PHỔ PLASMON TRONG HỆ 3 LỚP GRAPHENE LỚP KÉP

Recent research demonstrates that graphene has unique properties and applications in many technological fields. This paper presents results calculated within random phase approximation at zero temperature for collective excitations, an important characteristic of materials, in a three-layer structure consisting of three bilayer graphene sheets in an inhomogeneous background dielectric. Numerical calculations show that one optical and two acoustic branches exist in the system. The optical branch becomes overdamped quickly while the two acoustic branches continue and disappear at single-particle excitation boundaries. The increase in carrier density in the layers significantly decreases the frequencies of plasmon modes. The inhomogeneity of the background dielectric decreases the frequency of the higher branches but increases that of the lower branch. The effects of interlayer separation on plasmon modes are similar to those in homogeneous systems. Our results may provide more information and contribute to improving the theory of graphene.

ON d+id DENSITY WAVE AND SUPERCONDUCTING ORDERINGS IN HOLE-DOPED CUPRATES

The d+id-density wave (chiral DDW) order, at the anti-ferromagnetic wave vector Q = (π, π), is assumed to represent the pseudo-gap (PG) state of a hole-doped cuprate superconductor. The pairing interaction U(k, k′) required for d+id ordering comprises of (Ux2-y2(k, k′), Uxy(k, k′)), where [Formula: see text] and [Formula: see text] with U1 > U2. The d-wave superconductivity (DSC), driven by an assumed attractive interaction of the form [Formula: see text] where V1 is a model parameter, is discussed within the mean-field framework together with the d+id ordering. The single-particle excitation spectrum in the CDDW + DSC state is characterized by the Bogoluibov quasi-particle bands — a characteristic feature of SC state. The coupled gap equations are solved self-consistently together with the equation to determine the chemical potential (μ). With the pinning of the van Hove-singularities close to μ, one is able to calculate the thermodynamic and transport properties of the under-doped cuprates in a consistent manner. The electron specific heat displays non-Fermi liquid feature in the CDDW state. The CDDW and DSC are found to represent two competing orders as the former brings about a depletion of the spectral weight (and Raman response function density) available for pairing in the anti-nodal region of momentum space. It is also shown that the depletion of the spectral weight below Tc at energies larger than the gap amplitude occurs. This is an indication of the strong-coupling superconductivity in cuprates. The calculation of the ratio of the quasi-particle thermal conductivity αxx and temperature in the superconducting phase is found to be constant in the limit of near-zero quasi-particle scattering rate.

A Theoretical Approach to Pseudogap and Superconducting Transitions in Hole-Doped Cuprates

We consider a two-dimensional fermion system on a square lattice described by a mean-field Hamiltonian involving the singlet id-density wave (DDW) order, assumed to correspond to the pseudo-gap (PG) state, favored by the electronic repulsion and the coexisting -wave superconductivity (DSC) driven by an assumed attractive interaction within the BCS framework. Whereas the single-particle excitation spectrum of the pure DDW state consists of the fermionic particles and holes over the reasonably conducting background, the coexisting states corresponds to Bogoliubov quasi-particles in the background of the delocalized Cooper pairs in the momentum space. We find that the two gaps in the single-particle excitation spectrum corresponding to PG and DSC, respectively, are distinct and do not merge into one “quadrature” gap if the nesting property of the normal state dispersion is absent. We show that the PG and DSC are representing two competing orders as the former brings about a depletion of the spectral weight available for pairing in the anti-nodal region of momentum space where the superconducting gap is supposed to be the largest. This indicates that the PG state perhaps could not be linked to a preformed pairing scenario. We also show the depletion of the spectral weight below at energies larger than the gap amplitude. This is an important hallmark of the strong coupling superconductivity.