Title: Beyond Drude transport in hydrodynamic metals

Speaker: Dr. Ashish Shukla, CPHT, Ecole Polytechnique

Abstract: Understanding the transport of charge and heat in metals has been a problem of interest for a long time. In typical metals, due to the inelastic scattering of electrons with lattice phonons as well as impurities happening at scales comparable to the elastic electron-electron scattering, the conduction of charge/heat does not conserve momentum and is diffusive in nature. This is qualitatively captured by the Drude model of transport, leading to conductivities inversely proportional to the momentum-relaxation rate. However, with the availability of ultra-clean materials in modern times, such as Graphene, it has now become possible to approach a transport regime in metallic phases where the conduction of charge/heat is hydrodynamic in nature. In such “hydrodynamic metals” momentum relaxes at a slow rate causing a Drude-like peak in the conductivities. Efforts have also been made in recent years to model such transport using the holographic Anti de Sitter/Conformal Field Theory (AdS/CFT) correspondence, where perturbations to bulk spacetime geometries arising as solutions to Einstein-Maxwell-Scalar theories lead to momentum-relaxation in the boundary theory. In this colloquium, I will provide an overview of hydrodynamic transport with approximate momentum conservation, as well as the holographic models that try to capture it via the AdS/CFT correspondence. I will also highlight the latest efforts to construct effective hydrodynamic theories for such transport employing background scalar fields that lead to a controlled breaking of spatial translation invariance, and hence a weak relaxation of momentum. These effective theories are quite powerful as they are able to capture both the leading and subleading momentum-relaxing effects, and lead to nontrivial experimentally observable consequences for thermoelectric transport.