Abstract
We investigate localized states of a quantum ring confinement in
monolayer graphene defined by a circular mass-related potential, which
can be induced e.g. by interaction with a substrate that breaks the
sublattice symmetry, where a circular line defect provides a change in
the sign of the induced mass term along the radial direction. Electronic
properties are calculated analytically within the Dirac-Weyl
approximation in the presence of an external magnetic field. Analytical
results are also compared with those obtained by the tight-binding
approach. Regardless of its sign, a mass term Delta is expected to open
a gap for low-energy electrons in Dirac cones in graphene. Both
approaches confirm the existence of confined states with energies inside
the gap, even when the width of the kink modelling the mass sign
transition is infinitely thin. We observe that such energy levels are
inversely proportional to the defect line ring radius and independent on
the mass kink height. An external magnetic field is demonstrated to lift
the valley degeneracy in this system and easily tune the valley index of
the ground state in this system, which can be polarized on either K or
K' valleys of the Brillouin zone, depending on the magnetic field
intensity. Geometrical changes in the defect line shape are considered
by assuming an elliptic line with different eccentricities. Our results
suggest that any defect line that is closed in a loop, with any
geometry, would produce the same qualitative results as the circular
ones, as a manifestation of the topologically protected nature of the
ring-like states investigated here.
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