General context

Since the discovery of graphene, two-dimensional (2D) materials have become the core of the modern material physics. Typically, the 2D limit is reached in layered materials with strong in-plane bonds and weak, van der Waals-like coupling between layers, which enables atomically-precise cleaving or their layer-by-layer growth. Tremendous effort has been put into advances to not only fabricate, but also functionalize 2D materials, in order to meet the technological grand challenges in sustainable energy solutions and device miniaturization. In that respect, it is now well established that 2D materials are very susceptible to chemical functionalization by dopant atoms, electric gating, strain, and/or interface interplay with the substrate, making them far more versatile than their 3D counterparts.

Driven by a similar idea, a separate lane of research over the past two decades has been devoted to tailoring the properties of superconductors by confinement - when reduced in size to mesoscopic scale, comparable to characteristic length-scales of superconductivity, but also beyond - to true nanoscale. In the former case, the critical properties (critical magnetic field and current) of the given superconductor could be significantly enhanced, which is of both fundamental and technological interest. In the latter case, new quantum-mechanical effects were foreseen in the direction of strong confinement. It soon became obvious that ultrathin films harbor the best of both worlds, so that longitudinally the almost macroscopic superconductivity can be preserved, while being strongly confined and quantum-engineered in transverse direction. The problem was that at such small thicknesses, thermodynamic fluctuations, proximity effects, scattering, could all break Cooper-pairs and destroy superconductivity. It was thus a great surprise that superconductivity survived in few-monolayer crystalline films of Pb [1], followed by observation of conventional superconductivity and vortices in one monolayer Pb and In on Si(111) [2]. However, it was immediately shown that the latter is not pure surface-state superconductivity, since the Si substrate played an essential role. This was an indication that very little can be done theoretically unless first-principles studies based on density-functional theory (DFT) are undertaken. Further experimental advances and observation of 2D superconductivity in van der Waals materials, e.g. an isolated single layer of doped graphene [3], (gated) transition metal chalcogenides and carbides [4], and iron-selenide on SrTiO3 (with surprisingly high critical temperature Tc>100K [5]), created an enormous buzz in the community and raised a serious challenge for the theory to (a) explain the observed features, and (b) make further predictions towards functional alterations of those materials and possible ultra-small devices. Unfortunately, while modern experimental techniques are enabling increasingly multifold studies of superconductivity (in-situ synthesis, functionalization, transport and/or scanning-probe measurements), the community has witnessed an increasing gap between the ab initio calculations and those on mean-field levels, and even more to the desired device modelling at the ultrathin limit. This workshop aims to change this unsatisfying picture: to bring together some of the experts in the field, on both theoretical and experimental end, and discuss the needed multi-scale characterization of atomically thin superconductors, in order to identify the main challenges and further exploration avenues in this booming field of research, with envisaged applications in ultra-low power and ultra-light electronics, as well as novel functional materials.

Selected topics include:

- Superconductivity in elementary superconductors at ultrathin limit

2D superconductivity of elementary metals (Pb, In) on Si(111) is well stablished, but still quite superficially understood. Many different few-monolayer metals were realized, where different organizations of a same element on a given substrate had very different (or no) superconducting properties, which requires thorough theoretical discussion based on ab initio theory and state-of-the-art experimentation. Further the community needs to address the emergent physics in compounds: for example, the 2D compound of Tl with Pb on Si(111) is a 2D material that combines the giant Rashba-type spin splitting with superconductivity, which results in a combination of superconductivity and spin polarization. Therefore, in this workshop, other 2D compounds made of (heavy) metals with strong spin-orbit coupling will be considered, to form a broader base for 2D superconducting spintronic devices.

- Superconductivity in 2D TMDs

2D semiconducting transition metal dichalcogenides (TMDs) have already found applications in a variety of electronic and opto-valleytronic devices. Only recently the superconductivity has been added to the list of exciting properties. Since it is known that properties of 2D TMDs can be effectively tuned in a wide range through for example intercalation, heterostructuring, gating, pressure, and lighting, the scientific community wonders about such dependence of superconductivity in atomically thin TMDs, and the possibility of stacking various dichalcogenides into heterojunctions for advanced superconducting properties.

- Superconductivity in 2D iron-chalcogenides

The observation of a large superconducting-like energy gap which opens at very high temperatures in single unit cell (UC) iron selenide films on SrTiO3 has generated tremendous interest. During the workshop, we will consider the data from the measurements on 1UC and multi-UC thick FeSe films grown on STO to clarify the reasons for strong cross-interface electron-phonon coupling in single UC, and possibly further increase superconducting Tc by e.g. methods outlined in the paragraph on TMDs. A complete understanding of the mechanism underpinning high-temperature superconductivity (HTS) is notoriously elusive, but a growing body of evidence suggests that HTS in monolayer iron selenide is an ideal model system for testing theoretical ideas.

- Superconductivity in alkali-doped graphene and boron nitride

The recent prediction of superconductivity in Li-doped graphene has just been confirmed by the ARPES measurements, and further observed in few-layer Li-doped graphene and Ca-doped graphene. Many of the participants in the workshop have vast experience in further enhancement of superconductivity by quantum confinement, which may be achieved in e.g. doped-graphene nanoribbons (GNRs), based on the fact that the quantum-size effects due to the nanoscale confinement in the ribbons, together with the formation of a system of multiple subbands, amplify the density of states (DOS) and thereby enhance the pairing gap. In that respect, an artificial van der Waals solid of boron-nitride and graphene layers is also worth of discussion, where superconductivity can be combined with other advanced functionalities.

- Multigap superconductors at ultrathin limit, for high-temperature superconductivity

Recent years have seen a surge of new superconductors with high critical temperatures (iron-based and otherwise), mostly characterized by several electronic bands contributing to Cooper-pairing (so called multiband superconductors, typically exhibiting multiple superconducting gaps as well). It is a matter of intense research how the multiband/gap structure changes in the superconducting materials at the ultrathin limit. The main issue is how properties can be controlled artificially at atomic level to make them favorable to exhibit high temperature superconductivity. All the relevant properties will clearly be susceptible to further engineering by strain, doping, gating, etc. which will inevitably lead to tunable superconducting performance not possible otherwise. Understanding those is at the core of the present workshop proposal.

- Tunable properties of engineered oxide interfaces

Advances in growth technology of oxide materials allow single atomic layer control of heterostructures. In particular delta doping, extensively used in semiconductor technology, is now also available for oxides. That enables an electric-field-tunable spin-polarized and superconducting quasi-2D electron system to be artificially created at the interface between LaAlO3 and SrTiO3 oxides. The occurrence of magnetic interactions, superconductivity and spin–orbit coupling in the same material makes the oxide-interface system an extremely intriguing platform for the emergence of novel quantum phases in low-dimensional materials.

- Other emergent topics in the field.