Absence of a quantum limit to charge diffusion in bad metals

Abstract

Good metals are characterized by diffusive transport of coherent quasiparticle 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, $D\ensuremath{\gtrsim}\ensuremath{\hbar}{v}_{F}^{2}/({k}_{B}T)$, 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 renormalized value ${v}_{F}^{*}$. 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, ${D}_{s}\ensuremath{\sim}1.3\ensuremath{\hbar}/m$, where $m$ is the fermion mass, experimentally observed and theoretically calculated in a cold degenerate Fermi gas in the unitary limit of scattering.