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Modified London equation in \(N\)-gap superconductors. (English) Zbl 1187.82152

The paper investigates the structure of vortices in N-gap superconductors. An N-gap superconductor is described by an N-favor Ginzburg-Landau (GL) free energy functional. It allows one to obtain the equation for the supercurrent via the probability current density. Due to the complex scalar fields which represent N gaps that cannot be constant interspecies of Josephson coupling are included in the GL free energy. The author studies vortices structures by using the Dirac delta function and gives a universal modified London law in N-gap superconductors. Because the current density in the core is gradually suppressed, the vorticity of the probability current density is expressed by the Dirac delta function, so the energy and dissipation are centered in the vortex line. In this paper vortices are classified by the Hopf index and Brouwer degree that characterizes the direction of the vortex line and states vortex and anti-vortex. Then, the circulation equation of the vortex is obtained in which the vortices can be characterized by N integers. It is shown, that in N-gap superconductors the density in the vortex line can be not zero which is different from the case in one-gap superconductors. Without London approximation of the circulation of vortices, there are studied the cases of zero and non-zero current density. In the first case, it is shown that the magnetic flux caused by a vortex can be characterized only locally which is different from that on an one-gap superconductor. In the second case, there are obtained the magnetic flux equation of vortices in the N-gap superconductor and also the modified London equation. In London limit this universal equation is differed from usual due to one includes Hopf indices and Brouwer degree. This equation is rewritten by using the magnetic induction caused by a vortex which can be tested in an experiment. This magnetic induction consists of five terms, namely: (i) caused by the vorticity of a vortex, (ii) caused by the gradient of a function of the scalar fields representing N gaps, (iii) caused by the mass current and probability current, (iv) caused by the density current and superconductive current, and (v) caused by the mass current and superconductive current.

MSC:

82D55 Statistical mechanics of superconductors
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