Commensurate Vortex States of the Infinite Superconducting Microladder

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Abstract
The second order phase boundary of an artificial structure such as the microladder is shifted to higher temperatures when the order parameter is spatially modulated by a wave vector q compared to no modulation (q = 0). Commensurate solutions exist when q=π/m where m is an integer \geqslant2. For these solutions the relative order parameter, its phase and the current patterns along the ladder are calculated near the phase boundary. We found that the period of the phase is twice as large as that of the modulus of the order parameter and that of the vortex current pattern. When m is an even integer every m-th transverse branch contains a null of the order parameter across which the phase flips by π with no current passing through these branches.

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