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Twisted bilayer graphene (TBLG) subject to a sequence of commensurate external periodic potentials reveals the formation of moir\'{e} fractals (MF) that share striking similarities with the central place theory (CPT) of economic geography,…
We show that the twisted graphene bilayer can reveal unusual topological properties at low energies, as a consequence of a Dirac-point splitting. These features rely on a symmetry analysis of the electron hopping between the two layers of…
We show that the entire continuous model of twisted bilayer graphene (TBG) (and not just the two active bands) with particle-hole symmetry is anomalous and hence incompatible with a lattice model. Previous works, e.g., [Phys. Rev. Lett.…
The moire flat bands in twisted bilayer graphene have attracted considerable attention not only because of the emergence of correlated phases but also due to their nontrivial topology. Specifically, they exhibit a new class of topology that…
We show that the electronic structure of the low-energy bands in the small angle-twisted bilayer graphene consists of a series of semi-metallic and topological phases. In particular we are able to prove, using an approximate low-energy…
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.…
The observation of delicate correlated phases in twisted heterostructures of graphene and transition metal dichalcogenides suggests that moir\'e flat bands are intrinsically resilient against certain types of disorder. Here, we investigate…
Several numerical studies have shown that the electronic properties of twisted bilayers of graphene (TBLG) and transition metal dichalcogenides (TMDs) are tunable by strain engineering of the stacking layers. In particular, the flatness of…
Twisted bilayer graphene (TBG) is a recently discovered two-dimensional superlattice structure which exhibits strongly-correlated quantum many-body physics, including strange metallic behavior and unconventional superconductivity. Most of…
Low-energy moir\'e flat bands in magic-angle twisted bilayer graphene (tBG) have demonstrated incredible potentials to exhibit rich exotic quantum phenomena. Theoretically, the moir\'e flat bands of tBG are based on the extended structures,…
We investigate the electronic structure of a twisted multilayer graphene system forming a moir\'e pattern. We consider small twist angles separating the graphene sheets and develop a low-energy theory to describe the coupling of Dirac Bloch…
We investigate the effects of single, multiple, and extended defects in the form of non-magnetic impurities and vacancies in twisted bilayer graphene (TBG) at and away from the magic angle, using a fully atomistic model and focusing on the…
Twisted bilayer systems with discrete magic angles, such as twisted bilayer graphene featuring moir\'{e} superlattices, provide a versatile platform for exploring novel physical properties. Here, we discover a class of superflat bands in…
Twisted bilayer graphene (TBG) near "magic angles" has emerged as a rich platform for strongly correlated states of two-dimensional Dirac semimetals. Here we show that twisted bilayers of thin-film magnetic topological insulators (MTI) with…
The recent discovery of superconductivity in magic-angle twisted bilayer graphene has sparked a renewed interest in the strongly-correlated physics of $sp^2$ carbons, in stark contrast to preliminary investigations which were dominated by…
The generalized tight-binding model is developed to investigate the magneto-electronic properties in twisted bilayer graphene system. All the interlayer and intralayer atomic interactions are included in the Moire superlattice. The twisted…
Twisted bilayer graphene (TBG) can host the moir\'{e} energy flat bands with two-fold degeneracy serving as a fruitful playground for strong correlations and topological phases. However, the number of degeneracy is not limited to two.…
The existence of Bloch flat bands provides an facile pathway to realize strongly correlated phenomena in materials. Using density-functional theory and tight-binding approach, we show that the flat bands can form in twisted bilayer of…
We investigate magic-angle twisted bilayer graphene (MATBG) with proximity-induced Ising and Rashba spin-orbit couplings (SOC) in the top layer, as recently achieved experimentally. Utilizing the Bistritzer-MacDonald model with SOCs, we…
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…