A Nonlocal Description Of The Dispersion Relation And The Energy Flow Associated With Surface Electromagnetic Waves On Metals

Abstract

The nonlocal dispersion relation for electromagnetic surface waves on a metal -vacuum surface, obtained within the framework of the semiclassical infinite -barrier model, is reviewed. Limiting ourselves to the hydrodynamic approach, which allows collective excitations in the electron gas only, we have for the first time determined and identified the branches of the nonlocal dispersion relation, completely. Also, we address the question of how to treat the stationary energy flow associated with electromagnetic surface waves in the nonlocal regime.

Harnessing ultraconfined graphene plasmons to probe the electrodynamics of superconductors

“…In possession of the response functions epitomized by Eq. 1 , we employ the semiclassical infinite barrier (SCIB) formalism ( 23 , 39 ) to describe electromagnetic phenomena at a planar dielectric–superconductor interface ( 37 , 38 , 40 ). Within this framework, the corresponding reflection coefficient for -polarized waves is given by ( SI Appendix ) ( 23 , 39 ) with , and has the form where , and are the components of the superconductor’s nonlocal dielectric tensor (we take hereafter).…”

“…The graphene–superconductor separation is . Setup parameters: We take ; moreover, (so that and ), , and for the superconductor ( 38 , 40 , 41 ), and and , for graphene’s Drude-like optical conductivity ( 43 ).…”

“…Like ordinary conductors (44), superconductors can also sustain surface plasmon polaritons (SPPs) (45,46). In turn, these collective excitations can couple to the superconductor's Higgs mode moreover, n = 6 × 10 21 cm −3 (so that E F ≈ 1.20 eV and ωp ≈ 2.88 eV), γ = 1 µeV, and Tc = 93 K for the superconductor (38,40,41), and E gr F = 0.3 eV and γ gr = 1 meV, for graphene's Drude-like optical conductivity (43). (37,38).…”

“…The graphene-superconductor separation is t = 5 nm. Setup parameters: We take T = 1 K; moreover, n = 6 × 10 21 cm −3 (so that E F ≈ 1.20 eV and ωp ≈ 2.88 eV), γ = 1 µeV, and Tc = 93 K for the superconductor(38,40,41), and E…”

Surface waves on a strong-coupling superconductor

“…In this work one discusses the dispersion relations for SEW in a case of strong coupling superconductors in the spirit of the works [14] and [21]. In the framework of Debye approximation for phonon spectrum (aPh = v1q, v, is sound velocity) one can write that (10) (k,T) k (k,T) g2 (2q0 k +F(k)) (11) 22h 1-(g2 /2zr2h)F(k) ( …”