Theoretical study of the amperian pairing state

Until now, the unusual and complex behaviour observed in high-temperature superconductors remains unexplained. It is believed that understanding the processes within the pseudo-gap phase is necessary in order to describe the superconductive phase of the cuprates. The pseudo-gap phase is a region in the phase diagram which is reached by increasing temperature of the underdoped d-wave superconductive cuprate. The pair-density-wave (PDW) state consisting of Cooper pairs with nonzero net momentum is a promising concept that could interpret the pseudo-gap phase, especially the existence of the Fermi arcs and the charge-density-wave (CDW) order. An Amperean pairing state is a special type of PDW state with Cooper pairs carrying equal momenta. This state has been proposed in [1] and it represents a promising theoretical description of the cuprate pseudo-gap phase. It has been suggested that the Amperean pairing states are stabilized by current-current interactions, which originate from the gauge formulation of Anderson's resonating valence bond (RVB) theory. In this thesis the proposed Amperean states are studied by means of a fully self-consistent mean-field analysis. The Amperean pairing state was found to correctly describe the main physical properties of the cuprate pseudo-gap phase. Also, a surprising nontrivial self-consistent superconducting solution has been found in spite of the fact that the Amperean interacion is repulsive in the BCS channel. On the other hand, it is shown that the Amperean pairing states are not energetically optimal within the general class of PDW states and our lowest-energy solution is not compatible with the pseudo-gap phenomenology. (Author)