Dynamics of holes and spins in the Hubbard t-J model and high-temperature superconductivity.

Abstract

We study the t-J model as a microscopic model of high-temperature superconductors. The local constraints in the slave-fermion representation are solved by the projection operator onto the spin states and the ${\mathrm{CP}}^{1}$ spin variables. This resolution reveals that the antiferromagnetic (AF) J coupling of spins is accompanied with a four-Fermi interaction of charged holes. It describes attraction of fermionic holes on nearest-neighbor (NN) sites and induces formation of pairs of NN holes. Each pair carries two units of charge. Condensation of such hole pairs breaks the global U(1) charge symmetry and generates the superconductivity. The possible phase-separation state may become unstable against the uniform superconducting state due to the kinetic energy of holes. We obtain an effective lattice model in the short-range AF state by integrating out the odd-site spin fluctuations in the short-range AF order. Spin fluctuations induce attractions between next-NN holes. The model includes the effective model of Shraiman and Siggia for mobile holes in AF magnets as its normal-state part.Global magnetic properties, such as the N\'eel state and the spiral state, are described by this model. To study the superconducting phase, we develop a hole-pair theory by introducing auxiliary link variables as a hole-pair field. Their effective action gives the ``gap'' equation. The Ginzburg-Landau theory of it describes the superconducting-normal phase transition. We identify its general structure, which takes a form very similar to U(1) lattice gauge theory coupled with Higgs field. The pure gauge part reflects the magnetic J coupling, while the Higgs part is supplied by the elctron-hopping t term. The hole-pair condensation is expected at sufficiently large hole density because the phases of pair field are to be stabilized there coherently through a Higgs mechanism. A superconducting ``flux'' state of pairs is favored energetically. In this background condensation, low-energy excitations of holes are described by normal hopping of Fermi-liquid-type plus relativistic massive Dirac particles in a parity doublet. They are coupled with the gauge fields of ${\mathrm{CP}}^{1}$ spins in a U(1) gauge-invariant manner. This composes the hole part of our effective field theory in the superconducting phase. The spin part is the familiar nonlinear ${\mathrm{CP}}^{1}$ \ensuremath{\sigma} model. Our microscopic derivation of the effective field theory at low-temperature relates its parameters to those of the original t-J model. Throughout the study, we recognize a global and strong correlation between the magnetism and the superconductivity, or spins and holes, reflecting their common origin, i.e., the J coupling. The study of a simple solvable model presents a plausible critical line of superconductivity in the temperature-concentration plane.