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arXiv:1606.06669 · Nature Communications

Bad-metal relaxation dynamics in a Fermi lattice gas

Wenchao Xu, William McGehee, William Morong, Brian DeMarco

Published Apr 8, 2019• 27 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41467-019-09526-x

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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.
We report the discovery of phenomena consistent with bad-metal relaxation dynamics in the metallic regime of an optical-lattice Hubbard model. The transport lifetime induced by inter-particle scattering for a mass current of atoms excited by stimulated Raman transitions is measured, and the corresponding analog of resistivity is inferred. By exploring a range of temperature, we demonstrate incompatibility with weak-scattering theory and a key characteristic of bad metals: anomalous resistivity scaling consistent with TTT-linear behavior. We also observe the onset of two behaviors---incoherent transport and the approach to the Mott-Ioffe-Regel limit---associated with bad metals. The interaction and temperature scaling of resistivity are verified to be consistent with dynamic mean-field theory (DMFT) predictions of a bad metal, which is associated with the reduction of quasiparticle weight by strong interactions.
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.
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.
We use 40K atoms trapped in a cubic optical lattice to simulate the Fermi-Hubbard model. The work in this thesis focuses on investigating dynamics in the Fermi-Hubbard model and developing techniques for engineering Hamiltonians beyond the minimal Hubbard model. We discussed three experiments. In the first, we investigated the transport properties of a Fermi lattice gas by directly measuring the transport lifetime at various interaction strengths and temperatures. The resistivity is inferred from the measured transport lifetime. We observe anomalous transport behavior, which is analogous to bad-metal behavior in strongly correlated electronic materials. The second experiment presents the first realization of correlated, density-dependent tunneling in a Fermi-Hubbard optical lattice model by applied Raman laser fields. This correlated tunneling involves spin-flips and the generation of doublons, which have been observed experimentally. We also confirmed that the amplitude of correlated tunneling is suppressed when neighboring lattice sites are unoccupied. The last experiment explores the possibility to introduce long-range interactions for fermions trapped in optical lattices via Rydberg-dressed states. We developed a novel velocity-selective spectroscopy method to measure the transition between the 5P_1/2 and Rydberg states via electromagnetically induced transparency. This measurement is a first step toward inducing Rydberg-dressed interactions in optical lattices.
Strong interactions in many-body quantum systems complicate the interpretation of charge transport in such materials. To shed light on this problem, we study transport in a clean quantum system: ultracold lithium-6 in a two-dimensional optical lattice, a testing ground for strong interaction physics in the Fermi-Hubbard model. We determine the diffusion constant by measuring the relaxation of an imposed density modulation and modeling its decay hydrodynamically. The diffusion constant is converted to a resistivity by using the Nernst-Einstein relation. That resistivity exhibits a linear temperature dependence and shows no evidence of saturation, two characteristic signatures of a bad metal. The techniques we developed in this study may be applied to measurements of other transport quantities, including the optical conductivity and thermopower.
A key challenge for optical lattice experiments focused on simulating models of strongly correlated electronic solids has been achieving lower temperatures. Although cooling of lattice-well vibrational states has been demonstrated, the motion of atoms through the lattice, characterized by their quasimomentum, has not been cooled directly. Furthermore, quasimomentum equilibration, which is necessary for cooling, has remained unexplored. Here, we use quasimomentum-selective stimulated Raman transitions to directly measure rethermalization rates and cool quasimomentum for a bosonic lattice Hubbard gas. The measured relaxation rate is consistent with a short-range, two-particle scattering model without free parameters at high lattice depths, despite an apparent violation of the Mott-Ioffe-Regel (MIR) bound. Efficient cooling exceeding heating rates is achieved by iteratively removing high quasimomentum atoms from the lattice. Our results may have implications for models of unusual transport phenomena in materials with strong interactions, such as heavy fermion materials and transition metal oxides, and the cooling method we have developed is applicable to any species, including fermionic atoms.