Thilo discussed the periodicity of the ground-state energy and

the supercurrent as a function of the magnetic flux threading

a superconducting ring. He presented a joint work by F. Loder,

A. Kampf, J. Mannhart, C.W. Schneider, Yu.S. Barash and himself.

He first reviewed what is historically

known: flux quantization, periodicity of the ground-state energy,

and of the supercurrent in units of phi=h/2e. He recalled for us

that the states corresponding to q times phi, where q is an even

integer (London states) are related by a gauge transformation.

However, there is no such a relation between states corresponding

to q even and odd. The degeneracy between q even and odd is lifted

in s-wave superconductors when the diameter of the ring is smaller

than the coherence length of the system, since in this case, the

discrete nature of the electronic states becomes relevant showing

in general differences between half-integer and integer flux

quanta. The aim of the work by Thilo and collaborators was to look

for a mesoscopic superconducting system where h/e periodicities

become observable.

The theoretical work consisted in the numerical solution of the

Bogoliubov-de Gennes equations for a BCS-Hamiltonian with a Peierls

phase factor corresponding to the coupling to a vector potential

for a magnetic field threading a 100x100 lattice through a 30x30 hole.

The superconducting order parameter was chosen to be a d-wave one.

The idea is that while the main contribution to the supercurrents

comes from the states closest to the Fermi energy (E_F=0), most of the

condensation energy comes from the lobes. In such a way a d-wave

superconductor is protected from reaching the critical value of

the superfluid velocity by the Doppler shift, in contrast to s-wave

superconductors.

Due to the nodal character of the order parameter, discrete states

very close to E=0 are present. Thilo discussed first the evolution

of the eigenenergies as a function of flux close to q=0. As the

magnetic flux is increased, supercurrents are present and the discrete

states of the finite system shift accordingly (e.g. the states closest

to zero increase their energy). However, an abrupt change takes place

very close to h/4e (where the parabolas in the infinite case cross).

From there on, one enters the regime with q=1. Both the ground-state

energy and the supercurrent show an h/e periodicity, and the change

from states with increasing q takes place at odd integer multiples

of h/4e. At such points, the condensate reconstructs.

The finite size effects discussed by Thilo vanish as 1/R, where R

is the radius of the ring. Claudio Castellani asked whether an estimate

can be given for the sizes required to see the effect. Thilo said

this should be the case of rings in the micrometer range where a

percent effect should be still observable. Zlatko Tesanovic pointed

out that in an s-wave superconductor presumably a length scale should

exist, where the effect essentially vanishes.

## Thursday, August 30, 2007

### Thilo Kopp: h/e periodicity in loops of nodal superconductors.

Posted by Alejandro Muramatsu at 4:51 PM

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## 28 comments:

The work presented is by F. Loder, A. Kampf, J. Mannhart, C.W. Schneider, Yu. S. Barash and myself.(T.K)

one smal story, Interesting in monochrome. Reminds me how I once spotted a butterfly but when I got my camera I discovered it was dead. I was too sad to take pictures.

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Nodal Superconductors, This is the first time I am hearing of this term and its use.

Thanks for taking the time to discuss this, but I am firmly convinced of this and love to learn more about the subject. If possible, acquire knowledge, would you update your blog with more information? It is very helpful to me

The electronic states becomes relevant showing

in general differences between half-integer and integer flux

quanta...

I seriously think that people have a lot of variety in themselves.

Superconductivity is indeed a heavy subject to work on.

This is the first time I am hearing of this term and its use.

In recent years, a number of nodal superconductors have been identified; d-wave superconductors in high Tc cuprates, CeCoIn5 and κ-(ET)2Cu(NCS)2, two-dimensional (2D) f-wave superconductor in Sr2RuO4, and hybrid s+g-wave superconductor in YNi2B2C. In this work we conduct a theoretical study of nodal superconductors in the presence of supercurrent..Nice post, thansk alot

The post is very nicely written and it contains many useful facts. I am happy to find your distinguished way of writing the post. Now you make it easy for me to understand and implement. Thanks for sharing with us.

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well.I can't understand about periodicity in loops of nodal superconductors.What thilo sketch on board is just look like sine and cosine thing for me.

The theoretical work consisted in the numerical solution of the

Bogoliubov-de Gennes equations for a BCS-Hamiltonian with a Peierls

phase factor.

This equation proves the flux quantization and the periodicity which is important and relates to the other matter.

Very interesting post.

the Brandt-Pesch-Teward approximation again the averaged zero-bias DOS was calculated, this time also covering the high field region.

That is a good work. Understanding periodicity in loops of nodal superconductors will be more easier now.

I dont really understand your post here but i am confident that your future articles will enlighten me.

So much helpful data for me!

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