Electrical current in conventional metals is carried by electrons that retain their individual character. Bad metals, such as the normal state of some high-temperature superconductors, violate this scenario, and the complete picture for their behavior remains unresolved. Here, we report phenomena consistent with bad-metal behaviour in an optical-lattice Hubbard model by measuring the transport lifetime for a mass current excited by stimulated Raman transitions. We demonstrate incompatibility with weak-scattering theory and key characteristics of bad metals: anomalous resistivity scaling consistent with T-linear behavior, the onset of incoherent transport, and the approach to the Mott-Ioffe-Regel limit. Our work demonstrates a direct method for determining the transport lifetime, which is critical to theory but difficult to measure in materials, and exposes minimal ingredients for bad-metal behavior.
Strange or bad metallic transport, defined by incompatibility with the conventional quasiparticle picture, is a theme common to many strongly correlated materials, including high-temperature superconductors. The Hubbard model represents a minimal starting point for modeling strongly correlated systems. Here we demonstrate strange metallic transport in the doped two-dimensional Hubbard model using determinantal quantum Monte Carlo calculations. Over a wide range of doping, we observe resistivities exceeding the Mott-Ioffe-Regel limit with linear temperature dependence. The temperatures of our calculations extend to as low as 1/40 of the noninteracting bandwidth, placing our findings in the degenerate regime relevant to experimental observations of strange metallicity. Our results provide a foundation for connecting theories of strange metals to models of strongly correlated materials.
Strongly correlated metals often display anomalous transport, including T-linear resistivity above the Mott-Ioffe-Regel limit. We introduce a tractable microscopic model for bad metals, by restoring in the well-known Hubbard model-with hopping t and on-site repulsion U-a "screened Coulomb" interaction between charge densities that decays exponentially with spatial separation. This interaction lifts the extensive degeneracy in the spectrum of the t=0 Hubbard model, allowing us to fully characterize the small t electric, thermal, and thermoelectric transport in our strongly correlated model. Throughout the phase diagram we observe T-linear resistivity above the Mott-Ioffe-Regel limit, together with strong violation of the Wiedemann-Franz law and a large thermopower that can undergo sign change.
Bad metals display transport behavior that differs from what is commonly seen in ordinary metals. One of the most significant differences is a resistivity that is linear in temperature and rises to well above the Ioffe-Regel limit (where the mean-free path is equal to the lattice spacing). Using an exact Kubo formula, we show that a linear resistivity naturally occurs for many systems when they are in an incoherent intermediate-temperature state. First, we provide a simple analytic model to give intuition for this phenomenology. Then, we verify the analytic arguments with numerical calculations for a simplified version of the Hubbard model which is solved with dynamical mean-field theory. Similar features have also been seen in Hubbard models, where they can begin at even lower temperatures due to the formation of resilient quasiparticles.
Good metals are characterized by diffusive transport of coherent quasiparticle states and the resistivity is much less than the Mott-Ioffe-Regel (MIR) limit,
e2ha, 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
vF 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
vF is replaced by its low-temperature renormalized value
vF∗. 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.
Ultracold fermionic atoms in a disordered optical lattice can realize the disordered Fermi-Hubbard model, allowing investigations of the nature of strongly-correlated fermions in a minimal setting. This thesis describes two such studies. In the first, we observe the momentum relaxation of strongly-correlated fermions in the absence of disorder. We find a violation of the weak-scattering prediction for the scaling with temperature, which is analogous to the linear-in-temperature scaling of resistivity in substances called ``bad metals.'' In the second, we probe a disordered and strongly-correlated system using quenches of the interaction strength that take it far from equilibrium. We find that the relaxation of double occupancies following the quenches has distinct dynamical regimes controlled by the interplay of interactions and disorder. We present a minimal picture of the relaxation process that illustrates the origin of these regimes, which are related to the Mott--metal--Anderson transitions of the ground state at half-filling.