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We review recent work on superlattices in monolayer and bilayer graphene. We highlight the role of the quasiparticle chirality in generating new Dirac fermion modes with tunable anisotropic velocities in one dimensional (1D) superlattices…
MXene-based heterostructures have received considerable interest owing to their unique properties. Herein, we examine various heterostructures of a prototypical MXene and graphene using density functional theory. We find that the adhesion…
Graphene is convenient material for nanomechanichal applications since high-frequency oscillations are easily accessible. In this Article, we consider graphene on a rough substrate attached to imperfections at random locations. We explore…
One of the intriguing characteristics of honeycomb lattices is the appearance of a pseudo-magnetic field as a result of mechanical deformation. In the case of graphene, the Landau quantization resulting from this pseudo-magnetic field has…
This paper is devoted to the construction of semiclassical spectrum and efficient (simple to implement) explicit semiclassical asymptotic eigenfunctions of the Dirac operator for relatively high-energy bound states in graphene in magnetic…
Theory of spin-orbit coupling in bilayer graphene is presented. The electronic band structure of the AB bilayer in the presence of spin-orbit coupling and a transverse electric field is calculated from first-principles using the linearized…
Chirality is one of the key features governing the electronic properties of single- and bilayer graphene: the basics of this concept and its consequences on transport are presented in this review. By breaking the inversion symmetry, a band…
Topological materials rely on engineering global properties of their bulk energy bands called topological invariants. These invariants, usually defined over the entire Brillouin zone, are related to the existence of protected edge states.…
In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of…
A notion of Paley-Wiener spaces is introduced on combinatorial graphs. It is shown that functions from some of these spaces are uniquely determined by their values on some sets of vertices which are called the uniqueness sets. Such…
The large-scale production of graphene monolayer greatly relies on epitaxial samples which often display stress-relaxation features in the form of wrinkles. Wrinkles of graphene on Ir(111) are found to exhibit a fairly well ordered…
We analyze symmetries of Bloch eigenfunctions at magic angles for the Tarnopolsky--Kruchkov--Vishwanath chiral model of the twisted bilayer graphene (TBG) following the framework introduced by Becker--Embree--Wittsten--Zworski. We show that…
Vortex is a universal and significant phenomenon that has been known for centuries. However, creating vortices to the atomic limit has remained elusive because that the characteristic length to support a vortex is usually much larger than…
We deal with isomorphic Banach-Stone type theorems for closed subspaces of vector-valued continuous functions. Let $\mathbb{F}=\mathbb{R}$ or $\mathbb{C}$. For $i=1,2$, let $E_i$ be a reflexive Banach space over $\mathbb{F}$ with a certain…
Graphene-based multilayer systems serve as versatile platforms for exploring the interplay between electron correlation and topology, thanks to distinctive low-energy bands marked by significant quantum metric and Berry curvature from…
Strong gate control of proximity-induced spin-orbit coupling was recently predicted in bilayer graphene/transition metal dichalcogenides (BLG/TMDC) heterostructures, as charge carriers can easily be shifted between the two graphene layers,…
The magneto-conductivity of a single graphene layer where the electrons are described by the Dirac Hamiltonian weakly modulated by a periodic potential is calculated. It is shown that Weiss oscillations periodic in the inverse magnetic…
The conformal invariance of the low energy limit theory governing the electronic properties of graphene is explored. In particular, it is noted that the massless Dirac theory in point enjoys local Weyl symmetry, a very large symmetry.…
Controlling the stacking and rotational registry of graphene layers provides a powerful handle on atomic-scale structural reconstructions that alter the electronic landscape at the nanoscale. In particular, this governs how massless and…
Due to the chiral nature of electrons in a monolayer of graphite (graphene) one can expect weak antilocalisation and a positive weak-field magnetoresistance in it. However, trigonal warping (which breaks p/-p symmetry of the Fermi line in…