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Electron-electron interactions play a critical role in many condensed matter phenomena, and it is tempting to find a way to control them by changing the interactions' strength. One possible approach is to place a studied system in proximity…
We deduce a non-linear continuum model of graphene for the case of finite out-of-plane displacements and small in-plane deformations. On assuming that the lattice interactions are governed by the Brenner's REBO potential of 2nd generation…
We present a new model to realize artificial 2D lattices with cold atoms investigating the atomic artificial graphene: a 2D-confined matter wave is scattered by atoms of a second species trapped around the nodes of a honeycomb optical…
Electrons in graphene behave like relativistic Dirac particles which can reduce velocity of light by two orders of magnitude in the form of plasmon-polaritons. Here we show how these properties lead to a peculiar nonlinear plasmon response…
We study the Dirac equation for quasiparticles in gapped graphene with two oppositely charged impurities by using the technique of linear combination of atomic orbitals and variational Galerkin--Kantorovich method. We show that for…
Defects play a key role in the electronic structure of graphene layers flat or curved. Topological defects in which an hexagon is replaced by an n-sided polygon generate long range interactions that make them different from vacancies or…
We study the quantum many-body ground states of electrons on the half-filled honeycomb lattice with short- and long-ranged density-density interactions as a model for graphene. To this end, we employ the recently developed truncated-unity…
Freestanding graphene displays an outstanding resilience to electron irradiation at low electron energies. Point defects in graphene are, however, subject to beam driven dynamics. This means that high resolution micrographs of point…
Application of secondary quantized self-consistent Dirac -- Hartree -- Fock approach to consider electronic properties of monolayer graphene with accounting of spin-polarized states allows to coherently explain experimental results on…
When graphene is exposed to a strong few-cycle optical field, a directional electric current can be induced depending on the carrier-envelope phase of the field. This phenomenon has successfully been explained by the charge dynamics in…
The aim of this habilitation thesis is to present recent results, obtained during the period 2012-2017, related to interaction effects in condensed matter physics systems such as planar Dirac liquids, e.g., graphene and graphene-like…
A new mechanism of particle acceleration, based on the resonant interaction of a classical electromagnetic wave (EM) with a quantum wave (associated with a relativistic particle), is explored. In a model illustrative calculation, we study…
Two-dimensional quantum materials offer a robust platform for investigating the emergence of symmetry-broken ordered phases owing to the high tuneability of their electronic properties. For instance, the ability to create new electronic…
Due to its unique structure, graphene provides a condensed-matter model of particle physics phenomena. One is the critical charge which is highly interested. The investigation of critical charge in gapped graphene is performed within single…
Electrons in two-dimensional graphene sheets behave as interacting chiral Dirac fermions and have unique screening properties due to their symmetry and reduced dimensionality. By using a combination of scanning tunneling spectroscopy…
We show that a generalized Dirac structure survives beyond the linear regime of the low-energy dispersion relations of graphene. A generalized uncertainty principle of the kind compatible with specific quantum gravity scenarios with a…
Motivated by recent proposals on strain-engineering of graphene electronic circuits we calculate conductivity, shot-noise and the density of states in periodically deformed graphene. We provide the solution to the Dirac-Kronig-Penney model,…
Graphene - a monolayer of carbon atoms densely packed into a hexagonal lattice - has one of the strongest possible atomic bonds and can be viewed as a robust atomic-scale scaffold, to which other chemical species can be attached without…
The effect of a varying pseudo-magnetic field, which falls as $1/x^2$, on a two dimensional electron gas in graphene is investigated. By considering the second order Dirac equation, we show that its correct general solution is that which…
We study theoretically the interaction of twisted light with graphene. The light-matter interaction matrix elements between the tight-binding states of electrons in graphene are determined near the Dirac points. We examine the dynamics of…