Narrow Results

We present a rigorous and rather self-contained analysis of the Verdet constant in graphene-like materials. We apply the gauge-invariant magnetic perturbation theory to a nearest-neighbor tight-binding model and obtain a relatively simple and exactly computable formula for the Verdet constant, at all temperatures and all frequencies of sufficiently large absolute value. Moreover, for the standard nearest-neighbor tight-binding model of graphene we show that the transverse component of the conductivity tensor has an asymptotic Taylor expansion in the external magnetic field where all the coefficients of even powers are zero.

The recent quantum Hall experiments in graphene have confirmed the theoretically well-understood picture of the quantum Hall (QH) conductance in fermion systems with continuum Dirac spectrum. In this paper we take into account the lattice and perform an exact diagonalization of the Landau problem on the hexagonal lattice. At very large magnetic fields the Dirac argument fails completely and the Hall conductance, given by the number of edge states present in the gaps of the spectrum, is dominated by lattice effects. As the field is lowered, the experimentally observed situation is recovered through a phenomenon which we call band collapse. As a corollary, for low magnetic fields, graphene will exhibit two qualitatively different QHE's: at low filling, the QHE will be dominated by the "relativistic" Dirac spectrum and the Hall conductance will be odd-integer; above a certain filling, the QHE will be dominated by a non-relativistic spectrum, and the Hall conductance will span all integers, even and odd.

We observe that H₃S has a BCC structure and, with nearest neighbor hopping only, a strong singularity occurs at zero energy. This singularity is accompanied with a highly nested Fermi surface, which is not conducive to a stable superconducting instability. Introduction of next-nearest-neighbor hopping removes the singularity, but a “robust” peak remains in the electron density of states. Solution of the BCS equations shows an enhanced superconducting $T_c$ due to this peak. Furthermore, nesting is no longer present, so other instabilities will not compete effectively with superconductivity. We find high critical temperatures are possible, even with very modest coupling strengths. We also examine a limit of the $T=0$ equations (in an Appendix) where an analytical solution is possible over the entire range of coupling strengths, and therefore the BCS-BEC crossover is fully covered.

We present a theoretical method based on Green’s function technique and tight-binding approach as well as harmonic approximation in order to calculate the coherent electronic conductance of an extended poly(p-phenylene) oligomer in the presence of thermal atomic vibrations. We study two proposed mass-spring models for atomic vibrations: one, including rigid benzene rings connected to each other by vibrating bonds; and in another, the bonds along the oligomer vibrate even in the benzene rings. The electron–phonon (e–ph) interaction influences the electron hopping energies linearly with respect to atomic displacements. The model shows that the conductance spectra exhibit some new energy gaps in the presence of e–ph interaction even at zero temperature. The conductance is more affected by e–ph interaction when the atomic vibrations are supposed to be present in the benzene rings. At the edges of the band energy and central gap, the phonon-assisted phenomena can be observed. Generally, the increasing e–ph interaction strength as well as temperature destroys the electronic conductance especially in the resonance region.

Tight-binding Hamiltonian on the prismatic pentagonal lattice is exactly solved to obtain the analytic expressions of dispersion relations and eigenvectors. This lattice is made of prismatic pentagon which is different from Cairo pentagon. Six different dispersion relations and total density of states are obtained. Dispersion relations are symmetric about the zero energy at a particular point in the parameter space. Although a large gap is found for the Cairo pentagonal lattice, no gap as well as no Dirac cone is found to appear in the tight-binding band structure for this prismatic pentagonal lattice. Instead, a pair of van Hove singularities has been identified at two different energy values in the band structure.

We report a quantitatively accurate description of the electronic structure of semiconductor nanocrystals using the sp³d⁵ orbital basis with the nearest neighbor and the next nearest neighbor interactions. The use of this model for II–VI and III–V semiconductors is reviewed in article. The excellent agreement of the theoretical predictions with the experimental results establishes the feasibility of using this model for semiconductor nanocrystals.

We have used the non-equilibrium Green's function formalism combined with a Tight-Binding and an Extended Hiickel Hamiltonian for the transport calculation of finite single-walled carbon nanotube systems attached to Au(111) metallic contacts. Findings have revealed the limits of the Tight-Binding approach regarding its use in the Carbon Nanotube context. Moreover, we have thoroughly investigated the channel-blocking effects provoked by interference from the metallic contacts as well as the changes in the transmission function caused by variations in the metal-tube interface geometry.