The focusing of electron flow in a bipolar Graphene ribbon with different chiralities

TL;DR

This paper investigates electron flow focusing in graphene ribbons with different chiralities, revealing how edge type, energy levels, and magnetic fields influence the focusing effect in p-n junctions.

Contribution

It provides a detailed analysis of electron focusing in graphene ribbons with armchair and zigzag edges, including effects of junction smoothness and magnetic fields, which was not previously comprehensively studied.

Findings

Perfect focusing in armchair ribbons across the Dirac regime.

Limited focusing in zigzag ribbons at low energies.

Focusing pattern persists despite junction smoothness, but magnetic fields smear the effect.

Abstract

The focusing of electron flow in a symmetric p-n junction (PNJ) of graphene ribbon with different chiralities is studied. Considering the PNJ with the sharp interface, in a armchair ribbon, the electron flow emitting from $(-L,0)$ in n-region can always be focused perfectly at $(L,0)$ in p-region in the whole Dirac fermion regime, i.e. in whole regime $E_0<t$ where $E_0$ is the distance between Dirac-point energy and Fermi energy and $t$ is the nearest hopping energy. For the bipolar ribbon with zigzag edge, however, the incoming electron flow in n-region is perfectly converged in p-region only in a very low energy regime with $E_0<0.05t$. Moreover, for a smooth PNJ, electrons are backscattered near PNJ, which weakens the focusing effect. But the focusing pattern still remains the same as that of the sharp PNJ. In addition, quantum oscillation in charge density occurs due to the interference between forward and backward scattering. Finally, in the presence of weak perpendicular magnetic field, charge carriers are deflected in opposite directions in the p-region and n-region. As a result, the focusing effect is smeared. The lower energy $E_0$, the easier the focusing effect is destroyed. For the high energy $E_0$ (e.g. $E_0=0.9t$), however, the focusing effect can still survive in a moderate magnetic field on order of one Tesla.