Artificial electric field and electron hydrodynamics

In the electron dynamics in quantum matter, the Berry curvature of the electronic wave function provides the artificial magnetic field (AMF) in momentum space, which leads to non-trivial contributions to transport coefficients. It is known that in the presence of electron-electron and/or electron-phonon interactions, there is an extra contribution to the electron dynamics due to the artificial electric field (AEF) in momentum space. In this work, we construct hydrodynamic equations for the electrons in time-reversal invariant but inversion-breaking systems and find the novel hydrodynamic coefficients related to the AEF. Furthermore, we investigate the novel linear and non-linear transport coefficients in presence of the AEF.