Landau levels in biased graphene structures with monolayer-bilayer interfaces

Abstract

The electron energy spectrum in monolayer-bilayer-monolayer and in bilayer-monolayer-bilayer graphene structures is investigated and the effects of a perpendicular magnetic field and electric bias are studied. Different types of monolayer-bilayer interfaces are considered as zigzag (ZZ) or armchair (AC) junctions which modify considerably the bulk Landau levels (LLs) when the spectra are plotted as a function of the center coordinate of the cyclotron orbit. Far away from the two interfaces, one obtains the well-known LLs for extended monolayer or bilayer graphene. The LL structure changes significantly at the two interfaces or junctions where the valley degeneracy is lifted for both types of junctions, especially when the distance between them is approximately equal to the magnetic length. Varying the nonuniform bias and the width of this junction-to-junction region in either structure strongly influence the resulting spectra. Significant differences exist between ZZ and AC junctions in both structures. The densities of states (DOSs) for unbiased structures are symmetric in energy whereas those for biased structures are asymmetric. An external bias creates interface LLs in the gaps between the LLs of the unbiased system in which the DOS can be quite small. Such a pattern of LLs can be probed by scanning tunneling microscopy.

Isolated and hybrid bilayer graphene rings

“…The plateau-like and oscillatory features appearing in the energy spectrum can be understood as hybridization of the energy levels of the terminated systems, MLG QD and BLG antidot. Similar behavior was found for previous studies of MLG-BLG junctions [57,63,64].…”

“…Similar behavior was also noted for the double MLG-BLG junctions studied in Ref. [63] when the spectra are plotted as a function of the center coordinate of the cyclotron orbit.…”

“…Topographic images have revealed that multilayer samples exfoliated from graphite often contain atomic steps and islands of one or few layers of graphene [50][51][52][53][54]. They have been previously investigated both theoretically and experimentally, in different configurations such as single MLG-BLG junction [55][56][57][58][59][60][61], double MLG-BLG junctions (MLG-BLG-MLG) [62,63], and hybrid QD structures [64]. In all these studies the interface between MLG and BLG regions was considered as zigzag or armchair junctions which modify considerably the electronic properties of such structures.…”

Single-layer graphene with electronic properties of a gated bilayer

“…2, which is pinned to the conduction band at the cone and approaches the zero energy for larger values of k. This is the trace of the edge state localized at the zigzag-edge of the upper layer of the left BLG. The presence of such states has been reported also for SLG-BLG interfaces [31]. As reported in [32,33], the zigzagedge states of the SLG are localized at one sublattice only (red B sublattice in this case, see Fig.…”

Electronic Mach-Zehnder interference in a bipolar hybrid monolayer-bilayer graphene junction

“…For more details see Refs. [19,37]. In the presence of a perpendicular magnetic field B = Bẑ the dynamics of the carriers in MLG is described by the Dirac-Weyl Hamiltonian (for the K valley) [19,38]…”