Geometry effects in topologically confined bilayer graphene loops

Abstract

We investigate the electronic confinement in bilayer graphene by topological loops of different shapes. These loops are created by lateral gates acting via gap inversion on the two graphene sheets. For large-area loops the spectrum is well described by a quantization rule depending only on the loop perimeter. For small sizes, the spectrum depends on the loop shape. We find that zero-energy states exhibit a characteristic pattern that strongly depends on the spatial symmetry. We show this by considering loops of higher to lower symmetry (circle, square, rectangle and irregular polygon). Interestingly, magnetic field causes valley splittings of the states, an asymmetry between energy reversal states, flux periodicities and the emergence of persistent currents.

Trivial and topological bound states in bilayer graphene quantum dots and rings

“…2d) the pattern of crossings is very regular and, as discussed in Ref. 23, can be explained with a quantization rule for 1d closed orbits, similar to the Bohr-Sommerfeld one. The topological ring of finite width (Fig.…”

“…We consider a 2d (xy) continuum model for the lowenergy excitations of BLG, already used in our previous works, 21,23 and also by many other authors (see Refs. 5 and 24 for reviews).…”

“…Previous works have investigated trivial dots and rings as well as topological rings, but the latter only with w = 0. 22,23 Here we will also explore the case of a topological ring with a finite w, where potential V a (r) vanishes and the electrons are essentially free to move.…”

“…They are topological because their motion is along the edge and exhibit valleymomentum locking [19][20][21] . When the wall forms a closed loop, one can create quantum dots and rings supporting topological bound states 22,23 . In this paper, we show that these states could be unambiguously detected by examining their behavior with an external magnetic field, which allows us to distinguish between both (trival and topological) binding mechanisms.…”

Trivial and Topological Bound States in Bilayer Graphene Quantum Dots and Rings

“…Previous works have investigated trivial dots and rings as well as topological rings, but the latter only with w ¼ 0. 22,23 Here, we will also explore the case of a topological ring with a finite w, where potential V a ðrÞ vanishes and the electrons are essentially free to move.…”