Seminar

In the standard treatment of electrical transport through a metallic wire, electrons are assumed to undergo collisions with impurities or lattice vibrations, which degrade their momentum. This picture underlies the usual derivation of Ohm's law. On the other hand, the transport of fluids (like water) through a pipe is fundamentally different because the fluid particles undergo momentumpreserving collisions among themselves. When momentum can be conserved in the bulk of the electron fluid, it is in principle possible to drive charge and heat heat currents through the application of a gradient in the flow velocity of the fluid and also to drive a momentum current by applying an electric field or a temperature gradient. In this talk, I will show that these responses can be expressed in terms of vortical coefficients in linear response. These coefficients complement the usual conductivities (the electrical, thermal and Peltier conductivities) in providing a complete description of transport of the electron fluid in the hydrodynamic regime. I will argue that inversion symmetry has to be broken for these coefficients to be non-zero which can be achieved if the electrons have a non-zero Berry curvature coming from band structure. General expressions for the coefficients will be derived within a semi-classical approximation and also for a microscopic toy model.