Coulomb repulsion, phase stiffnesses, and doping-induced superconductivity from the Mott insulator in the t−t′−U−J model of high-Tc cuprates

Abstract

The electronic t−t′−U−J model for the CuO2 plane in high-Tc superconducting cuprates is elaborated. It incorporates both charge transfer U and exchange correlation J with direct t and diagonal t′ hopping. Making use of the Yang concept of the off diagonal long range order (ODLRO) in the reduced density matrix of the electronic system we study the loss of quantum wave coherence (and thereby superconductivity) due to the Coulomb interaction. To this aim the second-quantized Hamiltonian of the model is translated to the phase representation with the help of the topologically constrained path integral formalism. As a result the electrons emerge as composite particles consisting of of spin-carrying neutral fermions and charged topological bosons in a form of “flux tubes” with the quantum phase variable dual to the local electron density. The charge carrying bose field forms a collective variable representing the correlated “sliding” motion of the entire electronic system. We found that the spin gap Δ which appears in one-particle spectrum is the result of valence bond pairing of neutral fermions without ODLRO and deduce the solution for Δ with “d-wave” symmetry. In the bosonic sector we derive the effective quantum rotor model along with microscopic phase stiffnesses setting the energy scale for superconductivity and point out the special role played by the diagonal hopping t′. We explore the relationship of the quantum rotor phase model and the Bose-Hubbard system emphasizing the ring topology of quantum phase variable. Furthermore, we obtain the ground state phase diagrams which facilitate the Mott insulator-superconductor transition scenario. We elucidate the role of the chemical potential (doping) and the huge degeneracy of the effective bosonic system in achieving ODLRO with long-range phase coherence in the presence of large Coulomb repulsion. Finally, we discuss a number of relevant issues pertaining to the the present work which include: theoretical aspects of the hierarchy of the energy scales in cuprates, “spin-charge separation” concepts, “local-pair” and “phase-fluctuation” scenarios as well as experimental findings related to the role of the “d-wave” symmetry of the spin gap and diagonal hopping t′ in cuprates.

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