Related papers: Magic angle (in)stability and mobility edges in di…
Breakthroughs in two-dimensional van der Waals heterostructures have revealed that twisting creates a moir\'e pattern that quenches the kinetic energy of electrons, allowing for exotic many-body states. We show that cold-atomic, trapped…
Magic-angle twisted bilayer graphene is the best studied physical platform featuring moire potential induced narrow bands with non-trivial topology and strong electronic correlations. Despite their significance, the Chern insulating states…
When two monolayers of graphene are stacked with a small relative twist angle, the resulting band structure exhibits a remarkably flat pair of bands at a sequence of 'magic angles' where correlation effects can induce a host of exotic…
The chiral Hamiltonian for twisted graphene bilayers is analyzed in terms of its squared Hamiltonian which removes the particle-hole symmetry and thus one bipartite lattice, allowing to write the Hamiltonian in terms of a $2\times 2$…
Using scanning probe microscopy and spectroscopy, we explore the spatial symmetry of the electronic wavefunctions of twisted bilayer graphene at the "magic angle" of 1.1 degrees. This small twist angle leads to a long wavelength moir\'e…
Motivated by recent Physical Review Letters of Wang-Liu and Ledwith-Vishwanath-Khalaf, we study Tarnopolsky-Kruchkov-Vishwanath chiral model of two sheets of $n$-layer Bernal stacked graphene twisted by a small angle using the framework…
The interest in the properties of edge states in Chern insulators and in $\mathbb{Z}_2$ topological insulator has increased rapidly in recent years. We present calculations on how to influence the transport properties of chiral and helical…
We investigate the effect of a magnetic field on the band structure of bilayer graphene with a magic twist angle of 1.08{\deg}. The coupling of a tight-binding model and the Peierls phase allows the calculation of the energy bands of…
We theoretically study the electronic structure of magic-angle twisted bilayer graphene with disordered moir\'e patterns. By using an extended continuum model incorporating non-uniform lattice distortion, we find that the local density of…
Bilayer graphene twisted at the angle of about 1.1{\deg} better known as magic angle, exhibits ultra-flat moir\'e superlattice bands that are a source of highly-tunable, exotic quantum phenomena. Such phenomena, like superconductivity,…
Multilayer moir\'e materials can exhibit topological electronic features yet are inherently quasiperiodic -- leading to wave function interference whose Anderson-localizing tendency can be mitigated by topology. We consider a quasiperiodic…
We investigate twisted bilayer graphene near charge neutrality using a generalized Bistritzer-MacDonald continuum model, accounting for corrugation effects. The Fermi velocity vanishes for particular twist angles properly reproducing the…
We present transport measurements of bilayer graphene with 1.38{\deg} interlayer twist and apparent additional alignment to its hexagonal boron nitride cladding. As with other devices with twist angles substantially larger than the magic…
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…
Theoretical and experimental studies have verified the existence of ``magic angles'' in twisted bilayer graphene, where the twist between layers gives rise to flat bands and consequently highly correlated phases. Narrow bands can also exist…
Angle disorder is an intrinsic feature of twisted bilayer graphene and other moir\'e materials. Here, we discuss electron transport in twisted bilayer graphene in the presence of angle disorder. We compute the local density of states and…
One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is the emergence of ferromagnetic Slater determinants as exact ground states for the interacting Hamiltonian at the chiral limit. This discovery…
We provide a mathematical account of the recent Physical Reviews Letter by Tarnopolsky--Kruchkov--Vishwanath. The new contributions are a spectral characterization of magic angles, its accurate numerical implementation and an exponential…
Recent experiments on bilayer graphene twisted near the magic angle have observed spontaneous integer quantum Hall states in the presence of an aligned hexagonal boron nitride (hBN) substrate. These states arise from valley ferromagnetism,…
The emergence of flat bands in twisted bilayer graphene at the magic angle can be understood in terms of a vanishing Fermi velocity of the Dirac cone. This is associated with van Hove singularities approaching the Fermi energy and becoming…