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Graphene flakes placed on hexagonal boron nitride feature in the presence of a magnetic field a complex electronic structure due to a hexagonal moir\'e potential resulting from the van der Waals interaction with the substrate. The slight…
The strongly correlated spin-electron system on a diamond chain containing localized Ising spins on its nodal lattice sites and mobile electrons on its interstitial sites is exactly solved in a magnetic field using the transfer-matrix…
Graphene properties can be manipulated by a periodic potential. Based on the tight-binding model, we study graphene under a one-dimensional (1D) modulated magnetic field which contains both a uniform and a staggered component. New chiral…
We consider properties of a two-dimensional electron system in a random magnetic field. It is assumed that the magnetic field not only influences orbital electron motion but also acts on the electron spin. For calculations, we suggest a new…
The role of electron-electron interactions on two-dimensional Dirac fermions remains enigmatic. Using a combination of nonperturbative numerical and analytical techniques that incorporate both the contact and long-range parts of the Coulomb…
We study electronic properties of graphene with finite concentration of vacancies or other resonant scatterers by a straightforward lattice Quantum Monte Carlo calculations. Taking into account realistic long-range Coulomb interaction we…
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…
We present a theoretical study of magnetic field driven spin transitions of electrons in coupled lateral quantum dot molecules. A detailed numerical study of spin phases of artificial molecules composed of two laterally coupled quantum dots…
When electrons are confined in two-dimensional (2D) materials, quantum mechanically enhanced transport phenomena, as exemplified by the quantum Hall effects (QHE), can be observed. Graphene, an isolated single atomic layer of graphite, is…
We investigate the effects of spin-momentum locking on the interference and diffraction patterns due to a double- or single-slit in an electronic \emph{Gedankenexperiment}. We show that the inclusion of the spin-degree-of-freedom, when…
Trilayer graphene allows systematic control of its electronic structure through stacking sequence and twist geometry, providing a versatile platform for correlated states. Here we report magnetotransport in alternating twisted trilayer…
Using the renormalized-ring-diagram approximation, we study the compressibility of the interacting electrons in bilayer graphene. The compressibility is equivalent to the spin susceptibility apart from a constant factor. The chemical…
We study various mechanisms of electron transmission across the corrugations in the graphene sheet. The spin dependence of the electron transmission probability in the rippled graphene is found. The electrons mean free path and transmission…
In this article we briefly review recent experimental and theoretical work on quantum Hall effect in graphene, and argue that some of the quantum Hall states exhibit spontaneous symmetry breaking that is driven by electron-electron…
In multiferroic oxides with a transverse helical magnetic order, the magnetization exchange coupling is sinusoidally space-dependent. We theoretically investigate the spin-dependent electron grating effect in…
The small spin-orbit interaction of carbon atoms in graphene promises a long spin diffusion length and potential to create a spin field-effect transistor. However, for this reason, graphene was largely overlooked as a possible spin-charge…
We report observation of the fractional quantum Hall effect (FQHE) in high mobility multi-terminal graphene devices, fabricated on a single crystal boron nitride substrate. We observe an unexpected hierarchy in the emergent FQHE states that…
The hyperfine interaction between the spins of electrons and nuclei is both a blessing and a curse. It can provide a wealth of information when used as an experimental probing technique but it can also be destructive when it acts as a…
The effects on the spin state of an electron in a time independent electric field are examined. The probability of spin flipping is calculated, and other effects are studied using the minimally coupled Dirac equation.
Several recent works have proposed that electron-electron interactions in bilayer graphene can be tuned with the help of external parameters, making it possible to stabilize different fractional quantum Hall states. In these prior works,…