary conditions

The bulk-edge correspondence (BEC) is the hallmark of topological systems. In continuous (nonlattice) Hermitian systems with an unbounded wave vector, it was recently shown that the BEC of Chern insulators is modified. How would it be further affected in non-Hermitian systems, experiencing loss and/or gain? In this work, we take the first step in this direction, by studying a bulk-Hermitian continuous system with non-Hermitian boundary conditions. We find in this case that edge modes emerge at the roots of the scattering matrix, as opposed to the Hermitian case, where they emerge at its poles (or, more accurately, coalescence of roots and poles). This entails a nontrivial modification to the relative Levinson's theorem. We then show that the topological structure remains the same as in the Hermitian case, and the generalized BEC holds, provided one employs appropriately modified contours in the wave-vector plane so that the scattering matrix phase winding counts the edge modes correctly. We exemplify all this using a paradigmatic model of waves in a shallow ocean or active systems in the presence of odd viscosity, as well as 2D electron gas with Hall viscosity. We use this opportunity to examine the case of large odd viscosity, where the scattering matrix becomes $2\ifmmode\times\else\texttimes\fi{}2$, which has not been discussed in previous works on the Hermitian generalized BEC.

Phase transitions and topological properties of the 52 quantum Hall states with strong Landau-level mixing

We numerically study a $\frac{5}{2}$ fractional quantum Hall system with even number of electrons using the exact diagonalization where both the strong Landau-level (LL) mixing and a finite width of the quantum well have been considered and adapted into a screened Coulomb interaction. With the principal component analysis, we are able to recognize a compressible-incompressible phase transition in the parameter space made of the magnetic field and the quantum well width by the competition between the first two leading components of the ground-state wave functions, which is consistent with the low-lying spectral feature and previous works in the odd-electron system. In addition, the presence of the subdominant third component suggests an incompressible transition occurring as the LL mixing strength grows into a certain parameter region associated with the ZnO experiments. We further investigate the strongly LL-mixed phase in this emerging region with the Hall viscosity, wave function overlaps, and the entanglement spectra. Results show it can be well described as a particle-hole symmetrized Pfaffian state with the dual topological properties of the Pfaffian and the anti-Pfaffian states.

Hall effect in Poiseuille flow of two-dimensional electron fluid

The hydrodynamic regime of charge transport has been recently realized in high-quality conductors. In the hydrodynamic as well as in the Ohmic regimes the main part of the Hall resistance of a long sample is determined by the balance between the Lorentz force and the electric force, acting on conduction electrons. Experimentally observed deviations of the Hall resistance in hydrodynamic samples from such ``standard'' value are usually associated with the Hall viscosity term in the Navier-Stokes equation. In this work we theoretically study the Hall effect in a Poiseuille flow of a two-dimensional electron fluid. We show that the near-edge semiballistic layers with the width of the order of the interparticle mean-free path, which inevitably appear near sample edges, give the contribution to the Hall resistance which is comparable with the bulk contribution from the Hall viscosity. In this way, the measured deviations of the Hall resistance from the ``standard'' one in hydrodynamic samples by the usual contact techniques should be associated with both the Hall viscosity in the bulk and the semiballistic effects in the near-edge layers.

Incompressible active phases at an interface. Part 1. Formulation and axisymmetric odd flows

Inspired by the recent realization of a two-dimensional (2-D) chiral fluid as an active monolayer droplet moving atop a 3-D Stokesian fluid, we formulate mathematically its free-boundary dynamics. The surface droplet is described as a general 2-D linear, incompressible and isotropic fluid, having a viscous shear stress, an active chiral driving stress and a Hall stress allowed by the lack of time-reversal symmetry. The droplet interacts with itself through its driven internal mechanics and by driving flows in the underlying 3-D Stokes phase. We pose the dynamics as the solution to a singular integral–differential equation, over the droplet surface, using the mapping from surface stress to surface velocity for the 3-D Stokes equations. Specializing to the case of axisymmetric droplets, exact representations for the chiral surface flow are given in terms of solutions to a singular integral equation, solved using both analytical and numerical techniques. For a disc-shaped monolayer, we additionally employ a semi-analytical solution that hinges on an orthogonal basis of Bessel functions and allows for efficient computation of the monolayer velocity field, which ranges from a nearly solid-body rotation to a unidirectional edge current, depending on the subphase depth and the Saffman–Delbrück length. Except in the near-wall limit, these solutions have divergent surface shear stresses at droplet boundaries, a signature of systems with codimension-one domains embedded in a 3-D medium. We further investigate the effect of a Hall viscosity, which couples radial and transverse surface velocity components, on the dynamics of a closing cavity. Hall stresses are seen to drive inward radial motion, even in the absence of edge tension.

TETHYS: A simulation tool for graphene hydrodynamic models

We present a simulation tool, TETHYS (i.e., Two-dimensional Emitter of THz, Hydrodynamic Simulation), developed with the aim of studying hydrodynamic models for electronic transport in graphene, being particularly tailored for the simulation of the configuration of top-gated graphene field-effect transistors (GFET) near room temperature. We present the model governing the system and briefly discuss its validity and physical parameters; then we proceed to discuss the algorithms and numerical methods used in its implementation, namely, two-step Richtmyer and weighted forward-time centred-space schemes, which address the hyperbolic and parabolic parts of the model, respectively. An abridged usage guide and description of the output are also provided, as well as two illustrative simulation cases: the Dyakonov–Shur instability and the boundary layer of pulsatile electric flow. The simulation program here brought forward is uncomplicated and lightweight, yet robust and accurate, having a wide variety of applicable scenarios and configurations to explore. Program summaryProgram Title: TETHYSCPC Library link to program files:https://doi.org/10.17632/s28zwgpnpw.1Developer's repository link:github.com/pcosme/TETHYS-Graphene-Hydrodynamic-SimulationLicensing provisions: MITProgramming language: C++Nature of problem: The main objective of this code is to simulate and analyse the electronic conduction on gated (mono-layer) graphene resorting to a hydrodynamic model [1]. Note that, given the Dirac-like dispersion relation of such material, the mass of the carriers is ill-defined; and, in fact, the mass of the fluid element varies with the number density, which sets this system apart from other 2D electron fluids [2]. The model assumes enough doping, so that only one kind of carriers, electrons or holes, participates in the dynamics of the system. Moreover, the simulation is limited to the fully degenerate limit.Thus, these assumptions correspond to the situation of a regular GFET and this application can be used to explore atypical phenomena arising from the effects of uniform and static magnetic field and Hall viscosity, and even spatially non-uniform gate capacitance.Furthermore, this software was designed with the intent of examining unstable nonlinear modes that may lead to the emission of radiation in the THz range [3].Solution method: The fluid equations (continuity, momentum and energy transport) are solved with a split-operator technique, with a second-order finite-volume Lax–Wendroff method [4] for the hyperbolic part and a forward-time centred-space of second-order stencil to tackle the dissipation and heat diffusion. That is, the fields of number density, velocity/momentum density and temperature are calculated over a rectangular grid and stored at a HDF5 file for further processing.Then, the obtained field profiles are used to compute the relevant macroscopic electronic quantities, such as drain-to-source current or dissipated power, and, particularly, the electric dipole moment of the charge distribution, which can subsequently be used to characterize the emitted far-field radiation. This is mostly done by numerically integrating the data in space, with the necessary time derivatives obtained by Gaussian convolution.

Nonrelativistic supergeometry in the Moore-Read fractional quantum Hall state

The Moore-Read state is one the most well known non-Abelian fractional quantum Hall states. It supports non-Abelian Ising anyons in the bulk and a chiral bosonic and chiral Majorana modes on the boundary. It has been recently conjectured that these modes are superpartners of each other and described by a supersymmetric conformal field theory [1]. We propose a non-relativistic supergeometric theory that is compatible with this picture and gives rise to an effective spin-3/2 field in the bulk. After breaking supersymmetry through a Goldstino, the spin-3/2 field becomes massive and can be seen as the neutral collective mode that characterizes the Moore-Read state. By integrating out this fermion field, we obtain a purely bosonic topological action that properly encodes the Hall conductivity, Hall viscosity and gravitational anomaly. Our work paves the way to the exploration of the fractional quantum Hall effect through non-relativistic supergeometry.

Viscosity of disordered Dirac electrons

Rejuvenation of hydrodynamic transport in solids provides a new window to study collective motion of electrons, where electrons behave like a viscous fluid akin to classical liquids. Experimental observations of such exotic states have not been realized until recent years, and an on-going quest is to amplify the hydrodynamic effect in electron fluids. Here we investigate the hydrodynamic properties of Dirac electron fluid in graphene from a microscopic viewpoint, and elucidate a novel way to enhance electron hydrodynamics. In particular, we present strong evidence that the shear viscosity of Dirac electrons can be enhanced by frequent electron-hole collisions, through three distinct aspects: promoting electrons and holes around the Dirac point by disorder, creating electron-hole shared zeroth Landau level by external magnetic field, and inducing electron-hole excitations by dynamic deformation. We also study Hall viscosity, which is closely related to the geometric topology and exhibits quantum behavior analogous to Hall conductivity. Therefore, our work demonstrates the exotic landscape of hydrodynamic electronics in graphene, and presents experimentally relevant responses to quantify the effects of electronic viscosity.

Surface wave and thermocapillary instabilities on flowing film under the sway of Hall viscosity

The present study investigates the influence of Hall/odd-viscosity on the surface wave and thermocapillary instabilities in a thin viscous film flowing down an inclined plane. A detailed analysis considering a generalized scaling for the velocity field to understand the effect of odd-viscosity in the hydrodynamic and thermocapillary modes of instabilities has been performed, and later the results are presented for a specific velocity scale. Starting with Orr–Sommerfeld (OS) linear stability analysis for all ranges of wavenumber and then constructing two low-dimensional models; namely, the Long wave expansion model (LWE) and the Weighted residual integral boundary layer model (WRIBL) under the assumption of small wavenumber are analysed for linear and nonlinear behaviour of the instabilities analytically and numerically. Two energy transferring mechanisms reinforce each other to the disturbance: hydrodynamic H-mode and thermocapillary S-mode are focused and found that the odd viscosity plays a stabilizing role for both the modes of instabilities. For small Reynolds number (Re) values, both LWE and WRIBL models give consistent results as that of the OS. However, for a large value of Re, WRIBL gives way better match with OS than LWE. Increasing odd viscosity flattens the streamlines in a moving frame of reference, confirming the odd viscosity’s stabilizing effect. However, being non-dissipative, odd viscosity has no significant influence on the temperature field. In a static frame, the intensity of capillary separation and flow reversal phenomena decreases with the increase of odd viscosity, confirming its stabilizing effect on the flow.

Hydrodynamic correlation functions of chiral active fluids

The success of spectroscopy to characterise equilibrium fluids, for example the heat capacity ratio, suggests a parallel approach for active fluids. Here, we start from a hydrodynamic description of chiral active fluids composed of spinning constituents and derive their low-frequency, long-wavelength response functions using the Kadanoff-Martin formalism. We find that the presence of odd (equivalently, Hall) viscosity leads to mixed density-vorticity response even at linear order. Such response, prohibited in time-reversal-invariant fluids, is a large-scale manifestation of the microscopic breaking of time-reversal symmetry. Our work suggests possible experimental probes that can measure anomalous transport coefficients in active fluids through dynamic light scattering.

On the Motion of Gravity\u2013Capillary Waves with Odd Viscosity

We develop three asymptotic models of surface waves in a non-Newtonian fluid with odd viscosity. This viscosity is also known as Hall viscosity and appears in a number of applications such as quantum Hall fluids or chiral active fluids. Besides the odd viscosity effects, these models capture both gravity and capillary forces up to quadratic interactions and take the form of nonlinear and nonlocal wave equations. Two of these models describe bidirectional waves, while the third PDE studies the case of unidirectional propagation. We also prove the well-posedness of these asymptotic models in spaces of analytic functions and in Sobolev spaces. Finally, we present a number of numerical simulations for the unidirectional model.