We demonstrate the existence of localized electron and hole states in a ring-shaped potential kink in biased bilayer graphene. Within the continuum description, we show that for sharp potential steps the Dirac equation describing carrier states close to the K (or K') point of the first Brillouin zone can be solved analytically for a circular kink/anti-kink dot. The solutions exhibit interfacial states which exhibit Aharonov-Bohm oscillations as functions of the height of the potential step and/or the radius of the ring

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 [Formula: see text] 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 [Formula: see text] 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.

A theoretical investigation of Jeans instability has been done incorporating dust charge gradient and dust polarization forces in a collisional magnetized dusty plasma. The dispersion relation is derived using three fluid theory by employing Boltzmann distribution of ions and electrons and retaining the complete dynamics of positively charged dust. To signify the effects of each parameter on Jeans instability the obtained general dispersion relation is further deduced considering parallel and perpendicular modes of propagation. It has been analyzed analytically as well as numerically that the growth rate of gravitational instability decreases with simultaneous presence of charge gradient force, collision frequency, thermal velocity and external magnetic field, but increases with the dust polarization force. The existence of dust charge gradient force and dust polarization force (along with external magnetic field) have been found to improve the criterion for Jeans instability. The relevance of the work to the collapse of dusty clouds has been discussed.

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