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Unlike the well-known Mott's argument that extended and localized states should not coexist at the same energy in a generic random potential, we provide an example of a nearest-neighbor tight-binding disordered model which carries both…

We show that if a graph contains few induced copies of a given graph then its edges are distribited unevenly.

We study electron transport properties of a monoatomic graphite layer (graphene) with different types of disorder. We show that the transport properties of the system depend strongly on the character of disorder. Away from half filling, the…

The wave nature of electrons in low-dimensional structures manifests itself in conventional electrical measurements as a quantum correction to the classical conductance. This correction comes from the interference of scattered electrons…

This paper is devoted to development of perturbation theory for studying the properties of graphene sheet of finite size, at nonzero temperature and chemical potential. The perturbation theory is based on the tight-binding Hamiltonian and…

In previous work, we have predicted novel effects, such as exchange broadening, anomalous scaling of the localization length and a blue shift of the absorption spectrum with increasing disorder strength, for static disorder models described…

Van der Waals heterostructures display a rich variety of unique electronic properties. To identify novel transport mechanisms, nonlocal measurements have been widely used, wherein a voltage is measured at contacts placed far away from the…

We introduce a model for amorphous grain boundaries in graphene, and find that stable structures can exist along the boundary that are responsible for local density of states enhancements both at zero and finite (~0.5 eV) energies. Such…

Mobility edges (ME), separating Anderson-localized states from extended states, are known to arise in the single-particle energy spectrum of certain one-dimensional lattices with aperiodic order. Dephasing and decoherence effects are widely…

In this article, we propose a new numerical model for computation of the transport of electrons in a graphene device. The underlying quantum model for graphene is a massless Dirac equation, whose eigenvalues display a conical singularity…

Spin transport experiments in graphene, a single layer of carbon atoms, indicate spin relaxation times that are significantly shorter than the theoretical predictions. We investigate experimentally whether these short spin relaxation times…

Anderson localization of electron states on graphene lattice with diagonal and off-diagonal (OD) disorder in the absence of magnetic field is investigated by using the standard finite-size scaling analysis. In the presence of diagonal…

The specific band structure of graphene, with its unique valley structure and Dirac neutrality point separating hole states from electron states has led to the observation of new electronic transport phenomena such as anomalously quantized…

We numerically investigate quantum rings in graphene and find that their electronic properties may be strongly influenced by the geometry, the edge symmetries and the structure of the corners. Energy spectra are calculated for different…

We investigate the in-plane oscillations of the relaxed shape graphene due to externally applied tensile edge stress along both the armchair and zigzag directions. We show that the total elastic energy density is enhanced with temperature…

We argue, for a wide class of systems including graphene, that in the low temperature, high density, large separation and strong screening limits the drag resistivity behaves as d^{-4}, where d is the separation between the two layers. The…

It is demonstrated that both transmission and reflection coefficients associated to the Klein paradox at a step barrier are positive and less than unity, so that the particle-antiparticle pair creation mechanism commonly linked to this…

We respond to the recent article by S. Goldstein, R. Tumulka, and N. Zangh\`i [arXiv:2309.11835] concerning the spin-dependent arrival-time distributions reported in [S. Das and D. D\"urr, Sci. Rep. 9: 2242 (2019)].

We use first-principles calculations to uncover and explain a new type of anomalous low-velocity stopping effect in proton-irradiated graphene. We attribute a shoulder feature that occurs exclusively for channeling protons to enhanced…

We theoretically investigate light propagation and Anderson localization in one-dimensional disordered superlattices composed of dielectric stacks with graphene sheets in between. Disorder is introduced either on graphene material…