Cooper pairs are responsible for enormous conductivity of the superconductors. Their existence can be proved by a tunneling experiment. I want to know if such experiments have been done for new ceramic superconductors.
The tunneling of Cooper pair was proved by the observation of the Josephson effect (see book by A.Barone and GF Paterno`, Physics and application of the Josephson effect). What kind of new ceramic superconductors do you mean?
Apart from Josephson effect, on can get this evidence from an examination of the Fermi Surface using Scanning Tunneling Spectroscopy.
Andreev reflection (see http://en.wikipedia.org/wiki/Andreev_reflection) gives direct evidence via the increase in current as holes are retro-reflected from the superconductor as new pairs are formed.
Josephson effect, Andreev reflection, the Josephson quasiparticle cycle involving charge qubits in Cooper pair boxes http://en.wikipedia.org/wiki/Charge_qubit
Attractive interaction between electrons forming a Cooper pair results in an energy gap appearance. Such gap can be directly observed in a tunneling experiment. The first such proof was given by Ivar Giaever in 1960. He was awarded with the Nobel Prize in 1973. So, check Giaever's work published in Phys. Rev. Lett. 5 (1960) 147.
One of the first such evidences was published in the article: JETP Letters, v.46 Supplement, pp. S52 (1987). It was the first observation of steps on I-V curve of an YBCO point contact under GHz radiation. The period of these steps shows the electrical charge of carriers in solids and appeared to be equal 2e-.
If I understood your question well, you ask about the following. You have a sample of a material which you suppose to be a superconductor (S) below a critical temperature Tc. You want to know a simplest tunneling experiment which can prove existence of Cooper pairs. Of course, the colleagues are right that the best way to do it would be the Josephson-effect experiment in an SIS junction (I is a nano-scaled insulating interlayer). But it is not enough to measure the supercurrent. You should measure the effect of the GHz radiation (see the comment by A.Varlashkin). When you compare the voltage positions of the steps in the current-voltage characteristics (the so-called Shapiro steps) with your frequency, you can use a simple formula and to check the charge of the pairs. It should be two. Indeed, it is a direct probe but it is too difficult.
You can perform tunneling experiments by evaporating over your sample ultrathin Al layer, oxidizing it and evaporating a counter electrode. The current-voltage characteristic will show you an energy gap (see the reply by K. Garg and A.Wawro) but it does not provide you the knowledge of the charge of pairs and if they are. So you can only show that the gap does exist and its origin remains unclear.
In my opinion, the simples experiment is the point-contact Andreev-reflection spectroscopy (see the reply by M.Salamon). You can read about how comparatively simple the experiment is, how to interpret it, and about some examples concerning new superconductors in the review by Daghero and Gonnelli (it is free in the arxiv database http://arxiv.org/abs/1009.1572). In my opinion, the best way to solve your problem. You should fabricate a direct contact between a counter electrode and your sample, to measure the differential conductance versus voltage curve. If the zero-bias conductance is twice larger than the conductance at high voltages and if you observe its fall at the energy gap value (you can estimate the latter value by using a BCS relation – it equals to 1.76 multiplied by Tc), then you will prove that you have just Cooper pairs. In my opinion, it would be the SIMPLEST way to do it.
In principle, performing tunnelling experiments is the best way to gain insight to the presence of Cooper pairs. However, scanning probe techniques require a very expensive equipment, so the point-contact spectroscopy, and here especially, the break-contact spectroscopy is a less expensive way of carrying out such experiments. And if one can do the spectroscopy in applied magnetic fields, it is possible to have a closer look to the resulting finestructure within the I/V-characteristics. One may enter here a regime called "inelastic tunnelling of Cooper pairs" (E.G. Maksimov, P.I. Arseyev, and N.S. Maslova, Solid State Commun. 111, 391 (1999), M. A. Lorenz et al., J. Low Temp. Phys. 117, 527 (1999).), which will prove the existence of Cooper pairs.
In this way, one can do the experiment with a relatively simple apparatus.
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