Precision photonic band structure calculation of Abrikosov periodic lattice in type-II superconductors

Abstract

We have performed a numerical solution for band structure of an Abrikosov vortex lattice in type-II superconductors forming a periodic array in two dimensions for applications of incorporating the photonic crystals concept into superconducting materials with possibilities for optical electronics. The implemented numerical method is based on the extensive numerical solution of the Ginzburg-Landau equation for calculating the parameters of the two-fluid model and obtaining the band structure from the permittivity, which depends on the above parameters and the frequency. This is while the characteristics of such crystals highly vary with an externally applied static normal magnetic field, leading to nonlinear behavior of the band structure, which also has nonlinear dependence on the temperature. The similar analysis for every arbitrary lattice structure is also possible to be developed by this approach as presented in this work. We also present some examples and discuss the results.

The physics and applications of superconducting metamaterials

“…Subsequent work showed that neglect of the quasiparticles introduces significant errors, although a strongly temperature dependent quasiparticle scattering rate (as seen in certain cuprate superconductors 67 ) can restore some of the temperature tunability. 58 Development of dielectric contrast from an Abrikosov vortex lattice to create a photonic crystal is a novel idea first proposed by Takeda, et al 68 , and studied by Kokabi, et al, 69 and Zandi, et al 70 Magnetic vortices form a long-range ordered lattice in an ideal superconductor, creating a regular dielectric contrast between normal metal core tubes and the superconducting background. Takeda, et al assumed the cores were described by a constant permittivity, while outside it is a dissipation-less Drude metal.…”

“…Development of dielectric contrast from an Abrikosov vortex lattice to create a photonic crystal is a novel idea first proposed by Takeda et al [68], and studied by Kokabi et al [69] and Zandi et al [70]. Magnetic vortices form a longrange ordered lattice in an ideal superconductor, creating a regular dielectric contrast between normal metal core tubes and the superconducting background.…”

“…They found that the PC band structure, and gaps, can be tuned by variation of the magnetic field (which changes the PC lattice parameter) and the Ginzburg-Landau parameter, κ [68]. Kokabi et al [69] and Zandi et al [70] calculated the superconducting electron density using the self-consistent Ginzburg-Landau formalism, and calculated the resulting PC band structure for both isotropic [69] and anisotropic [70] superconductors.…”