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First principles calculations are used to establish that the electronic structure of graphene ribbons with zig-zag edges is unstable with respect to magnetic polarisation of the edge states. The magnetic interaction between edge states is…

Electronic fluids bring into hydrodynamics a new setting: equipotential flow sources embedded inside the fluid. Here we show that nonlocal relation between current and electric field due to momentum-conserving inter-particle collisions…

We probe the local inhomogeneities of the electronic properties of graphene at the nanoscale using scanning probe microscopy techniques. First, we focus on the study of the electronic inhomogeneities caused by the graphene-substrate…

The sensitivity of charge, heat, or momentum transport to the sample geometry is a hallmark of viscous electron flow. Therefore, hydrodynamic electronics requires the detailed understanding of electron flow in finite geometries. The…

Electronic structures and optical excitations in Moebius conjugated polymers are studied theoretically. Periodic and Moebius boundary conditions are applied to the tight binding model of poly(para-phenylene), taking into account of the…

Recent advances in large-scale synthesis of graphene and other 2D materials have underscored the importance of local defects such as dislocations and grain boundaries (GBs), and especially their tendency to alter the electronic properties…

Intrinsic layered structure of graphite is the source of ongoing and expanding search of ways of obtaining low-cost and promising graphite thin layers. We report on a novel method of obtaining and separating rubbed graphite sheets by using…

Experimental investigation of hydrodynamics in electron fluids is a highly topical research area that emerged during the last few years. A recent measurement of the optical conductivity in graphene [P. Gallagher et.al, Science 364, 158…

We suggest a way of confining quasiparticles by an external potential in a small region of a graphene strip. Transversal electron motion plays a crucial role in this confinement. Properties of thus obtained graphene quantum dots are…

Recent experimental findings and theoretical predictions suggest that nitrogen-doped CVD-grown graphene may give rise to electronic band gaps due to impurity distributions which favour segregation on a single sublattice. Here we demonstrate…

We discuss the properties of interacting electrons on a finite chain with open boundary conditions. We extend the Haldane Luttinger liquid description to these systems and study how the presence of the boundaries modifies various…

The focusing of electric current by a single \textit{p-n} junction in graphene is predicted. We show that precise focusing can be achieved by fine-tuning the densities of carriers on the n- and p-sides of the junction to equal values,…

We provide numerical evidence that electronic pre-turbulent phenomena in graphene could be observed, under current experimental conditions, through detectable current fluctuations, echoing the detachment of vortices past localized…

Electronic states at domain walls in bilayer graphene are studied by analyzing their four and two band continuum models, by performing numerical calculations on the lattice, and by using quantum geometric arguments. The continuum theories…

Motivated by experiments on a hydrodynamic regime in electron transport, we study the effect of an oscillating electric field in such a setting. We consider a long two-dimensional channel of width $L$, whose geometrical simplicity allows an…

Using a four-band Hamiltonian, we study the phase boundary of spin-polarized-current state (SPCS) of interacting electrons in bilayer graphene. The model of spin-polarized-current state has previously been shown to resolve a number of…

We report on detailed microscopy studies of graphene and few-layer-graphene produced by mechanical exfoliation on various semi-conducting substrates. We demonstrate the possibility to prepare and analyze graphene on (001)-GaAs, manganese…

We report low temperature high magnetic field scanning tunneling microscopy and spectroscopy of graphene flakes on graphite that exhibit the structural and electronic properties of graphene decoupled from the substrate. Pronounced peaks in…

In ultra-pure materials electrons may exhibit a collective motion similar to the hydrodynamic flow of a viscous fluid, the phenomenon with far reaching consequences in a wide range of many body systems from black holes to high-temperature…

We consider a graphene sheet in the vicinity of a substrate, which contains charged impurities. An analytic expression for the probability distribution function of voltage fluctuations due to the charged impurities is derived. The…