Heating of inhomogeneous electron flow in the hydrodynamic regime: Current-inducedtemperature asymmetry

We study the temperature profile of an inhomogeneous 2D sample in the Hydrodynamic regime. The in-homogeneity is governed by the non-uniform momentum relaxation time of the constricted area. In this paper, we consider a circular-shape constriction where the inhomogeneity decays exponentially from its center. We have observed two features that have not been fully appreciated yet: (i) the asymmetry of the temperature profile ---- although the constriction is itself symmetric, and (ii) A 2D Landauer-dipole feature that is independent of the electron-electron interaction range. The similarity of this feature with that in 3D indicates the universality of Landauer-dipole in Hydrodynamic systems. Our phenomenological study further supports these two features.