Theoretical modeling of critical temperature increase in metamaterial superconductors

Abstract

Recent experiments have demonstrated that the metamaterial approach is capable of drastic increase of the critical temperature T c of epsilon near zero (ENZ) metamaterial superconductors. For example, tripling of the critical temperature has been observed in Al-Al 2 O 3 ENZ core-shell metamaterials. Here, we perform theoretical modelling of T c increase in metamaterial superconductors based on the Maxwell-Garnett approximation of their dielectric response function. Good agreement is demonstrated between theoretical modelling and experimental results in both aluminium and tin-based metamaterials. Taking advantage of the demonstrated success of this model, the critical temperature of hypothetic niobium, MgB 2 and H 2 S-based metamaterial superconductors is evaluated. The MgB 2 -based metamaterial superconductors are projected to reach the liquid nitrogen temperature range. In the case of an H 2 S-based metamaterial T c appears to reach ~250 K.Our recent theoretical [1,2] and experimental [3,4] work demonstrated that many tools developed in electromagnetic metamaterial research may be successfully used to engineer artificial metamaterial superconductors having considerably improved superconducting properties. This deep and non-trivial connection between the fields of electromagnetic metamaterials and superconductivity research stems from the fact that superconducting properties of a material, such as electron-electron pairing interaction, the superconducting critical temperature T c , etc. may be expressed via the effective dielectric response function  eff (q,) of the material [5]. For example, considerable enhancement of attractive electron-electron interaction may be expected in such actively studied metamaterial scenarios as epsilon near zero (ENZ) [6] and hyperbolic metamaterials [7] since in both cases  eff (q,) may become small and negative in substantial portions or the four-momentum (q,) space. Such an effective dielectric response-based macroscopic electrodynamics description is valid if the material may be considered as a homogeneous medium on the spatial scales below the superconducting coherence length. The metamaterial superconductor approach takes advantage of the recent progress in plasmonics and electromagnetic metamaterials to engineer an artificial medium or "metamaterial", so that its effective dielectric response function  eff (q,) conforms to almost any desired behaviour. It appears natural to use this newly found freedom to engineer and maximize the electron pairing interaction in such an artificial superconductor via engineering its dielectric response function  eff (q,). The most striking example of successful metamaterial superconductor engineering was recent observation of tripling of the critical temperature T c in Al-Al 2 O 3 epsilon near zero (ENZ) core-shell metamaterial superconductors compared to bulk aluminium [4]. However, both this result and the previous demonstration of T c increase in random ENZ mixtures [3] were based on qualitative theoretical guidelines, while numer...

Superconducting properties of tin-based ENZ and hyperbolic metamaterials

“…This figure demonstrates that the experimentally measured behaviour of T c as a function of n (which is defined by the Sn layer thickness) correlates well with the theoretical prediction. As discussed in detail in [21], smaller relative increases of T c in tin-based metamaterial superconductors compared to similar aluminium-based metamaterial geometries may be explained by considerably larger imaginary part  m " of the tin dielectric constant.…”

Metamaterial superconductors

“…It was also proposed to modify natural hyperbolic superconductors (such as HgBa 2 CuO 4+y ) via inhomogeneous charge density waves (CDW) [14]. Together with our electromagnetic metamaterial approach these strategies open up new areas in superconductivity research at the unconventional intersection of nanophotonics and solid state physics, which may potentially reach the scientific dream of achieving room temperature superconductivity [15].…”

Observation of plasmon-phonons in a metamaterial superconductor using inelastic neutron scattering

“…(4) the magnitude of  m is limited). The blue dashed line shows the predicted behaviour in the presence of both poles[3]. The experimentally measured data points from[5] are shown for comparison on the same plot.…”

“…The zero of the dielectric response function of the bulk metal (which occurs at =(q) where  m changes sign) maximizes the electron-electron pairing interaction given by Eq.(1). This simplified consideration of  m (q,) has been justified in [3].…”

“…(3) is proportional to n, which is justified by the fact that there are no free charges in the dielectric phase of the metamaterial. We assume that Im( d )~0 and neglect the dispersion of Im( m ) in this simplified estimate (the detailed calculations may be found in [3] (13) where  m "=Im( m ). Therefore, using Eq.…”