Metamaterial engineering to triple the critical temperature of a superconductor

Recent theoretical¹,² and experimental³ work has conclusively demonstrated that using metamaterials in dielectric response engineering can increase the critical temperature of a composite superconductor-dielectric metamaterial. This enables numerous practical applications, such as transmitting electrical energy without loss, and magnetic levitation devices. Dielectric response engineering is based on the description of superconductors in terms of their dielectric response function,⁴ which is applicable as long as the material may be considered a homogeneous medium on the spatial scale, below the superconducting coherence length. With this in mind, the next logical step is to use recently developed plasmonics and electromagnetic metamaterial tools to engineer and maximize the electron pairing interaction in an artificial ‘ metamaterial superconductor’^1,2 (see Figure 1) by deliberately engineering its dielectric response function. For example, we may expect considerable enhancement of attractive electron-electron interaction in metamaterial scenarios such as epsilon-near-zero (ENZ, an artificial material engineered such that its dielectric permittivity—usually denoted as ‘ epsilon’—becomes very close to zero) and hyperbolic metamaterials (artificial materials with very strong anisotropy that behave like a metal in one direction, and a dielectric in another orthogonal direction).

We have verified such phenomena in experiments with compressed mixtures of tin and barium titanate nanoparticles of varying composition.³ The results showed a deep connection between the fields of superconductivity and electromagnetic metamaterials. However, despite this initial success, the observed critical temperature increase was modest. We argued² that the random nanoparticle mixture geometry may not be ideal because simple mixing of superconductor and dielectric nanoparticles results in substantial spatial variations of the dielectric response function throughout a metamaterial sample. Such variations lead to considerable broadening and suppression of the superconducting transition.

To overcome this issue, we considered using an ENZ plasmonic core-shell metamaterial geometry designed to achieve partial cloaking of macroscopic objects.² The cloaking effect relies on mutual cancellation of scattering by the dielectric core and plasmonic shell of the nanoparticle, so that the effective dielectric constant of the nanoparticle becomes very small and close to that of a vacuum. For this purpose we may also use a plasmonic core with a dielectric shell. We can extend this approach to the core-shell nanoparticles that exhibit negative ENZ behavior, as required in the superconducting application. Synthesis of such individual ENZ core-shell nanostructures followed by nanoparticle self-assembly into a bulk ENZ metamaterial appears to be a viable way to fabricate an extremely homogeneous metamaterial superconductor.

We have undertaken the first successful realization of an ENZ core-shell metamaterial superconductor using compressed aluminum oxide (Al₂O₃)-coated 18nm-diameter aluminum (Al) nanoparticles (see Figure 1). This led to a tripling of the metamaterial critical temperature compared to the bulk aluminum.⁵ The material is ideal for proof-of-principle experiments because the critical temperature of aluminum is quite low (Tc_Al=1.2K), leading to a very large superconducting coherence length of ∼1600nm. Such length facilitates the metamaterial fabrication requirements. Upon exposure to the ambient conditions an ∼2nm-thick Al₂O₃ shell forms on the aluminum nanoparticle surface, which is comparable to the 9nm radius of the original aluminum nanoparticle. We achieved further oxidation by heating the nanoparticles in air. We compressed the resulting core-shell Al₂O₃-Al nanoparticles into macroscopic test pellets using a hydraulic press (see Figure 1).

Figure 1. Schematic geometry of the epsilon-near-zero metamaterial superconductor based on core-shell nanoparticle geometry. The nanoparticle diameter is 18nm. The inset shows typical core-shell metamaterial dimensions. Al: Aluminum. Al₂O₃: Aluminum oxide.

We determined the critical temperature of various Al-Al₂O₃ core-shell metamaterials by the onset of diamagnetism for samples with different degrees of oxidation (see Figure 2). Even though the lowest achievable temperature with our superconducting quantum interference magnetometer was 1.7K, we were able to observe a gradual increase of Tc that correlated with an increase of the Al₂O₃ volume fraction. The highest onset temperature of the superconducting transition reached 3.9K, which is more than three times as high as the critical temperature of bulk aluminum, Tc_Al=1.2K.

Figure 2. Temperature dependence of magnetization per unit mass M (emu/g) for several Al and Al₂O₃core-shell metamaterial samples with increasing degrees of oxidation measured in a magnetic field (B) of 10G. The highest onset of superconductivity at ∼3.9K is marked by an arrow. This temperature is 3.25 times higher than that of bulk aluminum (Tc=1.2K).

We anticipate that it may be possible to implement the same approach to other known superconductors with higher critical temperature, and our future work will focus on exploring these possibilities.