Valence bond glassy order and the pseudogap phase in underdoped high Tc cuprates

Different origins of the pseudogap phenomena in underdoped high Tc cuprate have been proposed over the years, but a consistent theory has been challenging. We argue that the low-energy fluctuations of the valence bond, originating from the superexchange interaction, are pinned by the doping induced electronic disorder to give rise to a valence bond glass (VBG) pseudogap phase Using an extended t-J model within the Gutzwiller approximation, we show that the normal state VBG phase exhibits a genuine Fermi arc and a V-shaped average density of state at low energies. In the superconducting phase below Tc, the VBG can coexist and compete with an inhomogeneous d-wave superconductor, leading to the two-gap phenomena. We discuss the evolution of the local and momentum-space spectroscopy with doping and temperature, which capture the salient properties of the pseudogap phenomena and electronic disorder observed by recent ARPES and STM experiments.