Asymmetry of nonlocal dissipation: From drift-diffusion to hydrodynamics

Abstract

We study dissipation in inhomogeneous two-dimensional electron systems. We predict a relatively strong current-induced spatial asymmetry in the heating of the electron and phonon systems -even if the inhomogeneity responsible for the electrical resistance is symmetric with respect to the current direction. We also show that the heat distributions in the hydrodynamic and impurity-dominated limits are essentially different. In particular, within a wide, experimentally relevant interval of driving fields, the dissipation profile in the hydrodynamic limit turns out to be asymmetric, and the characteristic spatial scale of the temperature distribution can be controlled by the driving field. By contrast, in the same range of parameters, impurity-dominated heating is almost symmetric, with the size of the dissipation region being independent of the field. This allows one to distinguish experimentally the hydrodynamic and impurity-dominated limits. Our results are consistent with recent experimental findings on transport and dissipation in narrow constrictions and quantum point contacts.arXiv:1906.03832v2 [cond-mat.mes-hall]

Dissipation without resistance: Imaging impurities at quantum Hall edges

“…Specifically, at a certain tip-impurity distance, the impurity level is fine-tuned by the tip voltage to resonance, which gives rise to the enhanced dissipation according to Eq. (15). The resonant character of dissipation in Eq.…”

“…The major result (15) only requires the existence of forward scattering at resonant impurities. However, edge reconstruction should be included to fully describe all the findings of Ref.…”

“…(B5) and (B6) by L/2 − x 0 , we get the expression for P imp as Eq. (15). Equations (B5) and (B6) indicate that the coupling between a chiral Fano system and the environment (the phonon bath) is enhanced by the on-resonance impurity.…”

“…This effect leads to dissipation (transfer of energy from electrons to phonons) along the quantum Hall edges with a homogeneous power density. It can be considered as an ultimate manifestation of nonlocal dissipation [14,15].…”

Heating of inhomogeneous electron flow in the hydrodynamic regime

“…A recent analysis [46] shows a great variety of different overheating regimes in a quasi-one-dimensional (quasi-1D) constriction [see Fig. 1(a)] with an inhomogeneous distribution of transport scattering rate.…”