相关论文: Hofstadter Butterfly in Graphene
We provide a systematic real space derivation of the continuum Hamiltonian for a graphene bilayer starting from a microscopic lattice theory, allowing for an arbitrary inhomogeneous smooth lattice deformation, including a twist. Two…
Under a magnetic field perpendicular to an monolayer graphene, the existence of a two-dimensional periodic scatter array can not only mix Landau levels of the same valley for displaying split electron-hole Hofstadter-type energy spectra,…
We present a mainly analytical study of the entanglement spectrum of Bernal-stacked graphene bilayers in the presence of trigonal warping in the energy spectrum. Upon tracing out one layer, the entanglement spectrum shows qualitative…
The Hofstadter butterfly (HB) and mobility edges (MEs) are hallmark phenomena of quasiperiodic systems, yet their interplay remains elusive. Here, we demonstrate their coexistence within a tilt-induced quasiperiodic potential on a square…
We use an exact solution of the relaxation-time Boltzmann equation in a uniform AC electric field to describe the nonlinear optical response of graphene in the terahertz (THz). The cases of monolayer, bilayer and ABA-stacked trilayer…
Moir\'e superlattice in twisted bilayer graphene has been proven to be a versatile platform for exploring exotic quantum phases. Extensive investigations have been invoked focusing on the zero-magnetic-field phase diagram at the magic twist…
I revisit the problem of a charged particle on a two-dimensional lattice immersed in a constant (electro)magnetic field, and discuss the energy spectrum - Hofstadter's butterfly - from a new, quantum field theoretical perspective. In…
A low twist angle between the two stacked crystal networks in bilayer graphene enables self-organized lattice reconstruction with the formation of a periodic domain. This superlattice modulates the vibrational and electronic structures,…
The energy spectrum of massless Dirac fermions in graphene under two dimensional periodic magnetic modulation having square lattice symmetry is calculated. We show that the translation symmetry of the problem is similar to that of the…
Motivated by the observation of polarization superlattices in twisted multilayers of hexagonal boron nitride ($h$-BN), we address the possibility of using these heterostructures for tailoring the properties of multilayer graphene by means…
We study the relation between the global topology of the Hofstadter butterfly of a multiband insulator and the topological invariants of the underlying Hamiltonian. The global topology of the butterfly, i.e., the displacement of the energy…
The electronic properties of bilayer graphene strongly depend on relative orientation of the two atomic lattices. Whereas Bernal-stacked graphene is most commonly studied, a rotational mismatch between layers opens up a whole new field of…
Moir\'e superlattices formed in stacks of two or more 2D crystals with similar lattice structures have recently become excellent platforms to reveal new physics in low-dimensional systems. They are, however, highly sensitive to the angle…
We consider a tight-binding model recently introduced by Timmel and Mele for strained moir\'e heterostructures. We consider two honeycomb lattices to which layer antisymmetric shear strain is applied to periodically modulate the tunneling…
We study the superlattice minibands produced by the interplay between moir\'e pattern induced by hexagonal BN substrate on graphene layer and the interlayer coupling in bilayer graphene with Bernal stacking (BLG). We compare moir\'e…
Integral Apollonian packing, the packing of circles with integer curvatures, where every circle is tangent to three other mutually tangent circles, is shown to encode the fractal structure of the energy spectrum of two-dimensional Bloch…
Moir\'e superlattices with long-range periodicity exhibit Hofstadter energy spectra under accessible magnetic fields, enabling the exploration of emergent quantum phenomena through a hierarchy of fractal states. However, higher-order…
The effects of the long range electrostatic interaction in twisted bilayer graphene are described using the Hartree-Fock approximation. The results show a significant dependence of the band widths and shapes on electron filling, and the…
We present a geometric construction of a lattice that emulates the action of a gauge field on a fermion. The construction consists of a square lattice made of polymeric sites, where all clustered atoms are identical and represented by…
We outline an approach to endow a plain vanilla material with topological properties by creating topological bands in stacks of manifestly nontopological atomically thin materials. The approach is illustrated with a model system comprised…