Electronic properties of a graphene antidot in magnetic fields

TL;DR

This paper explores unique electronic behaviors of graphene antidots in magnetic fields, revealing phenomena like near-complete electron confinement, wavefunction symmetry due to Klein tunneling, and coupling with edge states, with proposed experimental tests.

Contribution

It uncovers novel properties of graphene antidots, including wavefunction symmetries and edge state interactions, advancing understanding of Dirac electron behavior in nanostructures.

Findings

Electron probability can be nearly one inside the barrier

Existence of dot states with identical wavefunctions but different energies

Strong coupling between antidot states and zigzag edge states

Abstract

We report on several unusual properties of a graphene antidot created by a piecewise constant potential in a magnetic field. We find that the total probability of finding the electron in the barrier can be nearly one while it is almost zero outside the barrier. In addition, for each electron state of a graphene antidot there is a dot state with exactly the same wavefunction but with a different energy. This symmetry is a consequence of Klein tunneling of Dirac electrons. Moreover, in zigzag nanoribbons we find strong coupling between some antidot states and zigzag edge states. Experimental tests of these effects are proposed.