Emergent Hydrodynamics in Condensed Matter and
High-energy Physics

I will give an update on non-local transport measurements on delafossite layered metals, discussing the extent to which the observations are consistent with ballistic transport and whether viscous-like effects also play a role in determining the observed properties.

I will review theoretical results and experimental observations of charge and heat conduction in the hydrodynamics regime of transport in monolayer graphene. Among the many effects, the Wiedemann-Franz law, which connects heat and charge transport in metals, is intrinsically violated in the hydrodynamics regime. In doped systems, this fact can be used to increase thermoelectric conversion efficiencies of graphene-based devices. More stringent conditions yield, in undoped graphene, to a quantum-critical Dirac-fluid regime, where electronic heat can flow more efficiently than charge. We show that disorder is essential to observe the Dirac-fluid regime under transport conditions. Conversely, the transition to this regime can also be revealed, at room temperature, using spatiotemporal thermoelectric microscopy with femtosecond temporal and nanometre spatial resolution. Finally, I will comment on the violation of the Wiedemann-Franz law in compensated semimetals, on the role of electron-hole recombination in defining the direction of the violation, discussing how graphene can help shed light on this long-standing problem.

In the sixties, Luttinger introduced a convenient and widespread trick to calculate thermal transport caused by a thermal gradient, which is to restore equilibrium with an auxiliary, but small, gravitational field. Using thermal transport, a hand-full of recent experiments have been interpreted as a measurement of a gravitational anomaly, an elusive quantum mechanical phenomenon that is associated to strong gravitational fields, like those near black-holes. However, a direct link between the Luttinger trick and gravitational anomalies is absent. More problematically, these two ideas have been argued to be both related and unrelated to each other in the literature, a paradoxical approach that uncovers a deeper multidisciplinary problem: How can gravitational anomalies, that require strong gravitational fields, be measured in table-top experiments, that are performed in flat space-time? This is the question I will revisit in my talk. First, I will show how to generalize the Tolman-Ehrenfest temperature, the parent concept of the Luttinger trick, to include gravitational anomalies. This will allow us to revisit black hole, quench and Floquet physics to highlight novel instances where gravitational anomalies are at play, even when space-time itself is flat, as in condensed matter experiments.

Recently, much interest has emerged in fluid-like electric charge transport in various solid-state systems. The hydrodynamic behavior of the electronic fluid reveals itself as a decrease of the electrical resistance with increasing temperature (the Gurzhi effect) in narrow conducting channels, polynomial scaling of the resistance as a function of the channel width, substantial violation of the Wiedemann-Franz law supported by the emergence of the Poiseuille flow. Similarly to whirlpools in flowing water, the viscous electronic flow generates vortices, resulting in abnormal sign-changing electrical response driven by the backflow of electrical current. Experimentally, the presence of the hydrodynamic vortices was observed in low-temperature graphene as a negative voltage drop near the current-injecting contacts. However, the question of whether the long-ranged sign-changing electrical response can be produced by a mechanism other than hydrodynamics has not been addressed so far. Here we use polarization-sensitive laser microscopy to demonstrate the emergence of visually similar abnormal sign-alternating patterns in charge density in multilayer tungsten ditelluride at room temperature where this material does not exhibit true electronic hydrodynamics. We argue that this pseudo-hydrodynamic behavior appears due to a subtle interplay between the diffusive transport of electrons and holes. In particular, the sign-alternating charge accumulation in WTe2 is supported by the unexpected backflow of compressible neutral electron-hole current, which creates charge-neutral whirlpools in the bulk of this nearly compensated semimetal. We demonstrate that the exceptionally large spatial size of the charge domains is sustained by the long recombination time of electron-hole pairs.

We study propagation of an oscillatory electromagnetic field inside a Weyl semimetal. In conventional conductors, the motion of the charge carriers in the skin layer near the surface can be diffusive, ballistic, or hydrodynamic. We show that the presence of chiral anomalies, intrinsic to the massless Weyl particles, leads to a hitherto neglected transport regime, in which the relation between the current and the electric field becomes nonlocal as a result of the diffusion of the valley charge imbalance into the bulk of the material. We propose to use this novel regime as a diagnostic of the presence of chiral anomalies in optical conductivity measurements. These results are obtained from a generalized kinetic theory which includes various relaxation mechanisms, allowing us to investigate different transport regimes of Weyl semimetals.

I will discuss several puzzles related to the electromagnetic response of topological superconductors in 3+1 dimensions, in partcular the role of the theta term in the effective action of the superconducting Weyl gas. Work based on arXiv:2103.08960 by Marcus Stålhammar, MS, Masatoshi Sato and Thors Hans Hansson.

I review recent works with A. Abanov. In these works, we show that anomalies of quantum field theories with Dirac fermions appear as kinematic properties of the classical Euler equation for a perfect fluid.

Electron quasiparticles in Dirac semimetals may exhibit a hydrodynamic regime under certain conditions. Since the corresponding quasiparticle fluid is relativistic-like, anomalous, and electrically charged, it has a range of unusual properties. Anomalous physics affects properties of low-energy collective modes, relativistic-like effects show up in novel instabilities, and the charged nature of the electron fluid is responsible for the strong suppression of convection. In this talk, I will review some of these unusual properties of the electron fluid in Dirac semimetals.

Electrical resistance usually originates from lattice imperfections. However, even a perfect lattice has a fundamental resistance limit, given by the Landauer conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin to appear at the contacts of electronic devices, sets the ultimate conduction limit of non-interacting electrons. Recent years have seen growing evidence of hydrodynamic electronic phenomena, prompting recent theories to ask whether an electronic fluid can radically break the fundamental Landauer-Sharvin limit. In this talk I will present our single-electron-transistor imaging of electronic flow in high-mobility graphene Corbino disk devices that answer this question. First, by imaging ballistic flows at liquid-helium temperatures, we observe a Landauer-Sharvin resistance that does not appear at the contacts but is instead distributed throughout the bulk. This underpins the phase-space origin of this resistance - as emerging from spatial gradients in the number of conduction modes. At elevated temperatures, by identifying and accounting for electron-phonon scattering, we reveal the details of the purely hydrodynamic flow. Strikingly, we find that electron hydrodynamics eliminates the bulk Landauer-Sharvin resistance. Finally, by imaging spiraling magneto-hydrodynamic Corbino flows, we reveal the key emergent length-scale predicted by hydrodynamic theories – the Gurzhi length. These observations demonstrate that electronic fluids can dramatically transcend the fundamental limitations of ballistic electrons, with important implications for fundamental science and future technologies.

So far, graphene is the material of choice for experimentally realizing hydrodynamic behaviour of strongly coupled electrons in a solid. However, in graphene the effective electron-electron coupling is only of order one, still far away from the infinite coupling limit studied in holographic hydrodynamics. We propose a new Dirac material, Scandium-substituted Herbertsmithite, in which the electron-electron coupling is enhanced by a factor 3.2 as compared to graphene. Using a holographic approach that involves finite-coupling higher-curvature corrections to the famous holographic result of 1/4 pi for the ratio of shear viscosity over entropy density (eta/s), we estimate eta/s in the coupling regime of the proposed new material. The associated range of Reynolds numbers even puts turbulent behaviour within reach. - Moreover, I will briefly report on recent results for the Hall viscosity and its impact for electron flows in channel geometries.

We show that the chiral anomaly of quantum field theories with Dirac fermions subject to an axial background field is an inherent property of kinematics of a perfect classical fluid. Celebrated Beltrami flows (stationary solutions of Euler equations with extensive helicity) exhibit the chiral anomaly equivalent to that known for Dirac fermions. A prominent effect of the chiral anomaly is the transport electric current at equilibrium. We show that it is also a property of Beltrami flows.

The current response in a Weyl or Dirac semimetal becomes nonlocal due to the chiral anomaly activated by an applied magnetic field. The nonlocality can develop in diffusive, hydrodynamic, and crossover regimes of transport. In the first part of my talk, I will show how nonlocality develops in the response to an electromagnetic field under the conditions of the normal skin effect. The nonlocality is related to the valley (chiral) charge imbalance generated by the combined effect of the electric field of the impinging wave and the static magnetic field. The signatures of this nonlocality can be found in the transmission and reflection of electromagnetic waves. In view of a weaker decay of the anomalous components of the electric field in the nonlocal regime, it is possible to achieve an enhancement of the electromagnetic wave penetration depth. In the hydrodynamic and crossover regimes of transport, a nontrivial valley charge distribution allows for an unusual nonmonotonic dependence of the magnetic-field-dependent part of the electric conductivity on temperature dubbed the anomalous Gurzhi effect. This effect is realized in sufficiently clean semimetals where the electron-electron scattering dominates and the relaxation of the valley-imbalance charge density happens at the boundaries.

For more than 60 years, there have been analogies between the hydrodinamic flow of particles and the electron flow on electron gases of different dimensionality. In this work we address and re visit the direct experimental confirmation of the hydrodynamic theories that predict Knudsen and Poiseuille flow of electrons, developed by Gurzhi et. al. in the 1960s for 2 dimensional electron gases constricted in electrostatically defined channels. Our results coincide with the first realizations by Molenkamp et. al. in GaAs/AlGaAs heterostructures for zero magnetic field, and under an external out of plane magnetic field, they show at least 3 new hydrodynamic regimes that mimic the carrier behavior and confirm the theories of the previously elusive Gurzhi-Shevchenko orbits diffusion model, the never previously seen Poiseuille flow of cyclotron orbits at high enough magnetic fields and, presumably, 1D-Diffusion of carriers at small magnetic fields.

We study hydrodynamic electron transport in Corbino and Hall bar graphene devices. In Corbino geometry due to the irrotational character of the flow, the forces exerted on the electron liquid are expelled from the bulk. We show that in the absence of Galilean invariance, force expulsion produces qualitatively new features in thermoelectric transport: (i) it results in drops of both voltage and temperature at the system boundaries and (ii) in conductance measurements in pristine systems, the electric field is not expelled from the bulk. We obtain thermoelectric coefficients of the system in the entire crossover region between charge neutrality and high electron density regime. The thermal conductance exhibits a sensitive Lorentzian dependence on the electron density. The width of the Lorentzian is determined by the fluid viscosity. This enables determination of the viscosity of electron liquid near charge neutrality from purely thermal transport measurements. In general, the thermoelectric response is anomalous: it violates the Matthiessen's rule, the Wiedemann-Franz law, and the Mott relation. For Hall bar devices subject to long-range inhomogeneities we show that the effective electrical conductivity of the system may significantly exceed the intrinsic conductivity of the electron liquid.

The flow of momentum and energy in a fluid is typically associated with dissipative transport coefficients: viscosity and thermal conductivity. Fluids that break certain symmetries such as mirror symmetry and time-reversal invariance can display non-dissipative transport coefficients called odd (or Hall) viscosities and thermal conductivities. The goal of this paper is to elucidate the microscopic origin of these dissipationless transport coefficients using kinetic theory. We show that odd viscosity and odd thermal conductivity arise when the linearized collision operator is not Hermitian. This symmetry breaking occurs when collisions are chiral, i.e. not mirror symmetric. To capture this feature in a minimalistic way, we introduce a modified relaxation time approximation in which the distribution function is rotated by an angle characterizing the average chirality of the collisions. In the limit of an infinitesimal rotation, the effect of the parity-violating collisions can be described as an emergent effective magnetic field.

Fracton phases are characterized by that their elementary excitations have restricted mobility. In the context of hydrodynamics it has been shown theoretically, and confirmed experimentally, that such restricted mobility leads to novel emergent scaling laws. In this talk, I will introduce the hydrodynamics of fractons with translation symmetry, focusing on the simplest case where dipole moment is the only additional conserved quantity. This hydrodynamics turns out to have rather exotic properties, owing to the fact that translation invariance leads to a non-trivial extension of spacetime symmetries. Using an effective field theory approach that allows accounting for stochastic fluctuations, I will show that this hydrodynamics contains relevant nonlinearities that lead to the emergence of a stochastic non-Gaussian universality class, thus constituting a breakdown of its local hydrodynamic description.

Tensor product states are powerful tools for simulating area-law entangled states of many-body systems. The applicability of such methods to the non-equilibrium dynamics of many-body systems is less clear due to the presence of large amounts of entanglement. New methods seek to reduce the numerical cost by selectively discarding those parts of the many-body wavefunction, which are thought to have relatively litte effect on dynamical quantities of interest.  We present a theory for the sizes of “backflow corrections”, i.e., systematic errors due to these truncation effects and introduce the dissipation-assisted operator evolution (DAOE) method for calculating transport properties of strongly interacting lattice systems in the high temperature regime. In the DAOE method, we represent the observable as a matrix product operator, and show that the dissipation leads to a decay of operator entanglement, allowing us to capture the dynamics to long times. We benchmark this scheme by calculating spin and energy diffusion constants in a variety of physical models and compare to other existing methods.

Symmetric gauge fields mediate the interaction between certain class of fracton excitations. However, the global symmetries associated to those theories are peculiar because they restrict the free movement of fractons, having as consequence the symmetry group is a spacetime symmetry group. In this talk, I will discuss the gauging of such type of symmetries, and its relevance for the construction of low energy models for fractons.

Since its inception several decades ago by Phil Anderson, the spinon Fermi surface state has remained a fascinating but elusive state of matter. In the first part of this talk, I will describe some ideas on how to look for this traditional spinon fermi surface state in experiments. For example, I will describe how to detect them via cyclotron resonance experiments and also how their transverse electrical conductivity resembles that of an ordinary metal, which can be probed via NV center magnetic noise spectroscopy. In the second part, I will describe a new “pseudo-scalar” variant of Anderson's spinon Fermi surface state. This state is motivated by recent experiments in alpha-RuCl3. The emergent magnetic field in this state behaves sharply differently from the usual magnetic field experienced by electrons or the traditional Anderson spinons. In particular, the emergent magnetic field in this pseudo-scalar state is non-chiral and can exist even when the system has a mirror symmetry. This allows to understand why spinons in alpha-RuCl3 can display quantum oscillations of the thermal conductivity without an accompanying thermal Hall effect.

We formulate a fracton-elasticity duality for twisted moiré superlattices, taking into account that they are incommensurate crystals with dissipative phason dynamics. From a dual tensor-gauge formulation, as compared to standard crystals, we identify twice the number of conserved charges that describe topological lattice defects, namely, disclinations and a new type of defect that we dub discompressions. The key implication of these conservation laws is that both glide and climb motions of lattice dislocations are suppressed, indicating that dislocation networks may become exceptionally stable. We also generalize our results to other planar incommensurate crystals and quasicrystals. We then formulate the sub-diffusive hydrodynamics of these systems

Electronic materials can sustain a variety of symmetry and topologically protected touchings of valence and conduction bands, featuring different low-energy dispersions and topological charges. I will argue that different members of the family of nodal semimetals can be distinguished by elastic and optical responses. In particular, depending on the underlying monopole charge and the band curvature, the shear viscosity in the collisionless (high-frequency) regime displays a unique power-law scaling with frequency at low temperatures, therefore bearing the signatures of the band topology. Furthermore, I will discuss nonlinear Hall conductivity as a probe of 2D tilted Weyl semimetal, which exhibits, for instance, the tilt-driven splitting of the resonances. Most interestingly, the nonlinear Hall conductivity gets suppressed in a non-Fermi liquid emerging from the line of the quantum-critical points and can be used to distinguish this non-Fermi liquid from its tilt-free counterpart. Finally, I will briefly discuss universal features of the optical conductivity in a disordered Weyl semimetal.

Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the \emph{collisionless} regime ($\hbar \omega \gg k_B T$) in the vicinity of a relativistic quantum critical point, separating two-dimensional ($d=2$) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such critical point gapless fermionic and bosonic excitations are strongly coupled, leading to a \emph{universal} suppression of the inter-band OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in $1/N_f$- and $\epsilon$-expansions, where $N_f$ counts fermion flavor number and $\epsilon=3-d$. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from non-pertubative gauge-gravity duality, for example.

I will discuss two questions. First, do the equations of relativistic hydrodynamics make sense? And second, how universal are the long-distance, late-time predictions of classical hydrodynamics?

Fractons are excitations with unusual properties like restricted mobility in some or all spatial directions. Their presence is linked to symmetry transformations depending on the spatial coordinates, like dipole or subsystem symmetries, which sometimes are emergent in the low energy effective description. I discuss the role of these symmetries in some particular systems with broken translation invariance and hydrodynamics.

In this talk I will discuss how in active Micropolar/Cosserat solids odd elasticity can emerge naturally in the presence of a pre-twist. I will discuss some phenomenological aspects of such a Cosserat solid with odd elasticity.

Fluids composed of spinning objects such as active rotors or vortex filaments exhibit exotic response coefficients. In this talk, I will discuss a few surprising phenomena that arise in such fluids due to the presence of so-called odd viscosity (equivalently, Hall viscosity). I will mention how odd viscosity interplays with fluid acoustics to give rise to topological edge states. Uniquely, fluids can break bulk-boundary correspondence, leading to non-Hermitian phenomena such as the absorption of topological modes. I will then focus on non-linear shallow water waves in fluids composed of vortex filaments [Doak et al, arXiv:2204.09375]. In these fluids, odd viscosity leads to novel non-linear terms distinct from their equilibrium counterparts. These terms allow for two-dimensional lump solitons, where odd viscosity acts analogously to a non-equilibrium surface tension. Within these non-linear waves, odd viscosity leads to a unique signature in the fluid flow due the breaking of detailed balance.

In this talk, I will summarize our recent investigations of edge modes in two-dimensional elastic solids with broken time-reversal symmetry. First, I will discuss the elastic Rayleigh edge wave traveling along a boundary of a two-dimensional skyrmion lattice hosted inside a thin-film chiral magnet. We found that the direction of propagation of the Rayleigh modes is determined not only by the chirality of the magnet but also by the Poisson ratio of the crystal. Next, I will argue that in a superfluid vortex crystal chiral Rayleigh waves are absent, but will present evidence for high-frequency chiral surface waves in the lowest Landau level regime.

Many recent experiments addressed manifestations of electronic crystals, particularly the charge density waves, in nano-junctions, under electric field effect, at high magnetic fields, together with real space visualizations by STM and micro X-ray diffraction. This activity returns the interest to stationary or transient states with static and dynamic topologically nontrivial configurations: electronic vortices as dislocations, instantons as phase slip centers, and ensembles of microscopic solitons. Describing and modeling these states and processes calls for an efficient phenomenological theory which should take into account the degenerate order parameter, various kinds of normal carriers and the electric field. Here we notice that the commonly employed time-depend Ginzburg-Landau approach suffers with violation of the charge conservation law resulting in unphysical generation of particles which is particularly strong for nucleating or moving electronic vortices. We present a consistent theory which exploits the chiral transformations taking into account the principle contribution of the fermionic chiral anomaly to the effective action. The resulting equations clarify partitions of charges, currents and rigidity among subsystems of the condensate and normal carriers. On this basis we perform the numerical modeling of a spontaneously generated coherent sequence of phase slips - the space-time vortices - serving for the conversion among the injected normal current and the collective one. Performed and published with N. Kirova: Annals of Physics, 403 (2019) 184–197. arXiv:1807.05512

In this talk I will discuss two aspects of continuum field theories of fractons. These models have been of recent interest to condensed matter and high energy theorists. On the one hand they are candidates for new phases of quantum matter, and on the other, they have features which seem impossible to describe in continuum field theory, including quasiparticles of restricted mobility and a ground state degeneracy which depends sensitively on the ultraviolet. The two aspects I will discuss are (i.) some soluble interacting large N versions of these models, and (ii.) the lessons they teach us for building a theory of transport.

The interaction between a peregrine falcon and a dove is visibly non-reciprocal. What happens to the well established framework of phase transitions in non-reciprocal systems far from equilibrium? In this talk, I will answer this question by looking at three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Simple demonstrations with robots will be presented along with naturally occurring phenomena from various domains of science that share a common feature: reciprocity has no reason to exist. In all these cases, the emergence of unique time-dependent many-body phases can be captured by combining insights from non-Hermitian quantum mechanics and bifurcation theory. This approach is a step towards a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle.

This talk discusses two examples of unconventional hydrodynamic limits in the long-time dynamics of interacting quantum spin systems. Integrable systems are known to support an unusual kind of hydrodynamics governed by an infinite set of conservation laws. One of the most surprising consequences is the emergence of Kardar-Parisi-Zhang hydrodynamics in the quantum Heisenberg chain at high temperature, and we discuss the conditions for this phenomenon and its experimental observation using neutron scattering. We then turn to higher-dimensional spin systems, where fewer exact results are known, particularly for dynamical properties. The possibility of spin liquids on the triangular and honeycomb lattices are discussed using a combination of analytical and computational methods to model their dynamical signatures.

Rotating photon gas exhibits a chirality separation along the angular velocity, which is manifested through a generation of helicity and zilch currents. In my talk, I will show how to derive the corresponding Wigner function and construct elements of the covariant chiral kinetic theory for photons from first principles. I will further consider the zilch and helicity currents and show that both manifestations of the chirality transport originate in the Berry phase of photons, similarly to other chiral effects. I will also briefly comment on the possible relation between vortical responses in rotating systems of massless particles and the anomalies of underlying quantum field theory.

Spin has become an important observable in relativistic heavy ion collisions over the past few years. Hydrodynamic predictions of the spin polarization of particles emitted in these collisions turned out to be successful in reproducing the size and the momentum dependence. The inclusion of a purely quantum mechanical object such a spin in relativistic hydrodynamics involves a reconsideration of its foundations within a quantum statistical mechanical framework. I will report about the main results and the most recent advances, emphasizing the importance of quantum corrections to local thermodynamic equilibrium.

We study the effect of a small fermion mass in the formulation of the chiral kinetic theory. Using effective field theory methods, we study how besides the left-handed and right handed distribution functions components needed in the massless case, distribution functions describing quantum coherent mixtures of left and right handed fermions are also required, which also enter in the chiral anomaly equation. We study how these two different set of functions are related by Lorentz symmetry transformations.

There is an ongoing effort the relativistic heavy ion collider (RHIC) to search for signals of a possible critical end point in the QCD phase diagram. Results from the second phase of the RHIC beam energy scan are expected to be released in the near future. This experimental effort motivates a theory program aimed at understanding the dynamics of critical fluctuations in the vicinity of a critical end point. I will present some results on stochastic effective actions, and the results from numerical simulations of the relaxation rate of higher order cumulants.