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Graphene strips folded in similar fashion to origami paper could be used to build microchips that are up to 100 times smaller than conventional chips, found physicists – and packing phones and laptops with those tiny chips could significantly boost the performance of our devices. New research from the University of Sussex in the UK shows that changing the structure of nanomaterials like graphene can unlock electronic properties and effectively enable the material to act like a transistor…..Continue reading…
Source: ZDNET
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Graphene is a zero-gap semiconductor, because its conduction and valence bands meet at the Dirac points. The Dirac points are six locations in momentum space, on the edge of the Brillouin zone, divided into two non-equivalent sets of three points. The two sets are labeled K and K’. The sets give graphene a valley degeneracy of gv = 2. By contrast, for traditional semiconductors the primary point of interest is generally Γ, where momentum is zero.
Four electronic properties separate it from other condensed matter systems. However, if the in-plane direction is no longer infinite, but confined, its electronic structure would change. They are referred to as graphene nanoribbons. If it is “zig-zag”, the bandgap would still be zero. If it is “armchair”, the bandgap would be non-zero. Graphene’s hexagonal lattice can be regarded as two interleaving triangular lattices.
This perspective was successfully used to calculate the band structure for a single graphite layer using a tight-binding approximation. The cleavage technique led directly to the first observation of the anomalous quantum Hall effect in graphene in 2005, by Geim’s group and by Philip Kim and Yuanbo Zhang. This effect provided direct evidence of graphene’s theoretically predicted Berry’s phase of massless Dirac fermions and the first proof of the Dirac fermion nature of electrons.
These effects had been observed in bulk graphite by Yakov Kopelevich, Igor A. Luk’yanchuk, and others, in 2003–2004. When the atoms are placed onto the graphene hexagonal lattice, the overlap between the pz(π) orbitals and the s or the px and py orbitals is zero by symmetry. The pz electrons forming the π bands in graphene can therefore be treated independently.
Within this π-band approximation, using a conventional tight-binding model, the dispersion relation (restricted to first-nearest-neighbor interactions only) that produces energy of the electrons with wave vector k iswith the nearest-neighbor (π orbitals) hopping energy γ0 ≈ 2.8 eV and the lattice constant a ≈ 2.46 Å. The conduction and valence bands, respectively, correspond to the different signs.
With one pz electron per atom in this model the valence band is fully occupied, while the conduction band is vacant. The two bands touch at the zone corners (the K point in the Brillouin zone), where there is a zero density of states but no band gap. The graphene sheet thus displays a semimetallic (or zero-gap semiconductor) character, although the same cannot be said of a graphene sheet rolled into a carbon nanotube, due to its curvature.
Two of the six Dirac points are independent, while the rest are equivalent by symmetry. In the vicinity of the K-points the energy depends linearly on the wave vector, similar to a relativistic particle. Since an elementary cell of the lattice has a basis of two atoms, the wave function has an effective 2-spinor structure. Graphene’s unit cell has two identical carbon atoms and two zero-energy states: one in which the electron resides on atom A, the other in which the electron resides on atom B.
However, if the two atoms in the unit cell are not identical, the situation changes. Hunt et al. show that placing hexagonal boron nitride (h-BN) in contact with graphene can alter the potential felt at atom A versus atom B enough that the electrons develop a mass and accompanying band gap of about 30 meV [0.03 Electron Volt(eV)].
The mass can be positive or negative. An arrangement that slightly raises the energy of an electron on atom A relative to atom B gives it a positive mass, while an arrangement that raises the energy of atom B produces a negative electron mass. The two versions behave alike and are indistinguishable via optical spectroscopy. An electron traveling from a positive-mass region to a negative-mass region must cross an intermediate region where its mass once again becomes zero.
This region is gapless and therefore metallic. Metallic modes bounding semiconducting regions of opposite-sign mass is a hallmark of a topological phase and display much the same physics as topological insulators. If the mass in graphene can be controlled, electrons can be confined to massless regions by surrounding them with massive regions, allowing the patterning of quantum dots, wires, and other mesoscopic structures.
It also produces one-dimensional conductors along the boundary. These wires would be protected against backscattering and could carry currents without dissipation. Graphene’s unique optical properties produce an unexpectedly high opacity for an atomic monolayer in vacuum, absorbing πα ≈ 2.3% of light, from visible to infrared.
Here, α is the fine-structure constant. This is a consequence of the “unusual low-energy electronic structure of monolayer graphene that features electron and hole conical bands meeting each other at the Dirac point… [which] is qualitatively different from more common quadratic massive bands. Based on the Slonczewski–Weiss–McClure (SWMcC) band model of graphite, the interatomic distance, hopping value and frequency cancel when optical conductance is calculated using Fresnel equations in the thin-film limit.
Although confirmed experimentally, the measurement is not precise enough to improve on other techniques for determining the fine-structure constant. Multi-Parametric Surface Plasmon Resonance was used to characterize both thickness and refractive index of chemical-vapor-deposition (CVD)-grown graphene films.
The measured refractive index and extinction coefficient values at 670 nm (6.7×10−7 m) wavelength are 3.135 and 0.897, respectively. The thickness was determined as 3.7Å from a 0.5mm area, which agrees with 3.35Å reported for layer-to-layer carbon atom distance of graphite crystals. The method can be further used also for real-time label-free interactions of graphene with organic and inorganic substances.
Furthermore, the existence of unidirectional surface plasmons in the nonreciprocal graphene-based gyrotropic interfaces has been demonstrated theoretically. By efficiently controlling the chemical potential of graphene, the unidirectional working frequency can be continuously tunable from THz to near-infrared and even visible.
Particularly, the unidirectional frequency bandwidth can be 1– 2 orders of magnitude larger than that in metal under the same magnetic field, which arises from the superiority of extremely small effective electron mass in graphene.
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