# Matthias’ List — Check it Twice

Bernd Matthias was a prominent chemist/physicist and who played a major role in the history of superconductivity. He discovered nearly 1,000 superconducting compounds in his career and most notably discovered the NbTi and Nb$_3$Sn superconductors, which found commercial use in MRI instruments.

Using his vast experience in the synthesis of (classic BCS) superconducting materials, he made an empirical list of the rules he followed in searching for new superconductors.

1. High symmetry is good; Cubic symmetry is best
2. High density of electronic states is good
3. Stay away from oxygen
4. Stay away from magnetism
5. Stay away from insulators
6. Stay away from theorists

It is worth reflecting upon this list and thinking about how Matthias came to these conclusions (even the last item). First of all, many of the items in the list are not in any way embodied by BCS theory (1, 3, and 5 in particular). Secondly, the cuprates seems to disobey all of these items (except the last one)! It is interesting to note that Matthias was a vocal opponent of BCS theory for its failure to capture many aspects of superconductors he considered essential and for its inability to predict transition temperatures and new superconducting materials.

Matthias’ list has inspired many in the field of unconventional superconductivity to make lists similar to his. For those of you who read this blog regularly, you are probably aware that I am fond of lists (see here and here for instance), because they help synthesize key experimental observations. You are also likely to find out some of your own biases when making a list. Below is a Matthias-style list of unconventional superconductivity put forth by Igor Mazin, which contains items that I find myself generally agreeing with:

1. Layered structures are good
2. Carrier density should not be too high
3. Transition metals of the fourth period are good
4. Magnetism is essential
5. Proper Fermi surface geometry is essential
• Must match the spin excitation structure
6. Enlist theorists, at least to compute Fermi surface structures

As we near the winter holiday period (in the northern hemisphere!), please feel free to share your own list, add an item to the one above, or even share some misgivings about Mazin’s list.