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Intermediate-coupling theory
Published in A. S. Alexandrov, Theory of Superconductivity From Weak to Strong Coupling, 2003
We should also take the Coulomb electron–electron interaction into account because the corresponding vertex is singular in the long-wavelength limit, Vc(q) = 4πe2/q2. This leads to a drastic renormalization of the long wavelength behaviour of πe. In the ‘bubble’ or random phase approximation (RPA), we obtain figure 3.2 as in the case of the electron–ion plasmon interaction, figure 3.1(f), but with the Coulomb (dashed-dotted) line instead of the dotted phonon line. In the analytical form, we have Πe(q,ω)=Πe(0)(q,ω)1−(4πe2/q2)Πe(0)(q,ω).
The Electron-Phonon Interaction and Strong-Coupling Superconductors
Published in R. D. Parks, Superconductivity, 2018
Keeping only the contribution from the first bubble diagram generates the random phase approximation with the Lindhard form (41) for the frequency-and wave vector-dependent dielectric constant. In the static limit the Lindhard dielectric function is () ∈RPA(q)=1+(ks/q)2u(q/2pF)
Particle-Based Device Simulation Methods
Published in Dragica Vasileska, Stephen M. Goodnick, Gerhard Klimeck, Computational Electronics, 2017
Dragica Vasileska, Stephen M. Goodnick, Gerhard Klimeck
The treatment of intercarrier interactions as binary collisions above neglects scattering by collective excitations such as plasmons or coupled plasmon–phonon modes. These effects may have a strong influence on carrier relaxation, particularly at a high carrier density. One approach is to make a separation of the collective and single particle spectrum of the interacting many-body Hamiltonian and treat them separately, i.e., as binary collisions for the single particle excitations and as electron–plasmon scattering for the collective modes [20]. Another approach is to calculate the dielectric response within the random phase approximation and associate the damping given by the imaginary part of the inverse dielectric function with the electron lifetime [21].
Dual quasi-bound states in the continuum in graphene/dielectric hybrid metamaterial from out-of-plane symmetry protection
Published in Journal of Modern Optics, 2022
Wudeng Wang, Huizhen Yan, Li Xiong, Yujie Zhang, Xiuguo Bi
Figure 1 shows a schematic diagram of the proposed graphene-dielectric optical modulator, which is composed of stair-like resonator and a graphene layer over the substrate. Geometrical parameters of the stair-like resonator, propagation direction, and polarization of the illumination wave are indicated in Figure 1. In our simulation, the structural symmetry breaking is determined by the Δh, which is the thickness difference between the two halves of the resonator along the out-of-plane direction. Electromagnetic simulations are performed using both the finite element and finite-difference time-domain methods, where periodic boundary conditions are applied along the x and y directions, and perfectly matched layers (PML) with 48 layers are considered in the z directions. We assume a uniform grid with the unit cell size of 3 × 3 × 3 nm3, which will be enough to guarantee the convergence of the results. The experimentally measured dielectric function is utilized for silicon and silica [29] and the surface conductivity of graphene is determined by both the interband and intraband transition in the near infrared region and is derived with the random-phase approximation theory [30].
Orbital optimisation in the perfect pairing hierarchy: applications to full-valence calculations on linear polyacenes
Published in Molecular Physics, 2018
Susi Lehtola, John Parkhill, Martin Head-Gordon
In the present manuscript, we describe how orbital optimisation can be efficiently implemented for the models within the PPH, and present their applications to full-valence calculations on linear polyacenes. Ever since preliminary calculations predicted linear polyacenes to have singlet diradical ground states [53], both linear and cyclacenes have been studied intensively using a variety of methods [54]. Famously, DMRG calculations have been used to show that the larger linear polyacenes exhibit strong correlation for their π electrons [55]. Other approaches used have included density functional theory [56–61], multiconfiguration pair-density functional theory [62], projected Hartree–Fock theory [63], the random phase approximation [64], configuration interaction [60] (CI), adaptive CI [27], GW theory [65], variational two-electron reduced density matrix (VRDM) theory [66–69], Møller–Plesset perturbation theory [61,70–73], spin-flip methods [74,75], CAS-SCF [53,59,71,72,76] as well as restricted-active space self-consistent field theory [77], valence bond [78] and CC valence bond (CCVB) theory [79,80], CC theory [70–72,80] and multireference averaged quadratic CC theory [81,82], an algebraic diagrammatic construction scheme [83], as well as PPH methods with approximate orbitals [50].
Electric field induced non-linear multisubband electron mobility in V-shaped asymmetric double quantum well structure
Published in Philosophical Magazine, 2020
Ajit K. Panda, Sangeeta K. Palo, Narayan Sahoo, Trinath Sahu
Here qjl = [kFj2 + kFl2−2kFjkFlcosθ]1/2, and kFj = (2m*EFj/ħ2)1/2. For single subband occupancy, the intersubband terms would be absent, and we haveIn VDQW structure, the channels are made of alloy layers. Therefore the alloy disorder (Al-) scattering has a major role in deciding μ, besides the ionised impurity (Imp-) scattering. We adopted the static dielectric response function method and obtained screened scattering potentials under the framework of random phase approximation [31]. The screened Imp/Al-scattering potentials are [10]:where, is the inverse of the static dielectric function matrix. In Eq. 21, ‘a’ is the lattice constant, ‘δV’ is the alloy disorder scattering potential, and ‘x’ is the alloy fraction in AlxGa1-xAs layer. The Imp-scattering arises from the δ-doped layers in the outer barriers while the alloy disorder scattering takes place throughout the structure (barriers and wells). The interface roughness scattering is normally negligible since the wells, and barriers are made of the AlGaAs material without a clear cut interface. The low-temperature mobility μ is obtained by using Matthiessen’s rule, i.e. 1/μ = 1/μImp + 1/μAl [31].