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A remarkable feature of the band structure of bilayer graphene at small twist angle is the appearance of isolated bands near neutrality, whose bandwidth can be reduced at certain magic angles (eg. $\theta\sim 1.05^\circ$). In this regime,…
Inter-twisted bilayers of two-dimensional (2D) materials can host low-energy flat bands, which offer opportunity to investigate many intriguing physics associated with strong electron correlations. In the existing systems, ultra-flat bands…
We investigate the effect of shear and strain in graphene bilayers, under conditions where the distortion of the lattice gives rise to a smooth one-dimensional modulation in the stacking sequence of the bilayer. We show that strain and…
Moir\'e superlattices created by the twisted stacking of two-dimensional crystalline monolayers can host electronic bands with flat energy dispersion in which interaction among electrons is strongly enhanced. These superlattices can also…
We theoretically study the lattice relaxation in the twisted bilayer graphene (TBG) and its effect on the electronic band structure. We develop an effective continuum theory to describe the lattice relaxation in general TBGs and obtain the…
Twisted bilayer graphene (tBLG) represents a family of unique materials with optoelectronic properties tuned by the rotation angle between the two layers. The presented work shows an additional way of tweaking the electronic structure of…
A theoretical model is presented to compute the electronic band structures and optical absorption spectra for twisted incommensurate few-layers graphene (tLFG) systems of arbitrary architecture. This is accomplished using an integrated…
We introduce a minimum tight-binding model with only three parameters extracted from graphene and untwisted bilayer graphene. This model reproduces quantitatively the electronic structure of not only these two systems and bulk graphite near…
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 investigate the topological heavy-fermion (THF) model of magic-angle twisted bilayer graphene (MATBG) in the projected limit, where only the flat bands are present in the low-energy spectrum. Such limit has been previously analyzed in…
In a groundbreaking experimental advance it was recently shown that by stacking two sheets of graphene atop of each other at a twist angle close to one of the so called "magic angles", an effective two-dimensional correlated system emerges.…
In this work, we propose a model with Lorentz symmetry violation which describes the electronic low energy limit of the AA-bilayer graphene (BLG) system. The AA-type bilayer is known to preserve the linear dispersion relation of the…
The low energy electronic spectra of rotationally faulted graphene bilayers are studied using a long wavelength theory applicable to general commensurate fault angles. Lattice commensuration requires low energy electronic coherence across a…
In graphene, charged defects break the electron-hole symmetry and can even give rise to exotic collapse states when the defect charge exceeds a critical value which is proportional to the Fermi velocity. In this work, we investigate the…
We investigate imaging of moire structures in free-standing twisted bilayer graphene (TBG) carried out by transmission electron microscopy (TEM) in diffraction and in-line Gabor holography modes. Electron diffraction patterns of TBG…
In the vicinity of the magic angle in twisted bilayer graphene (TBG), the two low-energy van Hove singularities (VHSs) become exceedingly narrow1-10 and many exotic correlated states, such as superconductivity, ferromagnetism, and…
We study the electronic properties of twisted bilayers graphene in the tight-binding approximation. The interlayer hopping amplitude is modeled by a function, which depends not only on the distance between two carbon atoms, but also on the…
We study the atomic structure of twisted bilayer graphene, with very small mismatch angles ($\theta \sim 0.28^0$), a topic of intense recent interest. We use simulations, in which we combine a recently presented semi-empirical potential for…
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…
We investigate twisted double bilayer graphene (TDBG), a four-layer system composed of two AB-stacked graphene bilayers rotated with respect to each other by a small angle. Our ab initio band structure calculations reveal a considerable…