• Suresh G Mishra

      Articles written in Bulletin of Materials Science

    • Vortices in superconductors

      Suresh G Mishra

      More Details Abstract Fulltext PDF

      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$$H_{0_1 } \left( { = \frac{{\phi _0 }}{{4\pi \lambda ^2 }}ln \lambda /\xi , \phi _0 = \frac{{hc}}{{2e}}} \right).$$ 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:

      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.

      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.

      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.

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