相关论文: An abstract formulation of the flat band condition
We show that Schr\"odinger-type operators on discrete connected periodic graphs do not have flat bands for generic potentials.
In this work, we study an interacting tight-binding model of magic-angle twisted bilayer graphene (MATBG), with a twist angle of $1.05^\circ$. We derive effective theories based on a mean-field normal state at charge neutrality, thereby…
We analyze a description of twisted graphene bilayers, that incorporates deformation of the layers due to the nature modern interlayer potentials, and a modification of the hopping parameters between layers in the light of the classic…
The newly realized twisted graphene systems such as twisted bilayer graphene (TBG), twisted double bilayer graphene (TDBG), and twisted trilayer graphene (TTG) have attracted widespread theoretical attention. Therefore, a simple and…
Twisted graphene bilayers show a complex electronic structure, further modified by interaction effects. The main features can be obtained from effective models, which make use a few phenomenological parameters. We analyze the influence of…
Recent experiments discovered fractional Chern insulator states at zero magnetic field in twisted bilayer MoTe$_2$ [C23,Z23] and WSe$_2$ [MD23]. In this article, we study the MacDonald Hamiltonian for twisted transition metal…
We present a simple derivation of a continuum Hamiltonian for bilayer graphene with an arbitrary smooth lattice deformation -- technically in a fashion parametrized by displacement fields with small gradients. We show that this subsumes the…
Twisted bilayer graphene (TBLG) has emerged as an important platform for studying correlated phenomena, including unconventional superconductivity, in two-dimensional systems. The complexity of the atomic-scale structures in TBLG has made…
Twisted bilayer graphene (TBG) is known for exhibiting highly correlated phases at magic angles due to the emergence of flat bands that enhance electron-electron interactions. In the TBG chiral model, electronic wave function properties…
We show that bilayer graphene in the presence of a 2D superlattice potential provides a highly tunable setup that can realize a variety of flat band phenomena. We focus on two regimes: (i) topological flat bands with non-zero Chern numbers,…
This work theoretically explores how to emulate twisted double bilayer graphene with ultracold atoms in multiorbital optical lattices. In particular, the quadratic band touching of Bernal stacked bilayer graphene is emulated using a square…
Magic-angle twisted bilayer graphene (TBG) with its flat bands provides a rich platform for exploring emergent electronic orders. Similarly, periodically buckled monolayer graphene has been proposed as a tunable alternative for realizing…
We study flat bands and their topology in 2D materials with quadratic band crossing points (QBCPs) under periodic strain. In contrast to Dirac points in graphene, where strain acts as a vector potential, strain for QBCPs serves as a…
We address a simple but fundamental issue arising in the study of graphene, as well as of other systems that have a crystalline structure with more than one atom per unit cell. For these systems, the choice of the tight-binding basis is not…
We consider a family of periodic scalar operators for which one can define flat bands in the sense of Floquet-Bloch theory. One puzzling question originating in recent physics literature is a quantisation rule for the values of parameters…
We study the effects of heterostrain on moir\'e bands in twisted bilayer graphene and bilayer transition metal dichalcogenide (TMD) systems. For bilayer graphene with twist angle near $1^\circ$, we show that heterostrain significantly…
At a magic relative twist angle, magic angle twisted bilayer graphene (MATBG) has an octet of flat bands that can host strong correlation physics when partially filled. A key theoretical discovery in MATBG is the existence of ferromagnetic…
Twisted bilayer graphene exhibits isolated, relatively flat electronic bands near charge neutrality when the interlayer rotation is tuned to specific magic angles. These small misalignments, typically below 1.1{\deg}, result in long-period…
We consider four-component Dirac operators on domains in the plane. With suitable boundary conditions, these operators describe graphene quantum dots. The most general boundary conditions are defined by a matrix depending on four real…
The only kinematically-allowed phonon-scattering events for bands of subsonic fermions ($v_F < v_p$) are interband transitions, leading to different low-$T$ transport physics than in the typical supersonic case. We apply a kinetic theory of…