Phonon-mediated tuning of instabilities in the Hubbard model at half-filling

We obtain the phase diagram of the half-filled two-dimensional Hubbard model on a square lattice in the presence of Einstein phonons. We find that the interplay between the instantaneous electron-electron repulsion and electron-phonon interaction leads to new phases. In particular, a d$_{x^2-y^2}$-wave superconducting phase emerges when both anisotropic phonons and repulsive Hubbard interaction are present. For large electron-phonon couplings, charge-density-wave and s-wave superconducting regions also appear in the phase diagram, and the widths of these regions are strongly dependent on the phonon frequency, indicating that retardation effects play an important role. Since at half-filling the Fermi surface is nested, spin-density-wave is recovered when the repulsive interaction dominates. We employ a functional multiscale renormalization-group method that includes both electron-electron and electron-phonon interactions, and take retardation effects fully into account.Comment: 8 pages, 5 figure

On reference solutions and the sensitivity of the 2D Kelvin-Helmholtz instability problem

Two-dimensional Kelvin-Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the results in the literature differ considerably. This paper presents computational studies of a Kelvin-Helmholtz instability problem with high order divergence-free finite element methods. Reference results in several quantities of interest are obtained for three different Reynolds numbers up to the beginning of the final vortex pairing. A mesh-independent prediction of the final pairing is not achieved due to the sensitivity of the considered problem with respect to small perturbations. A theoretical explanation of this sensitivity to small perturbations is provided based on the theory of self-organization of 2D turbulence. Possible sources of perturbations that arise in almost any numerical simulation are discussed.Comment: 24 pages, 12 figures, 2 table

Validity of effective material parameters for optical fishnet metamaterials

Although optical metamaterials that show artificial magnetism are mesoscopic systems, they are frequently described in terms of effective material parameters. But due to intrinsic nonlocal (or spatially dispersive) effects it may be anticipated that this approach is usually only a crude approximation and is physically meaningless. In order to study the limitations regarding the assignment of effective material parameters, we present a technique to retrieve the frequency-dependent elements of the effective permittivity and permeability tensors for arbitrary angles of incidence and apply the method exemplarily to the fishnet metamaterial. It turns out that for the fishnet metamaterial, genuine effective material parameters can only be introduced if quite stringent constraints are imposed on the wavelength/unit cell size ratio. Unfortunately they are only met far away from the resonances that induce a magnetic response required for many envisioned applications of such a fishnet metamaterial. Our work clearly indicates that the mesoscopic nature and the related spatial dispersion of contemporary optical metamaterials that show artificial magnetism prohibits the meaningful introduction of conventional effective material parameters

Self-energy corrections to anisotropic Fermi surfaces

The electron-electron interactions affect the low-energy excitations of an electronic system and induce deformations of the Fermi surface. These effects are especially important in anisotropic materials with strong correlations, such as copper oxides superconductors or ruthenates. Here we analyze the deformations produced by electronic correlations in the Fermi surface of anisotropic two-dimensional systems, treating the regular and singular regions of the Fermi surface on the same footing. Simple analytical expressions are obtained for the corrections, based on local features of the Fermi surface. It is shown that, even for weak local interactions, the behavior of the self-energy is non trivial, showing a momentum dependence and a self-consistent interplay with the Fermi surface topology. Results are compared to experimental observations and to other theoretical results.Comment: 13 pages, 10 figure

Deformation of anisotropic Fermi surfaces due to electron-electron interactions

We analyze the deformations of the Fermi surface induced by electron-electron interactions in anisotropic two dimensional systems. We use perturbation theory to treat, on the same footing, the regular and singular regions of the Fermi surface. It is shown that, even for weak local coupling, the self-energy presents a nontrivial behavior showing momentum dependence and interplay with the Fermi surface shape. Our scheme gives simple analytical expressions based on local features of the Fermi surface.Comment: 7 pages, 3 figure

Relating localized nanoparticle resonances to an associated antenna problem

We conceptually unify the description of resonances existing at metallic nanoparticles and optical nanowire antennas. To this end the nanoantenna is treated as a Fabry-Perot resonator with arbitrary semi-nanoparticles forming the terminations. We show that the frequencies of the quasi-static dipolar resonances of these nanoparticles coincide with the frequency where the phase of the complex reflection coefficient of the fundamental propagating plasmon polariton mode at the wire termination amounts to $\pi$. The lowest order Fabry-Perot resonance of the optical wire antenna occurs therefore even for a negligible wire length. This approach can be used either to easily calculate resonance frequencies for arbitrarily shaped nanoparticles or for tuning the resonance of nanoantennas by varying their termination.Comment: Submitted to Phys. Rev.