Vortices in superconductors

In type II superconductors where the London penetration depthλ is larger than the coherence lengthξ, there is a possibility of flux penetration inside the sample for magnetic field greater than (H_{0_1 } left( { = frac{{phi _0 }}{{4pi lambda ^2 }}ln lambda /xi , phi _0 = frac{{hc}}{{2e}}} right).) The flux penetrates in the form of vortices with core of sizeξ. However these vortices differ from those in superfluid He⁴ in variation of currentj(r) circulating around them. For superconductorsj(r) ～ 1/r only up to a distanceλ and then it falls exponentially whilev(r) ～ 1/r for all distances in superfluids. The reason is that in superconductors vortex carries a magnetic flux which is screened by conduction electrons. This coupling of order parameter field (the pairing wavefunction) with the gauge field has many interesting implications for superconductors and for non-Abelian gauge theories. Some examples are as follows:

1. The energy of the vortices is reduced. The energy of vortex of lengthL (ind = 3 sample) is of orderL lnL for a superfluid, is of orderL in a superconductor, and (in ad = 2 sample) the energy of a vortex point which diverges like lnR (whereR is the size of the sample) in a superfluid becomes finite in a superconductor.
2. The superconducting-normal transition in three dimension is very weak first order, because the fluctuations of the gauge field, when summed over, add to Ginzburg Landau free energy a term proportional to |ψ|³, whereψ is the order parameter.
3. Because of the lnr behaviour of interaction energy of vortices, a two-dimensional superfluid sample can exhibit a Kosterlitz-Thouless type transition whereas a strictlyd = 2 superconductors should not have any. However for dirty superconducting films whereλ is large vortex binding-unbinding transition can be observed with quite a rich phase diagram.

The paper presented at the discussion meeting discusses the above in detail. Here we give only a brief summary of results and some relevant references.