Boundary Conditions for Electron Flow in Graphene in the Hydrodynamic Regime

TL;DR

This paper investigates how different boundary conditions affect electron flow in graphene's hydrodynamic regime, analyzing potential distributions for various boundary scenarios and source-sink orientations to guide experimental identification.

Contribution

It provides a systematic analysis of boundary conditions on electron flow in graphene and compares geometries for experimental detection of hydrodynamic behavior.

Findings

Potential distribution varies with boundary conditions

Certain geometries are more suitable for experimental identification

Boundary conditions influence flow characteristics

Abstract

Graphene has generated a lot of research interest due to its special properties, which include a hydrodynamic regime. It is not yet clear however which boundary condition such a hydrodynamic current flow satisfies. The aim of this paper is to investigate the effect of different boundary conditions on the potential in an infinite strip of graphene, in which the electrons can be treated hydrodynamically. The boundary conditions on the current range continuously from no-slip to a free boundary. We analyse the situation for two different orientations of the source and sink, inspired by recent papers. We discuss which geometry is better suited for identifying the hydrodynamic regime and experimentally determining the boundary conditions.