Related papers: Why Dirac points in graphene are where they are?
We derive a low-energy effective $\mathbf{k}\cdot\mathbf{p}$ Hamiltonians for monolayer C$_{3}$N at the $ \Gamma $ and $ M $ points of the Brillouin zone where the band edge in the conduction and valence band can be found. Our analysis of…
We demonstrate that the electronic spectrum of graphene in a one-dimensional periodic potential will develop a Landau level spectrum when the potential magnitude varies slowly in space. The effect is related to extra Dirac points generated…
The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a…
Rotated graphene multilayers form a new class of graphene related systems with electronic properties that drastically depend on the rotation angles. It has been shown that bilayers behave like two isolated graphene planes for large rotation…
We consider confinement of Dirac fermions in $AB$-stacked bilayer graphene by inhomogeneous on-site interactions, (pseudo-)magnetic field or inter-layer interaction. Working within the framework of four-band approximation, we focus on the…
Recent experiments have observed strongly correlated physics in twisted bilayer graphene (TBG) at very small angles, along with nearly flat electron bands at certain fillings. A good starting point in understanding the physics is a…
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…
We have studied how a generic bilayer kagome lattice behave upon layer rotation. We employed a Tight Binding model with one orbital per site and found (i) for low rotational angles, and at low energies, the same flat bands structure like in…
At magic twisted angles, Dirac cones in twisted bilayer graphene (TBG) can evolve into flat bands, serving as a critical playground for the study of strongly correlated physics. When chiral symmetry is introduced, rigorous mathematical…
We study the electronic properties of a twisted trilayer graphene, where two of the layers have Bernal stacking and the third one has a relative rotation with respect to the AB-stacked layers. Near the Dirac point, the AB-twisted trilayer…
A quantum graph model for a single sheet of graphene is extended to bilayer and trilayer Bernal-stacked graphene; the spectra are characterized and the dispersion relations explicitly obtained; Dirac cones are then proven to be present only…
The honeycomb lattice possesses a novel energy band structure, which is characterized by two distinct Dirac points in the Brillouin zone, dominating most of the physical properties of the honeycomb structure materials. However, up till now,…
The behaviour of a Dirac electron in graphene, under magnetic fields which are orthogonal to the layer, is studied. The initial problem is reduced to an equivalent one, where two one-dimensional Schr\"{o}dinger Hamiltonians $H^{\pm}$ are…
We investigate electronic band-structure images in reciprocal space of few layer graphene epitaxially grown on SiC(000-1). In addition to the observation of commensurate rotation angles of the graphene layers, the k-space images recorded…
We compute the energy spectrum of a nearest-neighbor electron hopping model for bi-layer graphene at commensurate twist angles. Specifically, we focus on the simplest bi-layer lattices, with moire patterns that have no subcells. The…
We consider magnetic breakdown in twisted bilayer graphene where electrons may hop between semiclassical $k$-space trajectories in different layers. These trajectories within a doubled Brillouin zone constitute a network in which an…
We study the band structures of hybrid graphene quantum dots subject to a magnetic flux and electrostatic potential. The system is consisting of a circular single layer graphene surrounded by an infinite bilayer graphene. By solving the…
Bilayer graphene twisted by a small angle shows a significant charge modulation away from neutrality, as the charge in the narrow bands near the Dirac point is mostly localized in the regions of the Moir\'e pattern with $AA$ stacking. The…
Graphene features topological edge bands that connect the pair of Dirac points through either sectors of the 1D Brillouin zone depending on edge configurations (zigzag or bearded). Because of their flat dispersion, spontaneous edge…
The Dirac equation is solved for triangular and hexagonal graphene quantum dots for different boundary conditions in the presence of a perpendicular magnetic field. We analyze the influence of the dot size and its geometry on their energy…