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- 1. High-Temperature Superconductors under pressure. NZIP2011 Ben Mallett Oct 2011
- 3. R. Hott et al , Supercondcuting materials: A topical overview, in “Frontiers in Superconducting Materials”, Springer-Verlag, 2004
- 4. Figure courtesy of S. Chong
- 5. Basic cuprate structure YBa 2 Cu 3 O 7-y
- 6. Figure courtesy of S. Chong
- 7. The phase diagram J.L. Tallon, Frontier in Superconducting Materials; Oxygen in High-Tc Cuprate Superconductors , Springer-Verlag, 2004. stripe phase
- 8. Cu O The undoped cuprates are anti-ferromagnetic, charge transfer insulators d x 2 -y 2 2p σ a b
- 9. The phase diagram J.L. Tallon, Frontier in Superconducting Materials; Oxygen in High-Tc Cuprate Superconductors , Springer-Verlag, 2004. stripe phase
- 10. Red triangles are external pressure measurement data reported by Wijngaarden et al ., Physica B , 265 , 128-135 (1999). LnBa 2 Cu 3 O 7-y
- 11. ‘ Chemical’ or ‘Internal’ pressure Guillaume et al.
- 12. Measuring Antiferromagnetic superexchange strength, J , with Raman spectroscopy Two excited magnons
- 13. LnBa 2 Cu 3 O 6
- 14. La 2 CuO 4 data from - Aronson et al ., Phys. Rev. B , 44 , 4657 (1991) YBa 2 Cu 3 O 6.2 pressure data from - Maksimov et al ., Phys. Rev. B , 49 , 15385, (1994)
- 15. Red triangles are external pressure measurement data reported by Wijngaarden et al ., Physica B , 265 , 128-135 (1999).
- 21. Smaller ion size
- 22. Bi 2 Sr 1.6-y A y RE 0.4 CuO 6+z Caveat; Likely to be additional effects influencing/suppressing Tc.
- 25. Hole dynamics a b Metal with residual AF correlations
Hinweis der Redaktion
- Welcome, Thanks for coming along to my talk on the ion-size effect.
- So Superconductivity is an electronic phase of matter. It’s characterised by two key features 1) All magnetic flux is expelled from the superconducting bits. 2) Zero resistance to DC current flow (provided it’s low enough). I straight up say that almost everything I tell you in this talk will be a ‘half truth’ – superconductors, and especially the ‘high temperature superconducting cuprates’, are complex beasts and there are often exceptions or caveats. For example 1) the magnetic field penetrates into the superconductor within a penetration depth and 2) If the current density is high enough there is DC resistance in the superconductor. I do endeavour to tell you all the relevant and interesting bits though. So you we lump phases of matter into classes such as ‘gas’, ‘liquid’, ‘solid’. So how do you describe what electronic phase of Al is? Sure you’d say it’s a metal, but below 1.9K it’s a superconductor. You’d call Si an semi-conductor, but squeeze it to 8GPa and it’s a superconductor below 8.5K. In fact, if you squeeze something hard enough, and make it cold enough, most elements become a superconductor. People first knew about this phase of matter in 1911. We thought had a good theory for how it all works by 1956 – BCS theory. What changed in 1986 was that a couple of researchers looking to increase the Jahn-Teller effect in insulating perovskite-oxides discovered something became a superconductor at a temperature higher than was thought possible with the old theory. Tc was up to something like 35K. And here’s a picture of the material. One of the first things people noticed was that if they squeezed this material – applied external pressure – it became a superconductor at higher temperatures. We call the temperature that a material becomes superconducting Tc – the critical temperature after the theory of Ginzberg and Landau on phase transistions. Now if you want to make a powerful magnet, or lossless, extremely high current density transmission line out of your superconductor, you don’t want to have to have it under pressure the whole time. You can employ a neat trick here instead – something called ‘chemical pressure’ or ‘internal pressure’. I bet you’ve already figured it out from the name, but just to show you, rather than squeezing the crystal from the outside, you put different sized ions in there to squeeze or expand it from the inside. Of course you won’t exactly replicate external pressure – there might not be equal shorteneing of all the bond lengths, but the analogy is there. Chu and his group took this approach – let’s replace this La ion here with the smaller Y ion. Two things happened; 1) they didn’t just change the La, they made a new material 2) Tc shot up to 90K. People got really excited now and within a few years we realised we’d come across a whole family of superconducting materials with Tcs very high compared to what we knew. These guys are called the cuprates – and they’re what I’m studying. Firstly, what sort of materials are the cuprates? Layered structures. Metal oxide layers. Layers have similar functions between members of the family. A and E can be many different metals. Ubiquitos is the CuO2 layers.
- 0.2 means 0.2 holes per Cu atom in the cuo layer. FEATURES OF PHASE DIAGRAM Note I’ve bodly titled this slide “the” phase diagram – that’s because scaled T/Tcmax pretty much the same for all members of the cuprates. That’s cool. That also immediately suggests all this action predominately arises cuo layer. In my first year I’ve learnt “Life with the cuprates” is full of caveats. “ the” phase diagram is no exception, and I would be happy to talk about this afterwards. This slide I feel nicely introduces the rich electronic physics of the cuprates
- 0.2 means 0.2 holes per Cu atom in the cuo layer. FEATURES OF PHASE DIAGRAM Note I’ve bodly titled this slide “the” phase diagram – that’s because scaled T/Tcmax pretty much the same for all members of the cuprates. That’s cool. That also immediately suggests all this action predominately arises cuo layer. In my first year I’ve learnt “Life with the cuprates” is full of caveats. “ the” phase diagram is no exception, and I would be happy to talk about this afterwards. This slide I feel nicely introduces the rich electronic physics of the cuprates
- As expected these smaller ions decrease the unit cell dimensions. Here I show cell volume versus ionic radii for RE123, but similar data is obtained for other axes.
- This can be measured by Raman spectroscopy. Magnons – or spin waves – are bosonic excitations of the AF spin lattice. It turns out two of them working together have a significant Raman cross section in certain geometries. The frequency shift at which they most efficiently scatter light is linearly related to J. I made these measurements on SINGLE CRYSTAL of Y123 stuff for different RE.
- Remains for me to thank these guys as I would not have been able to do this without their help.
- This I’ll call the `intrinsic’ increase in Tc as there are lots of Other effects that can occur under pressure. These also Confuse the interpretation of pressure experiments.
- Here’s data for many different cuprate systems. It shows those caveats in action.
- Pressure increases Tc.
- RE series good one as valence doesn’t change, with few specific Exceptions of Ce, Pr, and Tb, but ion size does. YBCO: Sub RE ion onto Y site. Bi2201: Partially sub La onto Sr site to dope the material. Then replace La for various RE. Also can use isovalent Ba or Ca to sub Sr.
- The same effect is seen in the Bi2201 system – this is recent data of Thierry Schneider, and mine. Thermopower can be related to doping. Up until now the decrease in Tc in this system with smaller RE ion substitution has always been attributed to disorder. Disorder induced scattering in a d-wave superconductor will reduce Tc. Our results show internal pressure is also an important effect. Subbing larger Ba ion for Sr increases the disorder but also stretches the lattice, simulating negative internal pressure. We see Tc increases slightly – the internal pressure the stronger one for Ba doped Bi2201. We can quantify, but take number with caution, in part to what I said before. The reduction in Tc is by no means linear.
- Either way this equation is a good starting point. Here is pairing boson energy scale. Here is density of states at the fermi level. Here is pairing potential. These parameters might not be the only ones in the final theory that describes cuprate Tc values, but I think its probable at least they’ll show up in there. Let’s then investigate this internal pressure/external pressure effect on these variables. If pairing mechanism is magnetic – which many believe it will be – pairing boson energy scale will be set by the antiferromangetic exchange strength.
- Here’s the Hamiltonian of a model often used to describe the electronic system on the cuo plane. The model’s called the t-J model. Why I’m putting this up is to introduce the antiferromagnetic super-exchange energy in the context of these materials. It’s this J here. It measures the Energy difference between a ferromagnetic and antiferromagnetic arrangement of the spins. T measures kinetic energy gain from hole hopping from one site to nearest neighbour. If xt<<J in regieme of metal. In the cuprates we’re in this regieme. What happens here? Some simplified solutions are out there but we’ll cut to the experimental results. It turns out we can map out a phase diagram.