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Abstract
The possibility of the emergence of a macroscopic amount of planar vortices with identical circulation in systems with pairing of spatially separated electrons and holes was predicted by us recently [S. I. Shevchenko, Phys. Rev. B56, 10355 (1997); ibid. B57, 14809 (1998)]. In the present work, we consider a structure formed by planar vortices in a disk-shaped sample in a magnetic field whose two-dimensional divergence differs from zero. The total number of vortices and the energy of a system of vortices are determined as functions of the external magnetic field and the sample size. It is found that the energy of the vortex structure is proportional to the volume of the system, and hence a vortex state is a new thermodynamic phase of the investigated system (analogous to the Shubnikov phase in conventional superconductors).
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