Toroid Current States in Doped Mott Insulators
  The free energy bounds for inhomogeneous current states in doped antiferromagnetic insulators and spatial configurations of spin and charge degrees of freedom in lightly and heavily underdoped phases of this strongly correlated electron system are considered. It is shown that states are characterized by a small parameter of geometric origin, which determines the degree of packing in the knots of filament manyfolds of the order parameter distributions. We found a hierarchy of the spatial scales for flat knots, which gives rise to a free energy gain. A toroid moment in an underdoped state is found for the first time. It is shown that in the percolation picture of charge density distributions, that surround antiferromagnetic nanoclusters, the optimal level of the hole density is in qualitative agreement with the experimentally observed value. 
Dmitry I. Iudin (1), Alexander P. Protogenov (1 and 2) ((1) Institute   of Applied Physics of the RAS, Nizhny Novgorod, Russ...