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Lattices of double-quanta vortices and chirality inversion in $p_x+ip_y$ superconductors

We investigate the magnetization processes of a standard Ginzburg-Landau model for chiral p-wave superconducting states in an applied magnetic field. We find that the phase diagram is dominated by triangular lattices of doubly quantized vortices. Only in close vicinity to the upper critical field, the lattice starts to dissociate into a structure of single-quanta vortices. The degeneracy between states with opposite chirality is broken in a nonzero field. If the magnetization starts with an energetically unfavorable chirality, the process of chirality-inversion induced by the external magnetic field results in the formation of a sequence of metastable states with characteristic magnetic signatures that can be probed by standard experimental techniques.