SFB 1170


    Hydrodynamics and gauge/gravity duality in condensed matter systems


    A very active current research topic concerns the question if and how hydrodynamics may be applied to electrons in a solid. In a general sense, hydrodynamics is a low-energy effective field theory for long wavelength fluctuations. For this project, we will construct a general hydrodynamic expansion relevant for electronic fluids in solids and calculate particular transport coefficients both at weak and at strong coupling. For strongly correlated systems, the success of applying hydrodynamics is intimately linked to the application of suitable generalizations of the AdS/CFT correspondence, which we will also use here. Generalizations of AdS/CFT are referred to as gauge/gravity duality. Moreover, we will apply our general results on hydrodynamics to two examples: Weyl semimetals and topological insulators (HgTe in particular). For HgTe, we will establish the parameter regimes for the transition between the ballistic Knudsen regime and the regime dominated by electron-electron scattering, leading to hydrodynamic behavior. For the Weyl semimetals we will take into account the influence of axial anomalies, both for charge and thermal transport. We will also study the influence of external magnetic fields. A second closely related focus of the project will be concerned with applying gauge/gravity duality to strongly correlated electrons interacting with a magnetic impurity. We will establish a new gravity model complementary to previous results, and apply it to helical liquids and to nonequilibrium configurations. In addition to these applications, new insights into the working mechanisms of gauge/gravity duality will be obtained by comparing the new dual gravity model to variants of the Kondo model.