# Numerical study of the negative nonlocal resistance and the backflow current in a ballistic graphene system

## TL;DR

This study uses non-equilibrium Green's function calculations to explore negative nonlocal resistance and backflow currents in ballistic graphene, revealing vortex formation and boundary collision effects.

## Contribution

It provides a detailed numerical analysis of vortex-induced negative resistance in ballistic graphene, highlighting the role of boundary collisions and nonlocal effects.

## Key findings

- Vortex formation causes negative nonlocal resistance.
- Boundary collisions induce the vortex in ballistic graphene.
- Breakdown of the nonlocal Wiedemann-Franz law observed.

## Abstract

Besides the giant peak of the nonlocal resistance $R_{NL}$, an anomalous negative value of $R_{NL}$ has been observed in graphene systems, while its formation mechanism is not quite understood yet. In this work, utilizing the non-equilibrium Green's function method, we calculate the local-current flow in an H-shaped non-interacting graphene system locating in the ballistic regime. Similar to the previous conclusions made from the viscous regime, the numerical results show that a local-current vortex appears between the nonlocal measuring terminals, which induces a backflow current and a remarkable negative voltage drop at the probe. Specifically, the stronger the vortex exhibits, the more negative $R_{NL}$ manifests. Besides, a spin-orbital coupling is added as an additional tool to study this exotic vortex, which is not a driving force for the arising vortex at all. Moreover, a breakdown of the nonlocal Wiedemann-Franz law is obtained in this ballistic system, and two experimental criteria are further provided to confirm the existence of this exotic vortex. Notably, a discussion is made that the vortex actually originates from the collision between the flowing current and the boundaries, due to the long electron mean free path and the consequent ballistic transport caused by the specific linear spectrum of graphene.