Spin Transport in a Mott Insulator of Ultracold Fermions
Matthew A. Nichols Lawrence W. Cheuk Melih Okan Thomas R. Hartke Enrique Mendez T. Senthil Ehsan Khatami Hao Zhang Martin W. Zwierlein














































Strongly correlated materials are expected to feature unconventional transport properties, such that charge, spin, and heat conduction are potentially independent probes of the dynamics. In contrast to charge transport, the measurement of spin transport in such materials is highly challenging. We observed spin conduction and diffusion in a system of ultracold fermionic atoms that realizes the half-filled Fermi-Hubbard model. For strong interactions, spin diffusion is driven by super-exchange and doublon-hole-assisted tunneling, and strongly violates the quantum limit of charge diffusion. The technique developed in this work can be extended to finite doping, which can shed light on the complex interplay between spin and charge in the Hubbard model.





Spin Transport in a Mott Insulator of Ultracold Fermions
    Martin W. Zwierlein
    December 30, 2023
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In materials, electrons are the elementary carriers of both spin and charge, and one might thus expect that the properties of spin and charge conduction are always closely related. However, strong electron correlations can lead to the separation of charge and spin degrees of freedom, such as in one-dimensional systems <cit.>. The unusual transport properties of the cuprate high-temperature superconductors in the normal state have been proposed to arise from decoupled spin and charge transport <cit.>. The simplest model believed to capture the essential features of the cuprate phase diagram, the Fermi-Hubbard model, features spin-charge separation in one dimension <cit.>. In two dimensions, relevant for the cuprates, strong correlations render calculations of transport properties highly challenging <cit.>. Simultaneous measurements of transport in both the charge and spin sectors would thus be of great relevance. However, in the cuprates, creating and manipulating spin currents is difficult.

Cold-atom quantum simulators can be used to experimentally study the Fermi-Hubbard model in a pristine, isolated environment, with full control of all Hubbard parameters <cit.>. The advent of quantum gas microscopes for fermionic atoms <cit.>, with their single-atom, single-lattice site resolution, has enabled precision measurements of the equation of state <cit.> and of spin and charge correlations <cit.> of the two-dimensional (2D) Fermi-Hubbard model. These microscopes are poised for the study of transport, as already demonstrated with bosonic atoms <cit.>. Previous measurements of fermionic charge transport were performed without the aid of single-atom resolution <cit.>. However, it has proven difficult to directly connect the observed dynamics of lattice systems to the transport coefficients of the underlying Hamiltonian. Recently, the optical charge conductivity of a dilute, harmonically trapped 3D Fermi-Hubbard system has been measured <cit.>, as well as the charge conductance through a mesoscopic lattice in a wire geometry <cit.>.

Here, we explored spin transport in the repulsive 2D Fermi-Hubbard model using ultracold fermionic ^40K atoms on a square lattice confined by a uniform box potential. A natural region in the Hubbard phase diagram where spin and charge transport could differ is near the Mott insulator at half-filling, where charge transport is strongly suppressed, whereas spin transport can occur via super-exchange. Previous experiments have studied spin transport in strongly interacting Fermi gases without a lattice, both in three dimensions <cit.> and in two dimensions <cit.>. In those studies, spin diffusion was observed to attain the quantum limit of ∼ħ/m, where ħ is Planck's constant h divided by 2π and m is the particle mass. Here, we measure both the spin diffusion coefficient D_S and the spin conductivity σ_S. These transport coefficients dictate the response of the system to a spin-dependent force and are related through the Einstein relation, σ_S=D_Sχ, where χ is the uniform spin susceptibility, which can be measured independently.

