Introduction
Superconductors have resisted miniaturization. The drive towards packing more circuits on a chip requires thinner and narrower conductors; however, superconductivity is suppressed when one or more dimensions of the sample is comparable to the 'size' of the electron pairs (about 1–100 nm) that make up the superconducting state. Shrinking a superconductor not only makes it difficult for electrons to pair up, but also it makes it harder for them to keep their act together — that is, to maintain the collective quantum state in which pairs act coherently and flow without resistance. For very thin films, thermal or quantum agitation can muddle up the phase coherence of the pairs and destroy the treasured zero-resistance property of a superconductor. In a magnetic field, in which superconductors find their most important technological applications — as wires for electromagnets, for example — things are even worse. In a thin-film superconductor, it is difficult to pin down the magnetic flux lines (vortices), the motion of which makes superconducting films resistive and dissipates energy. On page 173 of this issue1, Özer, Thompson and Weitering show that crystalline perfection makes a thin film a more robust conventional superconductor. Perhaps more remarkable is their demonstration that the nanoscale engineering of defects can be used to turn these lean films into 'hard' superconductors, in which magnetic flux lines are pinned strongly.
Making crystalline thin-films with a thickness of a few atomic layers is rather challenging. Metal atoms usually prefer to clump together instead of covering an insulator's surface evenly; hence most elemental superconductors grow in a granular or amorphous fashion on insulating substrates. Lead (Pb) is unusual in the sense that under certain growth conditions it forms extraordinarily smooth films on semiconductor surfaces, starting at just a few atomic layers2. These films exceed typical expectation, as their growth is not determined by energies associated with strain, or interfaces, but rather with the confinement and quantization of electronic states perpendicular to their thickness. Nanoscale imaging of these films with scanning tunnelling microscopy shows that the flatness of these films, for thicknesses larger than five monolayers, is mostly limited by the width of the atomic terraces in the underlying semiconductor.
Özer et al. take advantage of the 'quantum growth' of Pb films to investigate superconductivity in extremely thin and clean films. On making Pb samples that are progressively thinner, the authors find a systematic reduction of the superconducting transition temperature from the bulk value (7.2 K), which scales with inverse film thickness. They explained this observation by considering the relative importance of surface to bulk condensation energy, as more of the atoms in a thin film are at the surface rather than its bulk. However, the suppression of superconductivity is very gradual compared with those previously reported for amorphous or granular thin-films3. The strong reduction of the superconducting transition temperature with decreasing thickness in amorphous or granular films, has been associated with the increasing role of disorder. One effect of disorder is to enhance the effective repulsion between electrons, as it localizes them to small regions within the sample. This enhanced repulsion competes with the tendency for electrons to pair up and is detrimental to superconductivity. Another important effect is that disorder can disrupt the quantum coherence between the pairs, by reducing the energy cost for pairs to be out of step from each other — that is, to develop a phase slippage in their collective wavefunction. Making crystalline thin-films with minimal disorder side-steps both detrimental effects, and allows superconductivity to be more robust in the ultrathin Pb films.
The 'quantum growth' not only enables Özer et al. to maintain atomic order in their Pb films down to very few monolayers, it also provides them with the opportunity to create what turns out to be very useful nanoscale defects. An unusual matching of the wavelength of the highest occupied electronic states in Pb with atomic-layer spacing in their films dictates a bilayer-by-bilayer growth for these films. Consequently, if the growth of the film is interrupted just before a full monolayer is achieved, the films have a very smooth surface except for voids that are exactly two monolayers deep (as shown in Fig. 1). Similarly, interruption of growth after formation of a full monolayer gives rise to mesas defects that are two monolayers high. Such defects in overdosed or underdosed thin Pb films end up having an important influence on how they behave in magnetic fields.
Figure 1: Trapping vortices.
Magnetic field lines (black) can only penetrate a superconductor through a vortex, which has a non-superconducting core surrounded by supercurrent flow (red). The movement of vortices causes energy dissipation (finite resistance), but shallow pits (and mesas) on the lead surface serve as defect centres to pin the vortices in place, ensuring that current can flow without resistance.
Full size image (38 KB)A bulk Pb sample expels magnetic field from its interior until the field energy exceeds that of the superconducting condensation energy, at which point pairing is destroyed and a normal metallic state is recovered. In a thin-film sample, it turns out that it is energetically more favourable for a magnetic field to penetrate the films in the form of quantized magnetic flux lines — known as quantized vortices. In this so-called Abrikosov vortex state, the superconductor is broken up into superconducting regions and vortex cores, in which the magnetic field penetrates the sample and there are no superconducting pairs. Surrounding the vortices are circulating currents that add a twist to the phase of the superconducting electrons' wavefunction (Fig. 1). In the vortex state, zero resistance of a superconductor is maintained so as long as the vortices are stationary, as their motion changes the phase of the superconducting wavefunction and causes an associated voltage drop in the sample. It is therefore common to add disorder to a superconductor to provide locally suppressed pairing sites at which the vortex cores prefer to be pinned. The harder the vortices are pinned the larger the dissipationless currents the superconductor can carry in a magnetic field.
Özer et al. find that the voids created by the 'quantum growth' provide ideal pinning sites for vortices, hence making their clean and lean Pb films act like a dirty and 'hard' superconductor. The physical reason behind this behaviour is clear, as the two-layer-deep voids represent very strong local suppressions of the superconducting order in a film that is just a few monolayers thick. Analysis of magnetization measurements in these films shows that the local potential energy trapping the vortices at the voids is equivalent to an energy scale several times that of room temperature. Such deep traps enable quite sizable supercurrent flow through these Pb films in a magnetic field — surprisingly they are a reasonable fraction of the currents that break up the pairs themselves. Özer and co-authors further confirm their interpretations by showing that thin films with mesas are far less effective in pinning vortices and have far worse performance in a magnetic field.
The idea of engineering nanoscale barriers for vortex motion can also be applied to other thin superconductors, provided that, similar to Pb, the defects introduced to pin the vortices are not detrimental to superconductivity in such thin samples. The ultrathin Pb films with their sharp defect structures may prove to be a special case, as it is tough to 'dirty up' a thin superconductor cleanly. Ultimately, Özer et al. demonstrate that finding out what works requires the measurement and control of the nanoscale structure of the samples with high precision.