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A number of interesting properties of graphene and graphite are postulated to derive from the peculiar bandstructure of graphene. This bandstructure consists of conical electron and hole pockets that meet at a single point in momentum (k)…
We analyse the electrical response of narrow graphene nanogaps in search for transport signatures stemming from spin-polarized edge states. We find that the electrical transport across graphene nanogaps having perfectly defined zigzag edges…
Graphene is a two-dimensional material with strongly nonlinear electrodynamics and optical properties. We present some of our recent theoretical results on the quantum and non-perturbative quasi-classical theories of nonlinear effects in…
We review field theoretical studies dedicated to understanding the effects of electron-electron interaction in graphene, which is characterized by gapless bands, strong electron-electron interactions, and emerging Lorentz invariance deep in…
At near-parallel orientation, twisted bilayer of transition metal dichalcogenides exhibit inter-layer charge transfer-driven out-of-plane ferroelectricity that may lead to unique electronic device architectures. Here we report detailed…
A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is…
The nonlinear optical and optoelectronic properties of graphene with the emphasis on the processes of harmonic generation, frequency mixing, photon drag and photogalvanic effects as well as generation of photocurrents due to coherent…
In disordered lattices, itinerant electrons typically undergo Anderson localization due to random phase interference, which suppresses their motion. By contrast, in flat-band systems where electrons are intrinsically localized owing to…
Withdrawn by author - Superseded by arXiv:0910.5106 [math.FA].
We investigate an effective model of proximity modified graphene (or symmetrylike materials) with broken time-reversal symmetry. We predict the appearance of quantum anomalous Hall phases by computing bulk band gap and Chern numbers for…
Withdrawn by the authors
Using the tight binding model and the non-equilibrium Green function method, we study Andreev reflection in graphene-superconductor junction, where graphene has two nonequal Dirac Cones split in energy and therefore time reversal symmetry…
In two dimensions chaotic level-statistics is expected for massless Dirac fermions in the presence of disorder. For weakly disordered graphene flakes with zigzag edges the obtained level-spacing distribution in the Dirac region is neither…
We present an interpretation of recent experimental measurements of dmu/dn in suspended bilayer graphene samples. We demonstrate that the data may be quantitatively described by assuming a spatially varying band gap induced by local…
Using molecular simulation and continuum dielectric theory, we consider how electrochemical kinetics are modulated by twist angle in bilayer graphene electrodes. By establishing a connection between twist angle and the screening length of…
We study Schr\"odinger operators on quantum graphs where the number of edges between points is determined by orbits of a "shift of finite type". We prove Anderson localization for these systems.
We show that the ground state of zigzag bilayer graphene nanoribbons is non-magnetic. It also possesses a finite gap, which has a non-monotonic dependence with the width as a consequence of the competition between bulk and strongly…
Graphene, with its quantum Hall topological (Chern) number reflecting the massless Dirac particle, is shown to harbor yet another topological quantum number. This is obtained by combining Streda's general formula for the polarization…
Augmented graphs play a vital role in regularizing Graph Neural Networks (GNNs), which leverage information exchange along edges in graphs, in the form of message passing, for learning. Due to their effectiveness, simple edge and node…
Motivated by recent experimental observations of size quantization of electron energy levels in graphene quantum dots \cite{ponomarenko} we investigate the level statistics in the simplest tight-binding model for different dot shapes by…