Karl Müller (2004) - Some Remarks on the Symmetry of the Superconducting Wavefunction in the Cuprates

So I’ll try to make a more or less normal seminar. So I do make an introduction and then I’ll tell you a bit about surface sensitive experiments, just essentially one on the cuprates, saying for many of them. Then on bulk sensitive experiments and finish with a conclusion discussion. Now, I try to do it a bit in tutorial way. To remind you that superconductivity is a microscopic quantum phenomenon size. You describe the superconductivity with microscopic wave function, this is the square root of the density times an exponential. And it’s about that which I'm going to talk to you. This is a real quantity and the phase here is also a real quantity. What I describe to you is this conventional superconductivity, this has been mentioned earlier, where you have this gap here, this is now a cut near the fermi energy, so there is this gap and the density of states follows such a curve. There are no carriers here in between. What I describe to you is this conventional superconductivity, this has been mentioned earlier, where you have this gap here, this is now a cut near the fermi energy, so there is this gap and the density of states follows such a curve. There are no carriers here in between. However, you can have other types of dependencies on the energy, for instance, and I show you here, these are, for instance, D-ray functions. In an atom, you know you can have L=0, L=1, L=2, L=2 means 5 orbitals. And in the plain one can determine that in these cuprate superconductors it looks like, and I'm coming to that, such a D-way function, where you have say phase positive and negative here. If you have this it looks this way here. It’s now a picture for D-wave superconductor. So you have, if you go along this direction, the X direction, you have a gap plus, if you go the Y direction, you have a gap minus, if you go here, you have no gap. And this means that if you go along this direction, you have the same thing like here. However, if you go 45°, you have no gap, and it looks like if you have something like a funny metal where the density of state goes down. If you have impurities, it even stays finite. So how can you determine that? There have been propositions and a number of experiments which I'm not going into, I just want to show you the latest result. These are so called DC squits. Now, this looks awfully complicated I'm going now to try to bring you to this point here. Namely, now you can do a similar thing with a superconductor. I show you here a so called superconductive quantum interference device. I took this picture out of the Feynman lectures number 3, the last chapter, in which he describes rather as a seminar on superconductivity than a normal lecture. And those of you who are interested to start a bit learning superconductivity, I highly recommend you to read this chapter 21, 17 pages. He assumes normal quantum mechanics and brings you through the physics of the superconductor. Now, you can do a similar thing with a superconductor. I show you here a so called superconductive quantum interference device. I took this picture out of the Feynman lectures number 3, the last chapter, in which he describes rather as a seminar on superconductivity than a normal lecture. And those of you who are interested to start a bit learning superconductivity, I highly recommend you to read this chapter 21, 17 pages. He assumes normal quantum mechanics and brings you through the physics of the superconductor. Here what is used are two so called Josephson junctions after the discovery of Brian Josephson, so basically my experimental review was published in 2001 and his, too, the following. If you have a potential which is interacting between two nuclei and you have here the surface, then at the surface you should have D, also in the symmetry of the superconductor and then, depending on the depth of this potential, you may get S and D and if the point is not very deep, you stay S and D and if it’s very deep you get S symmetry.

Karl Müller (2004)

Some Remarks on the Symmetry of the Superconducting Wavefunction in the Cuprates

Karl Müller (2004)

Some Remarks on the Symmetry of the Superconducting Wavefunction in the Cuprates

Abstract

A large part of the community considers the macroscopic superconducting wavefunction in the cuperates to be of near pure d-symmetry. The pertinent evidence has been obtained by experiments in which mainly surface phenomena have been used such as tunneling or the well known tricrystal or tetracrystal experiments (1).

However recently, data probing the property in the bulk gave mounting evidence that inside the cuperate superconductor a substantial s-component is present, and therefore I proposed a changing symmetry from pure d at the surface to more s inside, at least (2).

This suggestion was made to reconcile the observations stemming from the surface and bulk. But such a behavior would be at variance with the accepted classical symmetry properties in condesed matter. (1,3).

In this respect, Iachello, applying the interacting boson-model, successful in nuclear theory, to the C4v symmetry of the cuperates, showed that indeed a crossover from a d-phase at the surface, over a d + s, to a pure s-phase could be present(4).

Attempts to estimate this crossover from known experiments will be presented. It makes also plausible why the face stiffness of the d-component is preserved over a whole sample, i.e. in a SQUID. Furthermore most recent experiments indicating a full gap in the bulk at low temperatures will be commented on.

References:

1) C.C. Tsuei and R.J. Kirtley, Rev. Mod. Phys. 72, 969 (2000)

2) K.A. Müller, Phil. Mag. Lett. 82, 270 (2002)

3) J.F. Annett, N.D. Goldenfeld, and J.J. Legett, 1996 in „Physical Properties of High-Temperature Superconductors V”, edited by D.M. Ginsberg (World Scientific, Singapore), p. 571

4)F. Iachello, Phil. Mag. Lett. 82, 289 (2002)

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