Tunneling Effect in Gapped Graphene Disk in Magnetic Flux and Electrostatic Potential

TL;DR

This paper studies quantum tunneling in a gapped graphene Corbino disk influenced by magnetic flux and electrostatic potential, revealing how energy gaps and potentials modulate transmission and shot noise.

Contribution

It provides an explicit analytical analysis of tunneling and transport in gapped graphene disks with magnetic flux, incorporating effects of electrostatic potential and deriving conditions for Klein tunneling.

Findings

Energy gap suppresses tunneling and creates zero transmission singularities.

Transmission oscillates with radius ratio, reaching unity at large gaps.

Electrostatic potential controls the band gap's influence on tunneling.

Abstract

We investigate the tunneling effect of a Corbino disk in graphene in the presence of a variable magnetic flux $\Phi_{i}$ created by a solenoid piercing the inner disk under the effect of a finite mass term in the disk region $ (R_1< r<R_2) $ and an electrostatic potential. Considering different regions, we explicitly determine the associated eigenspinors in terms of Hankel functions. The use of matching conditions and asymptotic behavior of Hankel functions for large arguments, enables us to calculate transmission and other transport quantities. Our results show that the energy gap suppresses the tunneling effect by creating singularity points of zero transmission corresponding to the maximum shot noise peaks quantified by the Fano factor $ F $. The transmission as a function of the radii ratio $ R_2/R_1 $ becomes oscillatory with a decrease in periods and amplitudes. It can even reach one (Klein tunneling) for large values of the energy gap. The appearance of the minimal conductance at the points $ k_F R_1=R_1 \delta$ is observed. Finally we find that the electrostatic potential can control the effect of the band gap.