Related papers: Quasicrystalline electronic states in 30$^\circ$ r…
We study theoretically many-body properties of magic-angle twisted bilayer graphene for different doping levels. Our investigation is focused on the emergence, stability, and manifestations of nematicity of the ordered low-temperature…
We theoretically study the effects of electron-electron interaction in twisted bilayer graphene in applied transverse dc electric field. When the twist angle is not very small, the electronic spectrum of the bilayer consists of four Dirac…
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…
Here we show that the Pfaffian state proposed for the $\frac52$ fractional quantum Hall states in conventional two-dimensional electron systems can be readily realized in a bilayer graphene at one of the Landau levels. The properties and…
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…
Quasicrystals represent a category of rarely structured solids that challenge traditional periodicity in crystal materials. Recent advancements in the synthesis of two-dimensional (2D) van der Waals materials have paved the way for…
In this paper, we propose a general mechanism for the existence of quasicrystals in spatially extended systems (partial differential equations with Euclidean symmetry). We argue that the existence of quasicrystals with higher order…
We investigate the effect of electron-phonon interactions (EPI) in systems exhibiting one or more flat electron bands close to the Fermi level and a comparatively large phonon energy scale. After solving the self-consistent full-bandwidth…
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…
Novel physical properties have been reported recently by stacking graphene-like systems in different configurations. Here, we explore the nature of emergent localized states at the edges of twisted bilayer graphene nanoribbons. Based on an…
Quasi-crystals are aperiodic structures that present crystallographic properties which are not compatible with that of a single unit cell. Their revolutionary discovery in a metallic alloy, less than three decades ago, has required a full…
Stacking two-dimensional layered materials such as graphene and transitional metal dichalcogenides with nonzero interlayer twist angles has recently become attractive because of the emergence of novel physical properties. Stacking of…
We calculate the electronic structure in quasiperiodic double-moir\'e systems of graphene sandwiched by hexagonal boron nitride, and identify the topological invariants of energy gaps. We find that the electronic spectrum contains a number…
Stacking two atomic crystals with a twist between their crystal axes produces moir\'e potentials that modify the electronic properties. Here we show that double moir\'e potentials generated by superposing three atomic crystals create a new…
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,…
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…
We study, within the tight-binding approximation, the electronic properties of a graphene bilayer in the presence of an external electric field applied perpendicular to the system -- \emph{biased bilayer}. The effect of the perpendicular…
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…
Charge neutral bilayer graphene has a gapped ground state as transport experiments demonstrate. One of the plausible such ground states is layered antiferromagnetic spin density wave (LAF) state, where the spins in top and bottom layers…
Incommensurately twisted graphene bilayers are described by long-wavelength theories, but to date such theories exist only at small angles of interlayer rotation. We construct a long wavelength theory without such a restriction, instead…