Competing energy scales in granular superconductors: phase-governed superfluid and pseudogap determine the superconducting dome

通过探索一个良好控制的介观系统，我们希望推进我们对它们相关量子态的理解。粒状铝的超导特性与块状铝的超导特性有很大的不同，粒状铝可以方便地生长成薄膜。特别是临界温度Tc增加到3倍，超过3 K。几十年来，这种增强的Tc的起源仍然不清楚，但我们最近使用光学太赫兹光谱表明，关键因素是当铝晶粒由于薄氧化物层而越来越去耦时，超导能隙的增加。然而，对于更多的解耦晶粒，抑制超流刚度进入Tc的限制因素。这种能隙和超流刚度的相互作用导致了颗粒铝的特征相图，其特征是具有宽的最大值，即所谓的超导圆顶。我们还发现了非常规行为的第一个迹象，如在光谱中的赝隙，在相图的高电阻率/绝缘侧。现在，我们想通过结合太赫兹和微波光谱学来详细探索高电阻率颗粒铝的特殊超导性质。我们想要回答的一个问题是，由于量子限制而增强的能隙如何随着Tc的降低而在相图的绝缘侧演变。这涉及到假定的超导体到绝缘体的转变以及赝能隙状态，这可能是由不能形成超导凝聚体的局部库珀对引起的。这是相图中特别有趣的部分，我们只能通过将实验扩展到光谱范围和温度中的低得多的能量来访问。我们目前对颗粒状铝的特殊相图的理解是纳米尺度上的电子约束的关键因素，在我们的情况下，铝颗粒的尺寸为2纳米。晶粒尺寸的进一步减小将导致超导能隙和Tc的进一步提高。因此，我们希望通过铝的热蒸发和沉积到冷却到4 He温度的衬底上来生长颗粒状铝薄膜。这种具有更小晶粒的薄膜将使我们能够将我们对超导颗粒铝的理解扩展到更高的能量，并且它们还将证明，在纳米尺度上控制结构特性可以导致超导性的故意增强，包括更高的Tc。这可以作为其他超导材料的例子。因此，我们也希望生长其他元素超导体作为颗粒膜，并表征它们的能量尺度。这些结果对于理解其他介观系统中的新电子态也有重要意义。

By exploring a well-controlled mesoscopic system we want to advance our understanding of their correlated quantum states. The superconducting properties of granular aluminum, which is conveniently grown as thin films, differ drastically from those of bulk aluminum. In particular there occurs an enhancement of the critical temperature Tc up to a factor of three, exceeding 3 K. The origin for this enhanced Tc remained unclear for decades, but using optical THz spectroscopy we recently showed that the key ingredient is an increase of the superconducting energy gap when the aluminum grains are more and more decoupled due to a thin oxide layer. For yet more decoupled grains, however, the suppressed superfluid stiffness enters as limiting factor for Tc. This interplay of energy gap and superfluid stiffness leads to the characteristic phase diagram ofgranular aluminum that features a broad maximum, the so-called superconducting dome. We also found first signs of unconventional behavior, such as a pseudogap in the optical spectra, on the high resistivity/insulating side of the phase diagram. Now we want to explore the peculiar superconducting properties of high-resistivity granular aluminum in detail by combining THz and microwave spectroscopy. One question that we want to answer is how the energy gap, which is enhanced due to quantum confinement, evolves on the insulating side of the phase diagram as Tc decreases. This concerns the putative superconductor-to-insulator transition as well as thepseudogap regime, which might be caused by localized Cooper pairs that cannot form a superconducting condensate. This particularly interesting part of the phase diagram we can only access by extending our experiments to much lower energies in spectral range as well as temperature. Our present understanding of the extraordinary phase diagram of granular aluminum has as key element the electron confinement on the nm scale, in our case aluminum grains of 2 nm size. Further reduction of grain size should lead to further enhancement of superconducting energy gap and Tc. Therefore, we want to grow granular aluminum thin films by thermal evaporation of aluminum and deposition onto substrates that are cooled to 4He temperatures. Such thin films with even smaller grains will allow us to extend our understanding of superconducting granular aluminum to yet higher energies, and they will also demonstrate that control of structural properties on the nm scale can lead to a deliberate enhancement of superconductivity including a higher Tc. This can then serve as example for other superconducting materials. Therefore, we also want to grow other elemental superconductors as granular films and characterize their energy scales. The results may also prove important in the understanding of novel electronic states in other mesoscopic systems.