Electronic confinement in graphene quantum rings due to substrate-induced mass radial kink

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 [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.

Valley filtering in graphene due to substrate-induced mass potential

“…Such symmetry breaking opens a gap in monolayer graphene band structure [19][20][21][22], that can be theor etically described as a mass for the Dirac fermions within the continuum model framework for low energy electrons in graphene [2]. A defect line in the substrate is then enough to create a mass kink [18,24] and thus create unidirectional chiral states in its energy spectrum, propagating through a channel parallel to the mass kink. Therefore, as an alternative to previously mentioned valley filtering devices, in this case, it is the substrate lattice, not the graphene lattice, that has to be modified to provide and control the valley filtering effect.…”

Gap opening in graphene nanoribbons by application of simple shear strain and in-plane electric field

“…A similar symmetry break also opens a gap when monolayer graphene is deposited on substrates that possess a honeycomb lattice consisting of different atomic elements (e.g. SiC [56][57][58] and hexagonal boro nitride [59][60][61][62][63]), due to the fact that interactions between carbon atoms in the graphene layer and the different species for different sublattices in the substrate result into a bias between the two sublattices of monolayer graphene. However, by distorting the zigzag GNR, one notice in figure 2(c) for γ = 10% and F = 0 that the main effect of the shear strain is to lift the levels degeneracy of the bulk states around k x = ±π/(a √ 3), as a consequence of the symmetry break of the hopping energy.…”

Magnetic field induced vortices in graphene quantum dots

“…The advantage of having such analytical expression for the eigenenergies lies on the possibility of identifying the angular momentum nature of the eigenstates obtained from the numerical TB approach. In cases where the circular symmetry is broken, such as in triangular and square dots, the eigenstates are no longer expected to exhibit simply circular currents along the dot edges, [32][33][34][35][36][37][38][39][48][49][50][53][54][55] but the analytical solution given here still provides important information on the vortex/antivortex pattern expected for these geometries, as we will see further.…”

“…Such infinite mass, described by a staggered potential M i = +V (−V ) for sites of sublattice A (B) of the honeycomb lattice of graphene, opens a gap in the energy spectrum, which avoid electrons to come out of the dot. Previous works studied theor etically the confined states by using a similar approach for graphene [32][33][34][35][36][37][38][39], bilayer [40,41], and trilayer [42] graphene nanostructures obtained by using the infinite mass potential. This is supposed to provide quantum confinement as much as cutting the graphene dot, but, as we will discuss latter on, edge effects play an important role in the latter case, making the energy spectrum and local current densities different as compared to the infinite mass case.…”