Strange metallic transport and superconductivity from spatially random interactions

“Strange” metals that do not follow the predictions of Fermi liquid theory are prevalent in materials that feature superconductivity arising from electron interactions. One potential way that their hallmark linear-in-temperature (T) resistivity survives down to low temperatures is through scattering by near-critical collective bosonic modes that exhibit spatial randomness. However, a clear picture of how this happens has not yet been provided in a realistic model free from artificial constructions, such as large-N limits and replica tricks. In this talk I will describe a realistic effective model of two-dimensional metals with spatially fully random antiferromagnetic interactions, in the vicinity of a spin-density wave transition. I will describe the solution of this model in a nonperturbative regime, using numerically exact, large-scale hybrid Monte Carlo simulation and exact averages over the quenched spatial randomness. Our simulations reproduce strange metals’ key experimental signature of linear-in-T resistivity with a universal “Planckian” transport scattering rate Γ_tr ~ k_BT/ℏ that is independent of coupling constants. We further find that strange metallicity in these systems is not associated with a quantum critical point and, instead, arises from a phase of matter with gapless antiferromagnetic fluctuations that lacks long-range correlations and spans an extended region of parameter space: a feature that is also observed in several experiments on cuprates. 

I will then describe how this phase diagram gets modified with the inclusion of a more realistic spatially uniform 'offset' of the interactions, which re-introduces the finite momentum of the spin-density wave fluctuations to the electrons.

I will further discuss how the numerically observed spatially localized overdamped modes mediate highly inhomogeneous superconductivity, which can be described by a modified Usadel equation in which the localized bosonic wave functions generate an effective large-scale correlated random potential and a random pairing vertex for the electrons.

Our work paves the way for an eventual microscopic understanding of the role of spatial disorder of collective excitations in determining important properties of correlated-electron materials.