Composite fermion theory for pseudogap phenomena and superconductivity in underdoped cuprate superconductors

We study pseudogap phenomena and Fermi-arc formation experimentally observed in typical two-dimensional doped Mott insulators, namely, underdoped cuprate superconductors. To develop a physically unequivocal theory, we start from the slave-boson mean-field theory for the Hubbard model on a square lattice. Our crucial step is to further take into account the charge dynamics and fluctuations. The extra charge fluctuations seriously modify low-energy single-particle spectra of doped Mott insulators near the Fermi level: An electron added around an empty site (or a hole added around a doubly occupied site) constitutes composite fermion (cofermion), called holo-electron (or doublo-hole) at low energy in distinction from the normal quasiparticles. These unexplored composite fermions substantiate the extra charge fluctuation. We show that the quasiparticles hybridize with the holo-electrons and doublo-holes. The resultant hybridization gap is identified as the pseudogap observed in the underdoped region of the high-T_c cuprates. Because the Fermi level crosses the top (bottom) of the low-energy band formed just below (above) the hybridization gap in the hole-doped (electron-doped) case, it causes a Fermi-surface reconstruction, namely, a topological change in the Fermi surface forced by the penetration of zeros of the quasiparticle Green's function. This reconstruction signals the emergence of a non-Fermi-liquid phase. The pseudogap and the resultant formation of pocket or arc of the Fermi surface reproduce the experimental results for the cuprate superconductors in the underdoped region. The pairing channel opens not only between two quasiparticles, but also between a quasiparticle and a cofermion. This pairing solves the puzzle of the dichotomy between the d-wave superconductivity and the precursors of the the insulating gap in the antinodal region. We propose and analyze them as the mechanism of the high-temperature superconductivity for the cuprates.