Notes from Materials Design for New Superconductors

Some notes as I read:

Just to note, this paper is pretty old (2016) and is before SuperCon and most computational/ML approaches to Tc prediction and material discovery. It seems like a somewhat desperate attempt to explain what's been found in lab, but with little data to support these ideas (no offense intended by this, they're doing the best with the tools they have). This kind of bottom-up explanation of how superconducting works and building intuition is important when you're limited by man-hours and the ability to actually synthesize these materials. Still, there are things we can learn.

"There have been several interesting attempts to apply both materials genome and materials design principles to the discovery of new superconductors. Here, these are reviewed, with some thoughts about where the field is headed."

One issue is that even if one has a good representation of the Eliashberg function, the actual value of Tc is suppressed due to Coulomb effects [14]. The calculation of this repulsive µ ? is on much less firm ground than the attractive electron-ion interaction, though recent progress has been made [15].

Because of the many-body effects and subtle interplay of electron-ion and electron-electron interactions, good Tc predictions are hard!

The true high temperature superconductors, at least at ambient pressures [17], are cuprates and iron pnictides. Here, we lack even a quantitative theory of what is going on, though most feel that the attractive interaction leading to the formation of Cooper pairs is likely due to magnetic correlations [18]. Still, one could in principle develop descriptors of such materials, and then use them to predict new superconductors.

Two classes we know of, but I'm betting there are more! I agree that Cooper pairs or other quasiparticles emergent from the lattice structure and geometry are still the main mechanism for superconductivity.

Most unconventional superconductors are indeed found in proximity to a magnetic phase. In Fig. 1, the phase diagrams are shown for several classes of superconductors: cuprates, pnictides, 2D-organics, and heavy fermions [30]. In all cases, the phase diagrams are similar, including the not shown example of Cs-doped C60 (buckyballs) [31]. One starts with a magnetic phase, typically an antiferromagnet (sometimes insulating, sometimes not), and then uses a control parameter (such as chemical doping or pressure) to suppress the magnetic phase, leading to a superconducting ‘dome’ that eventually gets suppressed itself as the tuning parameter increases even further. This design principle was realized early on by Gil Lonzarich’s group and led to the discovery by them of heavy fermion superconductivity in CePd2Si2 and CeIn3 [32].

This brings us to what I call the Goldilocks principle for high Tc. Quasi-1D superconductors tend to have low Tc since fluctuations kill superconductivity in lower dimensions. On the other hand, 3D materials are limited in Tc because interactions typically are weaker in higher dimensions. So, 2D is just right, and sure enough, the highest Tc materials, cuprates and pnictides, are layered materials.

Very, very interesting. We'll have to see if this is really a rule for high-Tc, but the author seems to think 2D materials are our best bet.

In essence, cuprates can be thought of as doped Mott insulators [43], with the high Tc thought to be due to the extremely large superexchange interaction of 120 meV between the Cu ions mediated by the intervening oxygen ions [42, 43].

Interesting. Seems like a pretty good explanation for this class of superconductor. All the more reason to nail quasiparticles, and it seems holes are another important one on top of phonons.

Now, how does materials design enter? One of the first attempts along this line was by Ole Andersen’s group [44]. They noticed that Tc scaled with the distance, d(Cu-apical O), between the copper and apical oxygen atoms (the copper-planar oxygen separation does not vary much). They realized that the pz orbital on the apical oxygen, along with the 4s orbital on the copper site, helped to mediate longer range hopping in the CuO2 planes, in particular an effective hopping integral that acts between planar oxygen ions, denoted as $t^1$, with $t^1$ and d(Cu-apical O) scaling together. This line of approach has subsequently been taken on by more sophisticated many-body techniques such as dynamical mean field theory (DMFT). Such studies [45] have shown a calculated correlation of Tc with not only these two parameters, but also with the separation of the energies of the d x2 -y2 and the planar oxygen 2p states (the smaller this energy difference, the higher Tc is).

This is huge. In our computational efforts, we want to make sure that our dataset has the necessary features that could play into Tc. Here, they mention the distance between the copper and apical oxygen atoms has an effect.

That is, designing superconductors requires not only tuning the electronic structure and interactions (via the choice of metal, ligand, and crystal structure), but also by tuning the carrier concentration (chemical doping or pressure) and the defect landscape (to enhance pinning). It is only by thinking about all three of these facets will we have a hope of designing ideal superconductors.