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Tuning interactions between Dirac states in graphene has attracted enormous interest because it can modify the electronic spectrum of the two-dimensional material, enhance electron correlations, and give rise to novel condensed-matter…
We discuss the novel electronic properties of graphene under an external periodic scalar or vector potential, and the analytical and numerical methods used to investigate them. When graphene is subjected to a one-dimensional periodic scalar…
We study the localized magnetic states of impurity in biased bilayer and trilayer graphene. It is found that the magnetic boundary for bilayer and trilayer graphene presents the mixing features of Dirac and conventional fermion. For zero…
Charge-neutral conducting systems represent a class of materials with unusual properties governed by electron-hole (e-h) interactions. Depending on the quasiparticles' statistics, band structure, and device geometry these semimetallic…
The electronic properties and optical excitations are investigated in the geometry- and field-modulated bilayer graphene systems, respectively, by using the tight-binding model and Kubo formula. The stacking symmetry of bilayer graphene can…
This article reviews the basic theoretical aspects of graphene, a one atom thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric…
Graphene-based systems have emerged as a rich platform for exploring emergent quantum phenomena-including superconductivity, magnetism, and correlated insulating behavior-arising from flat electronic bands that enhance many-body…
Two-dimensional atomic crystals can radically change their properties in response to external influences such as substrate orientation or strain, resulting in essentially new materials in terms of the electronic structure. A striking…
Electron-electron interactions play an important role in graphene and related systems and can induce exotic quantum states, especially in a stacked bilayer with a small twist angle. For bilayer graphene where the two layers are twisted by a…
It has been shown that the Kohn--Luttinger superconductivity mechanism interplaying with other types of ordering can be implemented in systems with a hexagonal lattice. A number of unusual properties of such systems in the normal phase have…
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…
Strain engineering of graphene takes advantage of one of the most dramatic responses of Dirac electrons enabling their manipulation via strain-induced pseudo-magnetic fields. Numerous theoretically proposed devices, such as resonant…
We extensively investigate the electronic and transport properties of a twisted bilayer graphene when subjected to both an external perpendicular electric field and a magnetic field. Using a basic tight-binding model, we show the flat…
This study theoretically investigated the magnetic properties and electronic structure of a graphene-based nano-spin-valve-like structure. Magnetic nickel layers on both sides of the graphene were considered. A spin-polarized…
We examine the magnetic properties of the localized states induced by lattice vacancies in bilayer graphene with an unrestricted Hartree-Fock calculation. We show that with realistic values of the parameters and for experimentally…
Controlling the electronic structure of two-dimensional materials using the combination of twist angle and electrostatic doping is an effective means to induce emergent phenomena. In bilayer graphene with an interlayer twist angle near the…
The interplay between localized magnetic moments and itinerant electrons gives rise to exotic quantum states in condensed matter systems. Two-dimensional moire superlattices offer a powerful platform for engineering heavy fermion states…
Superlattices from twisted graphene mono- and bi-layer systems give rise to on-demand many-body states such as Mott insulators and unconventional superconductors. These phenomena are ascribed to a combination of flat bands and strong…
We examine the conditions necessary for the presence of localized magnetic moments on adatoms with inner shell electrons in graphene. We show that the low density of states at the Dirac point, and the anomalous broadening of the adatom…
Fractional quantum anomalous Hall effects realized in twisted bilayer MoTe$_2$ and multilayer-graphene-based moir\'e heterostructures have captured a tremendous growth of interest. In this work, we propose that rhombohedral multilayer…