Theory of the square to rhomb structural phase transitions in the vortex lattice of type-II superconductors

The theory of structural transformation of the vortex lattice in a fourfold symmetric in a-b plane type-II superconductors is constructed using both the London and the lowest Landau level Ginzburg-Landau model. Thermal fluctuations and quenched disorder influence the location of the square to rhomb structural transition line. The self consistent harmonic approximation for lattice anharmonicity within the fourfold symmetric generalization of the London model is used. Without disorder in the T-B plane the slope of the line is generally negative: thermal fluctuations favour a more symmetric square lattice. The theoretical line's location and slope are in good agreement with the experimental "second magnetization peak" line measured in both LaSCCO and YBCO in a wide range of doping. We find that, while the thermal fluctuations are negligible for the transitions in low T_c materials, disorder plays an important role and creates a positive slope in the T-B plane since disorder favours a symmetric square lattice.