Absence of a quantum limit to charge diffusion in bad metals

Abstract

Good metals are characterised by diffusive transport of coherent quasi-particle states and the resistivity is much less than the Mott-Ioffe-Regel (MIR) limit, $\frac{ha}{e^2}$, where $a$ is the lattice constant. In bad metals, such as many strongly correlated electron materials, the resistivity exceeds the Mott-Ioffe-Regel limit and the transport is incoherent in nature. Hartnoll, loosely motivated by holographic duality (AdS/CFT correspondence) in string theory, recently proposed a lower bound to the charge diffusion constant, $D\gtrsim \hslash v_F^2/(k_{B}T)$, in the incoherent regime of transport, where $v_F$ is the Fermi velocity and $T$ the temperature. Using dynamical mean field theory (DMFT) we calculate the charge diffusion constant in a single band Hubbard model at half filling. We show that in the strongly correlated regime the Hartnoll's bound is violated in the crossover region between the coherent Fermi liquid region and the incoherent (bad metal) local moment region. The violation occurs even when the bare Fermi velocity $v_F$ is replaced by its low temperature renormalised value, $v_F^{\ast }$.The bound is satisfied at all temperatures in the weakly and moderately correlated systems as well as in strongly correlated systems in the high temperature region where the resistivity is close to linear in temperature. Our calculated charge diffusion constant, in the incoherent regime of transport, also strongly violates a proposed quantum limit of spin diffusion, $D_s\sim 1.3\hslash /m$, where $m$ is the fermion mass, experimentally observed and theoretically calculated in a cold degenerate Fermi gas in the unitary limit of scattering.

arXiv commentFinal version, 11 pages, 6 figures, accepted for publication in Physical Review B

References in corpus (33)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Quantum Cluster Theories
• Why does the Quark-Gluon Plasma at RHIC behave as a nearly ideal fluid ?
• Theory of universal incoherent metallic transport
• Universality of the Mott-Ioffe-Regel limit in metals
• Universal Quantum Viscosity in a Unitary Fermi Gas
• Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3
• Zero temperature metal-insulator transition in the infinite-dimensional Hubbard model
• Quantum frustration in organic Mott insulators: from spin liquids to unconventional superconductors
• Universal Spin Transport in a Strongly Interacting Fermi Gas
• The Hubbard Model at Infinite Dimensions: Thermodynamic and Transport Properties
• Mott transition and transport crossovers in the organic compound $\kappa -(BEDT-TTF{)}_{2}Cu[N(CN{)}_2]Cl$
• How bad metals turn good: spectroscopic signatures of resilient quasiparticles
• A New Iterative Perturbation Scheme for Lattice Models with Arbitrary Filling
• Transport properties of strongly correlated metals:a dynamical mean-field approach
• Quantum Critical Transport Near the Mott Transition
• Transverse Demagnetization Dynamics of a Unitary Fermi Gas
• Universal spin dynamics in two-dimensional Fermi gases
• Quantum criticality and black holes
• Hidden Fermi Liquid, Scattering Rate Saturation and Nernst Effect: a DMFT Perspective
• Quantum mechanical limitations to spin diffusion in the unitary Fermi gas
• Optical and DC conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point, including vertex corrections
• Quasiparticles at the verge of localization near the Mott metal-insulator transition in a two-dimensional material
• Optical spectral weights and the ferromagnetic transition temperature of CMR manganites: relevance of double-exchange to real materials
• Physics of the Pseudogap in 8-site Cluster Dynamical Mean Field Theory: photoemission, Raman scattering, in-plane and c-axis conductivity
• Fluid Dynamics and Viscosity in Strongly Correlated Fluids
• Optical conductivity in cluster dynamical mean field theory: formalism and application to high temperature superconductors
• Thermodynamics of a bad metal-Mott insulator transition in the presence of frustration
• Benchmark of a modified Iterated Perturbation Theory approach on the 3d FCC lattice at strong coupling
• Charge-transfer metal-insulator transitions in the spin-one-half Falicov-Kimball model
• Transport functions for hypercubic and Bethe lattices
• Perturbation study on the spin and charge susceptibilities of the two-dimensional Hubbard model

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