Beyond Drude transport in hydrodynamic metals
arXiv:2309.04033 · doi:10.1103/PhysRevB.109.165153
Abstract
In interacting theories, hydrodynamics describes the universal behavior of states close to local thermal equilibrium at late times and long distances in a gradient expansion. In the hydrodynamic regime of metals, momentum relaxes slowly with a rate , which formally appears on the right-hand side of the momentum dynamical equation and causes a Drude-like peak in the frequency dependence of the thermoelectric conductivities. Here we study the structure and determine the physical implications of momentum-relaxing gradient corrections beyond Drude, \emph{i.e.} arising at subleading order in the gradient expansion. We find that they effectively renormalize the weight of the Drude pole in the thermoelectric conductivities, and contribute to the dc conductivities at the same order as previously-known gradient corrections of translation-invariant hydrodynamics. Turning on a magnetic field, extra derivative corrections appear and renormalize the cyclotron frequency and the Hall conductivity. This relaxed hydrodynamics provides a field-theoretic explanation for previous results obtained using gauge-gravity duality. In strongly-coupled metals where quasiparticles are short-lived and which may be close to a hydrodynamic regime, the extra contributions we discuss are essential to interpret experimentally measured magneto-thermoelectric conductivities. Specializing to metals close to a Fermi liquid phase, the effective mass measured either through the specific heat or the spectral weight of the Drude-like peak are found to differ, as was indeed reported in overdoped cuprate superconductors. More generally, we expect such terms to be present in any hydrodynamic theory with approximate symmetries, which arise in many physical systems.
v1: 28 pages; v2: 29 pages, several clarifications and presentation improvements + additional references; v3: version accepted in PRB, clarifications on the boost-invariant limits and minor improvements
References in corpus (60)
- Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene
- Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
- Lectures on hydrodynamic fluctuations in relativistic theories
- A simple holographic model of momentum relaxation
- Change of carrier density at the pseudogap critical point of a cuprate superconductor
- Hydrodynamics of electrons in graphene
- Electron Viscosity, Current Vortices and Negative Nonlocal Resistance in Graphene
- Constraints on Fluid Dynamics from Equilibrium Partition Functions
- Towards hydrodynamics without an entropy current
- Holographic Q-lattices
- Charge transport in holography with momentum dissipation
- Holographic duality and the resistivity of strange metals
- Hydrodynamic description of transport in strongly correlated electron systems
- Momentum dissipation and effective theories of coherent and incoherent transport
- Thermodynamic signatures of quantum criticality in cuprates
- Novel metals and insulators from holography
- Quantum Critical Transport and the Hall Angle
- Impure AdS/CFT
- Non-Fermi liquids and the Wiedemann-Franz law
- Incoherent transport across the strange metal regime of highly overdoped cuprates
- Collective cyclotron motion of the relativistic plasma in graphene
- Universal theory of strange metals from spatially random interactions
- Zero Sound from Holography
- Holography and hydrodynamics with weakly broken symmetries
- Dissecting holographic conductivities
- Forced Fluid Dynamics from Gravity
- Incoherent transport in clean quantum critical metals
- Theory of hydrodynamic transport in fluctuating electronic charge density wave states
- Shaping black holes with free fields
- Scale-invariant hyperscaling-violating holographic theories and the resistivity of strange metals with random-field disorder
- Hydrodynamic transport in strongly coupled disordered quantum field theories
- Disordered horizons: Holography of randomly disordered fixed points
- Holographic zero sound at finite temperature
- Kinetic theory of transport for inhomogeneous electron fluids
- Colloquium: Hydrodynamics and holography of charge density wave phases
- Hydrodynamic theory of quantum fluctuating superconductivity
- Momentum relaxation from the fluid/gravity correspondence
- Slow relaxation and diffusion in holographic quantum critical phases
- Normal state specific heat in the cuprates LaSrCuO and BiSrLaCuO near the critical point of the pseudogap phase
- Emergent scale invariance of disordered horizons
- Origin of the Drude peak and of zero sound in probe brane holography
- Sound waves and resonances in electron-hole plasma
- Hydrodynamic electron transport near charge neutrality
- Impact of irrelevant deformations on thermodynamics and transport in holographic quantum critical states
- Hydrodynamics without boosts
- The Hall number across a van Hove singularity
- Approximate symmetries, pseudo-Goldstones, and the second law of thermodynamics
- Approximate higher-form symmetries, topological defects, and dynamical phase transitions
- Observation of cyclotron resonance and measurement of the hole mass in optimally-doped LaSrCuO
- Evolution of the cyclotron mass with doping in LaSrCuO
- Hydrodynamic charge and heat transport on inhomogeneous curved spaces
- Thermal conductivity at a disordered quantum critical point
- Hydrodynamics of plastic deformations in electronic crystals
- Cyclotron resonance and quantum oscillations of critical Fermi surfaces
- Zero sound and higher-form symmetries in compressible holographic phases
- Disordered quantum critical fixed points from holography
- Renormalization group in quantum critical theories with Harris-marginal disorder
- Forced Fluid Dynamics from Gravity in Arbitrary Dimensions
- Breakdown of emergent Lifshitz symmetry in holographic matter with Harris-marginal disorder
- Hydrodynamics of a relativistic charged fluid in the presence of a periodically modulated chemical potential