In a recent paper by Lucas and Das Sarma [Physical Review B 97, 115449 (2018)], a solvable model of collective modes in 2D metals was considered in the hydrodynamic regime. In the current work, we generalize the hydrodynamic theory to 3D metals for which the calculation of sound modes in a strongly-coupled quantum Coulomb plasma can be made explicit. The specific theoretical question of interest is how the usual linearly dispersing hydrodynamic sound mode relates to the well-known gapped 3D plasmon collective mode in the presence of long-range Coulomb interaction. We show analytically that both the zero sound in the collisionless regime and the first sound in the hydrodynamic region become massive in 3D, acquiring a finite gap because of the long-range Coulomb interaction, while their damping rates become quadratic in momentum. We also discuss other types of long-range potential, where the dispersion of sound modes is modified accordingly. The general result is that the leading order hydrodynamic sound mode is always given by the leading-order plasmon frequency in the presence of long-range Coulomb interaction, but the next-to-leading-order dispersion corrections differ in hydrodynamic and colllisionless regimes.
Using an analytically tractable kinetic model of a two dimensional Fermi liquid of electrons, we characterize the crossovers between zero sound, first sound and plasmons. For experimentally realized Fermi liquids in a hydrodynamic limit, both zero and first sound waves are essentially replaced by plasmons. The plasmon dispersion relation is robust against hydrodynamic effects, up to acquiring the viscous-limited decay rate of a first sound wave in the hydrodynamic limit. We discuss implications for experiments in clean two dimensional electron gases.
Hydrodynamic flow in two-dimensional electron systems has so far been probed only by dc transport and scanning gate microscopy measurements. In this work we discuss theoretically signatures of the hydrodynamic regime in near-field optical microscopy. We analyze the dispersion of acoustic plasmon modes in two-dimensional electron liquids using a non-local conductivity that takes into account the effects of (momentum-conserving) electron-electron collisions, (momentum-relaxing) electron-phonon and electron-impurity collisions, and many-body interactions beyond the celebrated Random Phase Approxi…
The plasmon is a ubiquitous collective mode in charged liquids. Due to the long-range Coulomb interaction, the massless zero sound mode of the neutral system acquires a finite plasmon frequency in the long-wavelength limit. In the zero-temperature state of conventional metals -- the Fermi liquid -- the plasmon lives infinitely long at long wavelength when the system is (effectively) translationally invariant. In contrast, we will show that in strongly entangled strange metals the protection of zero sound fails at finite frequency and plasmons are always short lived regardless of their waveleng…
Inspired by the recent experimental signatures of relativistic hydrodynamics in graphene, we investigate theoretically the behavior of hydrodynamic sound modes in such quasi-relativistic fluids near charge neutrality, within linear response. Locally driving an electron fluid at a resonant frequency to such a sound mode can lead to large increases in the electrical response at the edges of the sample, a signature which cannot be explained using diffusive models of transport. We discuss the robustness of this signal to various effects, including electron-acoustic phonon coupling, disorder, and l…
We study the hydrodynamic properties of ultraclean interacting two-dimensional Dirac electrons with Keldysh quantum field theory. We study it from a weak-coupling and a strong-coupling perspective. We demonstrate that long-range Coulomb interactions play two independent roles: (i) they provide the inelastic and momentum-conserving scattering mechanism that leads to fast local equilibration; (ii) they facilitate the emergence of collective excitations, for instance plasmons, that contribute to transport properties on equal footing with electrons. Our approach is based on an effective field theo…
We study the charge density response in holographic models with explicit translation symmetry breaking which is relevant in IR. In particular, we focus on Q-lattices and the Bianchy VII helix. We show that the hydrodynamic sound mode is removed from the spectrum due to the strong momentum relaxation and therefore, the usual treatment of the plasmon as Coulomb-dressed zero sound does not apply. Furthermore, the dominant coherent modes in the longitudinal channel, which control the neutral density-density correlator, are diffusive. We show these modes are strongly suppressed when the boundary Co…
We consider a simple class of holographic massive gravity models for which the dual field theories break translational invariance spontaneously. We study, in detail, the longitudinal sector of the quasi-normal modes at zero charge density. We identify three hydrodynamic modes in this sector: a pair of sound modes and one diffusion mode. We numerically compute the dispersion relations of the hydrodynamic modes. The obtained speed and the attenuation of the sound modes are in agreement with the hydrodynamic predictions. On the contrary, we surprisingly find disagreement in the case of the diffus…
Collective behavior is one of the most intriguing aspects of the hydrodynamic approach to electronic transport. Here we provide a consistent, unified calculation of the dispersion relations of the hydrodynamic collective modes in graphene. Taking into account viscous effects, we show that the hydrodynamic sound mode in graphene becomes overdamped at sufficiently large momentum scales. Extending the linearized theory beyond the hydrodynamic regime, we connect the diffusive hydrodynamic charge density fluctuations with plasmons.
In this work we analyze the hydrodynamics of a $p-$ wave superfluid on its strongly coupled regime by considering its holographic description. We obtain the poles of the retarded Green function through the computation of the quasi-normal modes of the dual AdS black hole background finding diffusive, pseudo-diffusive and sound modes. For the sound modes we compute the speed of sound and its attenuation as function of the temperature. For the diffusive and pseudo-diffusive modes we find that they acquire a non-zero real part at certain finite momentum.
We use holography to study sound modes of strongly-interacting conformal field theories with non-zero temperature, $T$, and $U(1)$ chemical potential, $μ$. Specifically, we consider charged black brane solutions of Einstein gravity in $(3+1)$-dimensional Anti-de Sitter space coupled to a $U(1)$ gauge field with Dirac-Born-Infeld action, representing a spacetime-filling brane. The brane action has two free parameters: the tension and the non-linearity parameter, which controls higher-order terms in the field strength. For all values of the tension, non-linearity parameter, and $T/μ$, and at suf…
We study the dynamics and the relaxation of bulk plasmons in strongly coupled and quantum critical systems using the holographic framework. We analyze the dispersion relation of the plasmonic modes in detail for an illustrative class of holographic bottom-up models. Comparing to a simple hydrodynamic formula, we entangle the complicated interplay between the three least damped modes and shed light on the underlying physical processes. Such as the dependence of the plasma frequency and the effective relaxation time in terms of the electromagnetic coupling, the charge and the temperature of the …
We present an effective hydrodynamic theory of electronic transport in graphene in the interaction-dominated regime. We derive the emergent hydrodynamic description from the microscopic Boltzmann kinetic equation taking into account dissipation due to Coulomb interaction and find the viscosity of Dirac fermions in graphene for arbitrary densities. The viscous terms have a dramatic effect on transport coefficients in clean samples at high temperatures. Within linear response, we show that viscosity manifests itself in the nonlocal conductivity as well as dispersion of hydrodynamic plasmons. Bey…
Relativistic fluids are Lorentz invariant, and a non-relativistic limit of such fluids leads to the well-known Navier-Stokes equation. However, for fluids moving with respect to a reference system, or in critical systems with generic dynamical exponent z, the assumption of Lorentz invariance (or its non-relativistic version) does not hold. We are thus led to consider the most general fluid assuming only homogeneity and isotropy and study its hydrodynamics and transport behaviour. Remarkably, such systems have not been treated in full generality in the literature so far. Here we study these equ…
We argue that the gravitational shock wave computation used to extract the scrambling rate in strongly coupled quantum theories with a holographic dual is directly related to probing the system's hydrodynamic sound modes. The information recovered from the shock wave can be reconstructed in terms of purely diffusion-like, linearized gravitational waves at the horizon of a single-sided black hole with specific regularity-enforced imaginary values of frequency and momentum. In two-derivative bulk theories, this horizon "diffusion" can be related to late-time momentum diffusion via a simple relat…
