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In this paper, we numerically study the bound electron states induced by long range Coulomb impurity in gapped graphene and the quasi-bound states in supercritical region based on the lattice model. We present a detailed comparison between our numerical simulations and the prediction of the continuum model which is described by the Dirac equation in (2+1)-dimensional Quantum Electrodynamics (QED). We also use the Fanos formalism to investigate the quasi-bound state development and design an accessible experiments to test the decay of the supercritical vacuum in the gapped graphene.
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In van der Waals bonded or rotationally disordered multilayer stacks of two-dimensional (2D) materials, the electronic states remain tightly confined within individual 2D layers. As a result, electron-phonon interactions occur primarily within layers and interlayer electrical conductivities are low. In addition, strong covalent in-plane intralayer bonding combined with weak van der Waals interlayer bonding results in weak phonon-mediated thermal coupling between the layers. We demonstrate here, however, that Coulomb interactions between electrons in different layers of multilayer epitaxial graphene provide an important mechanism for interlayer thermal transport even though all electronic states are strongly confined within individual 2D layers. This effect is manifested in the relaxation dynamics of hot carriers in ultrafast time-resolved terahertz spectroscopy. We develop a theory of interlayer Coulomb coupling containing no free parameters that accounts for the experimentally observed trends in hot-carrier dynamics as temperature and the number of layers is varied.
Wrinkling is a ubiquitous phenomenon in two-dimensional membranes. In particular, in the large-scale growth of graphene on metallic substrates, high densities of wrinkles are commonly observed. Despite their prevalence and potential impact on large-scale graphene electronics, relatively little is known about their structural morphology and electronic properties. Surveying the graphene landscape using atomic force microscopy, we found that wrinkles reach a certain maximum height before folding over. Calculations of the energetics explain the morphological transition, and indicate that the tall ripples are collapsed into narrow standing wrinkles by van der Waals forces, analogous to large-diameter nanotubes. Quantum transport calculations show that conductance through these collapsed wrinkle structures is limited mainly by a density-of-states bottleneck and by interlayer tunneling across the collapsed bilayer region. Also through systematic measurements across large numbers of devices with wide folded wrinkles, we find a distinct anisotropy in their electrical resistivity, consistent with our transport simulations. These results highlight the coupling between morphology and electronic properties, which has important practical implications for large-scale high-speed graphene electronics.
Since its inception in 2001, the science and technology of epitaxial graphene on hexagonal silicon carbide has matured into a major international effort and is poised to become the first carbon electronics platform. A historical perspective is presented and the unique electronic properties of single and multilayered epitaxial graphenes on electronics grade silicon carbide are reviewed. Early results on transport and the field effect in Si-face grown graphene monolayers provided proof-of-principle demonstrations. Besides monolayer epitaxial graphene, attention is given to C-face grown multilayer graphene, which consists of electronically decoupled graphene sheets. Production, structure, and electronic structure are reviewed. The electronic properties, interrogated using a wide variety of surface, electrical and optical probes, are discussed. An overview is given of recent developments of several device prototypes including resistance standards based on epitaxial graphene quantum Hall devices and new ultrahigh frequency analog epitaxial graphene amplifiers.
In the model of gapped graphene, we have shown how the recently predicted topological resonances are solely related to the presence of an energy band gap at the $K$ and $K^prime$ points of the Brillouin zone. In the field of a strong single-oscillation chiral (circularly-polarized) optical pulse, the topological resonance causes the valley-selective population of the conduction band. This population distribution represents a chiral texture in the reciprocal space that is structured with respect to the pulse separatrix as has earlier been predicted for transition metal dichalcogenides. As the band gap is switched off, this chirality gradually disappears replaced by an achiral distribution characteristic of graphene.
We study theoretically the interaction of ultrashort optical pulses with gapped graphene. Such strong pulse results in finite conduction band population and corresponding electric current both during and after the pulse. Since gapped graphene has broken inversion symmetry, it has an axial symmetry about the $y$-axis but not about the $x$-axis. We show that, in this case, if the linear pulse is polarized along the $x$-axis, the rectified electric current is generated in the $y$ direction. At the same time, the conduction band population distribution in the reciprocal space is symmetric about the $x$-axis. Thus, the rectified current in gapped graphene has inter-band origin, while the intra-band contribution to the rectified current is zero.
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