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Topology and electron interactions are two central themes in modern condensed matter physics. Here we propose graphene based systems where both the band topology and interaction effects can be simply controlled with electric fields. We…
A number of moir\'e graphene systems have nearly flat topological bands where electron motion is strongly correlated. Though microscopically these systems are only quasiperiodic, they can typically be treated as translation invariant to an…
We study the electronic structures and topological properties of $(M+N)$-layer twisted graphene systems. We consider the generic situation that $N$-layer graphene is placed on top of the other $M$-layer graphene, and is twisted with respect…
Twisted bilayer graphene (TBG) hosts a rich landscape of electronic phases arising from the interplay between strong electron-electron interactions and nontrivial band topology. While the flat bands near zero energy are central to many…
Two monolayers of graphene twisted by a small `magic' angle exhibit nearly flat bands leading to correlated electronic states and superconductivity, whose precise nature including possible broken symmetries, remain under debate. Here we…
Monolayer graphene placed with a twist on top of AB-stacked bilayer graphene hosts topological flat bands in a wide range of twist angles. The dispersion of these bands and gaps between them can be efficiently controlled by a perpendicular…
We propose that the electronic structure of twisted bilayer graphene (TBG) can be understood as Dirac fermions coupled with opposite pseudo magnetic fields generated by the moir\'e pattern. The two low-energy flat bands from each monolayer…
We study the electronic properties of commensurate faulted bilayer graphene by diagonalizing the one-particle Hamiltonian of the bilayer system in a complete basis of Bloch states of the individual graphene layers. Our novel approach is…
We consider twisted bilayer graphene on a transition metal dichalcogenide substrate, where proximity-induced spin-orbit coupling significantly alters the eight flat bands which occur near the magic angle. The resulting band structure…
We use a lowest Landau level model to study the recent observation of an anomalous Hall effect in twisted bilayer graphene. This effective model is rooted in the occurrence of Chern bands which arise due to the coupling between the graphene…
We investigate the band structure of twisted monolayer-bilayer graphene (tMBG), or twisted graphene on bilayer graphene (tGBG), as a function of twist angles and perpendicular electric fields in search of optimum conditions for achieving…
Moir\'e systems have emerged in recent years as a rich platform to study strong correlations. Here, we will discuss a simple, experimentally feasible setup based on periodically strained graphene that reproduces several key aspects of…
Twisted bilayer graphene aligned with hexagonal boron nitride (TBG/hBN) hosts rich topological and correlated quantum phases, such as (fractional) Chern insulators, whose character is dictated by the topology of the moir\'{e} flat band.…
We consider bilayer graphene in the presence of spin orbit coupling, to assess its behavior as a topological insulator. The first Chern number $n$ for the energy bands of single and bilayer graphene is computed and compared. It is shown…
Moir\'e materials host a wealth of intertwined correlated and topological states of matter, all arising from flat electronic bands with nontrivial quantum geometry. A prominent example is the family of alternating-twist magic-angle graphene…
Twisted trilayer graphene (TLG) may be the simplest realistic system so far, which has flat bands with nontrivial topology. Here, we give a detailed calculation about its band structures and the band topology, i.e. valley Chern number of…
We study the edge states of twisted bilayer graphene and their topological origin. We show that the twisted bilayer graphene has special edge states associated with the moir\'{e} pattern, and the emergence of these moir\'{e} edge states is…
Moir\'e structures formed by twisting three layers of graphene with two independent twist angles present an ideal platform for studying correlated quantum phenomena, as an infinite set of angle pairs is predicted to exhibit flat bands.…
Flatbands with extremely narrow bandwidths on the order of a few mili-electron volts can appear in twisted multilayer graphene systems for appropriate system parameters. Here we investigate the electronic structure of a twisted bi-bilayer…
Moir\'e superlattices engineer band properties and enable observation of fractal energy spectra of Hofstadter butterfly. Recently, correlated-electron physics hosted by flat bands in small-angle moir\'e systems has been at the foreground.…