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One of the most puzzling problems of high temperature cuprate superconductoris the pseudogap phase(PG) at temperatures above the superconducting transitiontemperature in the underdoped regime. The PG phase is found by theangle-resolved photoemission spectra(ARPES) to have a gap at some regions inmomentum space and a fraction of Fermi surface remained, known as Fermi arcs.The arc turns into a d-wave SC gap with a node below the SC transitiontemperature. Here, by studying a strongly correlated model at low temperatures,we obtained a phase characterized by two kinds of pairing order parameters withthe total momentum of the Cooper pair to be zero and finite. The finitemomentum pairing is accompanied with a spatial modulation of pairing order,i.e. a pair density wave (PDW). These PDW phases are intertwined withmodulations of charge density and intra-unit cell form factors. The coexistenceof the two different pairing orders provides the unique two-gaps like spectraobserved by ARPES for superconducting cuprates. As temperature raises, the zeromomentum pairing order vanishes while the finite momentum pairing orders arekept, thus Fermi arcs are realized. The calculated quasiparticle spectra hasthe similar doping and temperature dependence as reported by ARPES and scanningtunneling spectroscopy(STS). The consequence of breaking symmetry between x andy due to the unidirectional PDW and the possibility to probe such a PDW statein the PG phase is discussed.

Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate Superconductors