SuperconductorTimeLine

The timeline of superconductor families

Critical temperature of superconductors vs year of discovery. Notice the change of scale in the time axis at year 1980.

The figure shows how the critical temperatures of superconductors increased over years, following discoveries of new families of compounds. The early simple metals of Onnes and his contemporaries where type-I materials with {$T_c$} limited to 10 K or thereabout. The great leap forward provided by the 1950 theoretical developments (both BCS and the Ginzburg-Landau model) meant also concentrated material science efforts, particularly at Bell labs, where Bardeen was working a few years before, still in the semiconductor business. Intermetallic compounds known as A15 phases (Nb₃Ge, V₃Si, Nb₃Si) reached the temporary record of 23 K and for a long time no further breakthrough happened. In 1986, 75 years after Kamerlingh Onnes discovery, Alex Müller and Georg Bednorz produced unexpectedly a superconductor idoping a family of well known oxyde antiferromagnets, from the parent La₂CuO₄, with highest {$T_c=43$} K. The rush started again and a few months later Ching-Wu Chu and coworkers discovered YBa₂Cu₃O_7-y, with {$T_c=93$} K. The liquid N₂ barrier (77K) was broken.

The ultimate quest is perhaps for room temperature superconductivity, but the focus is more on understanding which materials become superconducting and how. Progress has been much faster since 1986, but it comes in flashes. They correspond to new classes of materials, highlighting new possible key ingredients. We can summarize the few most important flashes and the messages that they brought about:

• Metals and intermetallic compounds, dark green circles: the best metal do not superconduct at any reachable low temperature. That agrees with the fact that the electron-phonon interaction will be extremely small if the Coulomb screening is very effective. BCS describes them well.
• Heavy fermions, the light green stars: they are intermetallic compounds, containing rare earths. {$T_c$} are extremely low but the interest (and the name) is due to the fact that these materials, or their close neighbours in composition, show very large effective masses. They are very close to an instability that eventually results in a magnetic insulator. This agrees with the previous point.
• Cuprates, light blue diamonds: we come back later on them. Phonons are probably not the source of the electron-electron attraction and they are all the doped version of a Mott insulator (Cu is often magnetic in ionic oxides).
• Alkali Fullerides, purple triangles: alcali atoms A are interstitials in A₃C₆₀ in the big voids between the C₆₀ football shaped C molecules. They dope the molecules into a plastic crystal metal. They behave according to BCS, with a pretty high record {$T_c=40$} K under pressure, attributed to very high frequency C₆₀ cage vibrations. Surprisingly CsC₆₀ is normally a Mott insulator.
• Iron pnictides and chalcogenides, orange squares: their prototype is FeSe, their record is just below 60 K. Iron is most often a magnetic ion, thus Fe metal superconducts only under very large pressures, bringing the metal below the Stoner criterion. So this family underlines again that magnetic order is perhaps the enemy of superconductivity, but best conditions are found very close to magnetic order. As a matter of fact close-by compositions of nearly all these pnictides are again antiferromagnets (although often not Mott insulators).
• Finally, in the past five years (2015-2020), dense hydrogen compounds under very high pressure have shown {$T_c$} close to room temperature. Notice that 100 GPa is a million atmosphere and can be attained only with the use of a diamond anvil press over a very small volume (diamond, because it is the hardest material). Hydrogen itself has been long predicted t become a metal under high pressure (it does), and a superconductor (never seen yet, but LaH₁₀ is very nearly pure H). They are marked dark green circles again, since they are fully explained by phonon BCS.

The main messages out of this very broad sketch are perhaps the following. Superconductivity happens in many unexpected classes of materials. High {$T_c$} seems to arise close to the metal instability, just before a metal-insulator transition, typically a Mott transition. The main practical message is that these materials are often very good for niche applications (feed-through for current in conventional superconducting magnets at LHC or at the fusion reactor ITER), but not really yet viable for mass deployment in energy-saving uses, like for instance in power lines. The main reasons are cost, and very poor metallurgy (luckily for us metals are very good electrical conductors and ductile as well, so they can be easily threaded in flexible cables. High Tc superconductors generally make very bad cables. You should remember why you need a good metal to achieve ductility.

Index

Cuprates

Let us very briefly discuss cuprates. They are a fascinating but very complex family of materials. First of all they are at least ternary compounds (three or more different atoms). Secondly, they are layered: different cation oxide layers are stacked one on top of the other to form a regular periodic crystal. Thirdly, the parent compound is generally a Mott antiferromagnet (remember: it would be a half filled band system, but, due to very large Hubbard {$U$} it turns into a traffic jam insulator, and the favoured spin ordered state is the antiferromagnet.) The parent cuprate of each subfamily is a 2-D, spin {$S=1\frac 1 2$} Heisenberg antiferromagnet, the prototype of a quantum antiferromagnet (a pretty bad beast).

The most prominent feature, the so-called phase diagram of cuprates, is represented in the figure (here a cartoon, subtle variations appear from one sub-family of cuprates to the next)

The y-axis is transition temperatures, {$T_N$} for the antiferromagnet and {$T_c$} for the superconductor. The x-axis is the doping. It is proportional to the concentration of some ionic species. The main message here is that doping first kills magnetic order (quite rapidly), and then produces a superconducting dome, with the highest {$T_c$} in the middle, to then disappear again at higher doping, leaving space, one supposes, to a proper metal (a Fermi gas, or better, a Fermi liquid).

The doping calculation is simple in La₂CuO₄. The parent compound is neutral, with 2 La³⁺ cations, 1 Cu²⁺ cation and 4 O^2- anions: {$2\cdot3+2+4\cdot(-2)=0$}.

It is easy to calculate that La_2-xSr_{x'CuO'_4} has 2-x La³⁺ cations, x Sr²⁺ cations, 1 Cu²⁺ cation and 4 O^2- anion: {$(2-x)\cdot3+x\cdot2+2-4\cdot(-2)=-x$} would not be neutral and {$+x$} additional holes are indeed injected in the CuO₂ layer of this crystal. The conventional cuprate is thus a very special p-type semiconductor (also the n-type version exists).

Cuprates are type-II superconductors. Not only they have very high {$T_c$} (the record is 166K for a Hg cuprate under pressure). They also reach extremely high critical field values {$B_{c2}\approx 250$} T, hence they have an extremely small {$\xi$}, of order 2 nm (also extremely anisotropic, we are quoting the small component, in the CuO₂ plane). Viceversa they have a very large London penetration depth {$\lambda=1500$} nm. That means that {$m/n$} is large, because the density of electrons (of holes, really) is small. Thus screening currents are inefficient and {$\kappa\approx 1000$} (they are extreme type-II superconductor). They a probably provide the superconductor closest to an antiferromagnetic insulator that we know. The coherence length {$\xi$} is also a measure of the binding radius of a Cooper pair: they display the smallest pair known, the closest to a true composite boson. Notice, a true boson would undergo a Bose-Einstein condensation not a superconducting transition.

Index

Cuprates are defective perovskites, tetragonal, often orthorhombic. Spot the CuO2 layer (Cu orange, O green).