相关论文: Graphene quantum dot on boron nitride: Dirac cone …
Self-similarity and fractals have fascinated researchers across various disciplines. In graphene placed on boron nitride and subjected to a magnetic field, self-similarity appears in the form of numerous replicas of the original Dirac…
The moir\'e potential of graphene on hexagonal boron nitride (hBN) generates a supercell sufficiently large as to thread a full magnetic flux quantum $\Phi_0$ for experimentally accessible magnetic field strengths. Close to rational…
Lateral superlattices have attracted major interest as this may allow one to modify spectra of two dimensional electron systems and, ultimately, create materials with tailored electronic properties. Previously, it proved difficult to…
Van der Waals heterostructures comprise a new class of artificial materials formed by stacking atomically-thin planar crystals. Here, we demonstrate band structure engineering of a van der Waals heterostructure composed of a monolayer…
Van der Waals heterostructures of graphene and hexagonal boron nitride feature a moir\'e superlattice for graphene's Dirac electrons. Here, we review the effects generated by this superlattice, including a specific miniband structure…
The adhesion of graphene on slightly lattice-mismatched surfaces, for instance of hexagonal boron nitride (hBN) or Ir(111), gives rise to a complex landscape of sublattice symmetry-breaking potentials for the Dirac fermions. Whereas a gap…
Intricate interplay between the periodicity of the lattice structure and that of the cyclotron motion gives rise to a well-known self-similar fractal structure of the energy eigenvalue, known as the Hofstadter butterfly, for an electron…
The Schr\"odinger equation dictates that the propagation of nearly free electrons through a weak periodic potential results in the opening of band gaps near points of the reciprocal lattice known as Brillouin zone boundaries. However, in…
The fractal spectrum of magnetic minibands (Hofstadter butterfly), induced by the moir\'e super- lattice of graphene on an hexagonal crystal substrate, is known to exhibit gapped Dirac cones. We show that the gap can be closed by slightly…
The propagation of Dirac fermions in graphene through a long-period periodic potential would result in a band folding together with the emergence of a series of cloned Dirac points (DPs). In highly aligned graphene/hexagonal boron nitride…
In fractionally filled Landau levels there is only a small energy difference between broken translational symmetry electron-crystal states and exotic correlated quantum fluid states. We show that the spatially periodic substrate interaction…
We performed calculations of electronic, optical and transport properties of graphene on hBN with realistic moir\'e patterns. The latter are produced by structural relaxation using a fully atomistic model. This relaxation turns out to be…
In the presence of a magnetic field and an external periodic potential, the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter's butterfly. In this…
We calculate the electronic spectrum of bilayer graphene in perpendicular magnetic fields nonperturbatively. To accommodate arbitrary displacements between the two layers, we apply a periodic gauge based on singular flux vortices of phase…
Two-dimensional electron systems in both magnetic fields and periodic potentials are described by Hofstadter butterfly, a fundamental problem of solid-state physics. While moir\'e systems provide a powerful method to realize this spectrum,…
Electronic properties of the graphene layer sandwiched between two hexagonal boron nitride sheets have been studied using the first-principles calculations and the minimal tight-binding model. It is shown that for the ABC-stacked structure…
Recent progress in preparing well controlled 2D van der Waals heterojunctions has opened up a new frontier in materials physics. In this paper we address the intriguing energy gaps that are sometimes observed when a graphene sheet is placed…
We present an overview of the theoretical understanding of Hofstadter butterflies in monolayer and bilayer graphene. After a brief introduction on the past work in conventional semiconductor systems, we discuss the novel electronic…
Hexagonal Boron Nitride substrates have been shown to dramatically improve the electric properties of graphene. Recently, it has been observed that when the two honeycomb crystals are close to perfect alignment, strong lattice distortions…
We calculate the energy bands for graphene monolayers when electrons move through a periodic electrostatic potential in the presence of a uniform perpendicular magnetic field. We clearly demonstrate the quantum fractal nature of the energy…