Topological confinement in graphene bilayer quantum rings

Abstract

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

Graphene under spatially varying external potentials: Landau levels, magnetotransport, and topological modes

“…16,23 In the case of symmetric 1D electric field SLs in BLG, four anisotropic Dirac cones are generated, two at zero energy and two at finite energy. The existence of these Dirac points can be seen 23 to arise from a series of coupled "topological" modes 15,23,25,26 that emerge along the zero line, where the parity of interlayer bias reverses. Interestingly, these Dirac points are exceptionally robust to the size of the bias modulation.…”

Electronic properties of graphene-based bilayer systems

“…[169]. This "topological" confinement is based on the idea of I. Martin et al [170] (it will be discussed in more detail in subsection 7.3).…”

Helical scattering and valleytronics in bilayer graphene

“…In the past, such interfaces have attracted attention because they guide valley-dependent states 9 that propagate along the interface; for transport in the perpendicular direction, they realize a pseudospin variant of a spin valve, 10 which allows electronic confinement. 11 By resolving the transport across the interface angularly in each valley, we find that the direction of perfect transmission is skewed away from normal incidence, see Figs. 1͑c͒-1͑h͒.…”