Current distribution in a slit connecting two graphene half-planes

TL;DR

This paper studies how viscous and Ohmic dissipation influence electric current distribution in a graphene slit, revealing boundary-condition-dependent behaviors and providing insights for experimental observation.

Contribution

It analyzes the combined effects of viscous and Ohmic dissipation on current profiles in graphene, highlighting boundary condition impacts and experimental conditions.

Findings

Current profile shifts from concave to convex under no-slip conditions.

No qualitative difference between profiles in Ohmic and viscous limits with no-stress boundary.

Boundary conditions significantly affect current distribution behavior.

Abstract

We investigate the joint effect of viscous and Ohmic dissipation on electric current flow through a slit in a barrier dividing a graphene sheet in two. In the case of the no-slip boundary condition, we find that the competition between the viscous and Ohmic types of the charge flow results in the evolution of the current density profile from a concave to convex shape. We provide a detailed analysis of the evolution and identify favorable conditions to observe it in experiment. In contrast, in the case of the no-stress boundary condition, there is no qualitative difference between the current profiles in the Ohmic and viscous limits. The dichotomy between the behavior corresponding to distinct boundary conditions could be tested experimentally.