Related papers: Graphene as a quantum surface with curvature-strai…

In this paper we present generic properties of quantum transport in mono-layer graphene. In the scheme of the Kubo-Geenwood formula, we compute the square spreading of wave packets of a given energy with is directly related to conductivity.…

Quantum graphity offers the intriguing notion that space emerges in the low energy states of the spatial degrees of freedom of a dynamical lattice. Here we investigate metastable domain structures which are likely to exist in the low energy…

We investigate the gradient flow of the $L^2$ norm of the Riemannian curvature on surfaces. We show long time existence with arbitrary initial data, and exponential convergence of the volume normalized flow to a constant scalar curvature…

Quantum oscillations in graphene is discussed. The effect of interactions are addressed by Kohn's theorem regarding de Haas-van Alphen oscillations, which states that electron-electron interactions cannot affect the oscillation frequencies…

Suspended graphene samples are observed to be gently rippled rather than being flat. In [M. Friedrich, U. Stefanelli. Graphene ground states, arXiv:1802.05049], we have checked that this nonplanarity can be rigorously described within the…

We calculate the energy spectrum and eigenstates of a graphene sheet which contains a circular deformation. Using time-independent perturbation theory with the ratio of the height and width of the deformation as the small parameter, we find…

Molten metallic nanoparticles have recently been used to construct graphene nanostructures with crystallographic edges. The mechanism by which this happens, however, remains unclear. Here, we present a simple model that explains how a…

We show that the optical transparency of suspended graphene is defined by the fine structure constant, alpha, the parameter that describes coupling between light and relativistic electrons and is traditionally associated with quantum…

The dynamics of a classical branelike object in a curved background is derived from the covariant stress-energy conservation of the brane matter. The world sheet equations and boundary conditions are obtained in the pole-dipole…

The quantum Hall effect is a remarkable manifestation of quantized transport in a two-dimensional electron gas. Given its technological relevance, it is important to understand its development in realistic nanoscale devices. In this work we…

The properties of polycrystalline materials are often dominated by the size of their grains and by the atomic structure of their grain boundaries. These effects should be especially pronounced in 2D materials, where even a line defect can…

In this work, a new structure is suggested for spasing. The presented spaser is made up of a graphene nanosphere, which supports localized surface plasmon modes, and a quantum dot array, acting as a gain medium. The gain medium is pumped by…

In this review we focus on the effect of the Dirac nature of graphene quasiparticles on two separate aspects. The first of these involves transport across superconducting graphene junctions with barriers of thickness $d_0$ and arbitrary…

Graphene is a powerful membrane prototype for both applications and fundamental research. Rheological phenomena including indentation, twisting, and wrinkling in deposited and suspended graphene are actively investigated to unravel the…

In this chapter we take up the quantum Riemannian geometry of a spatial slice of spacetime. While researchers are still facing the challenge of observing quantum gravity, there is a geometrical core to loop quantum gravity that does much to…

The in-plane static screening of the field originated by a charge placed in a graphene sheet is investigated. A self-consistent field equation in the real space domain is obtained by using a suitable Thomas-Fermi procedure. Exact and…

Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…

We consider the dynamics on a quantum graph as the limit of the dynamics generated by a one-particle Hamiltonian in R^2 with a potential having a deep strict minimum on the graph, when the width of the well shrinks to zero. For a generic…

The plane wave scattering and absorption by finite and infinite gratings of free-space standing infinitely long graphene strips are studied in the THz range. A novel numerical approach, based on graphene surface impedance, hyper-singular…

The density of electron-hole pairs produced in a graphene sample immersed in a homogeneous time-dependent electrical field is evaluated. Because low energy charge carriers in graphene are described by relativistic quantum mechanics, the…