# The requirements for superconductivity

Which properties are sufficient evidence for a material to be not superconducting? I am looking for a set of statements like

If the material is semiconducting, it is not superconducting

Edit: I am not looking for a definition of superconductivity, or for introductional literature like the famous W. Buckel.

I am looking for properties, that would forbid superconductivity. If you have a source for it i would be very glad. As far I remember magnetic atoms will forbid superconductivity too, but i could not find a source yet.

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Properties are temperature dependent. For example, Ge is not semiconducting if it is too warm. Cuprates are Mott insulators, but become superconducting at sufficiently low temperatures. You may want to reformulate your question. –  Jen Nov 26 '12 at 20:03

This question has a semi-canonical answer; Matthias' rules for superconductivity. This was a real set of empirical criteria proposed well before the cuprates were discovered, but here is the tongue-in-cheek version (I'm not sure who to attribute this presentation to, however -- comments appreciated).

1. Symmetric lattices (i.e. cubic),
2. Avoid oxygen,
3. Avoid magnetism,
4. Avoid insulators,
5. Avoid theorists ;)

Obviously the cuprates are a knock against all of those, except the bit about theorists. But this should serve as a warning. There are some aspects of superconductivity that are very well understood, but trying to predict its presence or absence in a given material is not a productive activity.

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Can you explain what you mean with theorists –  Jonas Stein Nov 24 '12 at 2:08
This has been stated a number of times, most recently by Mazin in a Nature review on iron-based superconductors, where Mazin attributes the original Matthias formulation to Pickett: nature.com/nature/journal/v464/n7286/full/nature08914.html Mazin's work is quite a nice paper, and a good cautionary tale against just the exercise outlined in the original post. –  Jen Nov 27 '12 at 21:25
Very nice. Thanks @Jen! –  wsc Nov 28 '12 at 2:18
Mazin does however outline some new 'rules' though in that paper, paraphrased: Layered structures are good, Carrier density should not be too high (c.f. conventional metals). Period 4 Transition metals (V, Cr, Mn, Fe, Co, Ni and Cu) are good. Magnetism is essential. Fermi surface geometry is essential. Enlist theorists, at least to compute the Fermi surfaces. Also, materials of interest are likely to be complex chemical compounds — work closely with solid-state chemists. See also "Manifesto for a higher Tc" Basov, Nature 7, 272, (2011) –  Brendan Dec 9 '12 at 17:06
But Mazin does have a professional interest in making experimentalists care about electronic structure calculations. ;) Otherwise his new rules are helpful, but must always come with the caveat that they are descriptive of superconductors we already know. It's dangerous to turn around and treat them as prescriptive. –  wsc Dec 9 '12 at 19:07

I doubt that any such statement exists, as it would imply a very deep understanding of superconductivity we don’t currently have.

This holds especially as you apparently look for temperature-independent statements, whereas most metals can be made superconducting at sufficiently low temperatures, and all high-temperature (relatively, still a few hundred degrees below $0^\circ\textrm{C}$) superconductors are made of materials that are very bad conductors at higher temperatures (ceramics and the like). The converse that all ceramics are good superconductors is not true, either.

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A material is superconducting if the electrons in the electric current form "bosonic" cooper pairs.

A material is not superconducting if the current is formed of hadrons which interact with conductor.

I'm not an expert by any stretch of the imagination. Infact less than a beginner on the subject.

Introduction to Solid State Physics by C. Kittel has a basic chapter on superconductivity.

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The person above is right, that our understand of superconductors is not great. –  Joshua Siret Nov 22 '12 at 19:26

Here are two (equivalent) definitions of superconductivity:

• A material is superconducting, if it shows the Meissner effect.

• A material is superconducting, if a ring exhibits a persistent current when threaded by a magnetic field which is independent on the size of the ring.

Note that both definitions are via magnetic properties and not the fact that the resistance vanishes!

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