Magnetic field induced confinement–deconfinement transition in graphene quantum dots

Abstract

Massless Dirac particles cannot be confined by an electrostatic potential. This is a problem for making graphene quantum dots but confinement can be achieved with a magnetic field and here general conditions for confined and deconfined states are derived. There is a class of potentials for which the character of the state can be controlled at will. Then a confinement-deconfinement transition occurs which allows the Klein paradox to be probed experimentally in graphene dots. A dot design suitable for this experiment is presented.

Zero-energy states in graphene quantum dots and rings

“…4 As a result of Klein tunneling, many considerations of axially symmetric potential wells maintain that confinement inside electrostatic quantum dots is impossible. 5 Instead, focus has been placed on formation of confined states within graphene by the application of magnetic fields perpendicular to the graphene plane [6][7][8][9] or on engineering specialized devices which introduce mass-like terms. [10][11][12] Nonetheless, previous authors have studied the manipulation of charge carriers by electrostatic fields such as the creation of quasibound states in quantum dots, whose lifetimes are long but not infinite, as certain angular momenta correspond to trajectories incident on the potential barrier with low transmission probabilities.…”

Electron confinement in single layer graphene quantum dots: Semiclassical approach

“…Interestingly, there are potentials for which the confinement is experimentally tunable, that is the tail of the dot wave function can be changed from exponentially decaying to oscillatory just by varying the strength of the potential or the magnetic field. Further, the same effect occurs in a realistic model of a graphene dot [5].…”

“…This results in quasi-confined states [3,4] that are similar to scattering resonances. However it has recently been shown that it is possible to confine electrons with a combination of electric and magnetic fields [5]. The magnetic field gives the dot states an exponentially decaying tail while the electrostatic potential defines the centre around which the state is localised.…”

“…Confinement in this situation is conditional and the conditions for confinement are derived exactly in ref. [5]. These conditions depend on both the form of the potential and its parameters.…”

“…[5] were computed numerically but it is desirable to have analytic solutions to obtain maximum insight into the physics. Although there are very few cases where the two-component radial equations for a graphene dot can be solved exactly, it is possible to make some approximations that describe the confined states accurately.…”