We show that the low-energy fluctuations of the valence bond due to the superexchange are pinned by the electronic disorder from off-stoichiometric dopants, leading to a valence bond glass (VBG) pseudogap phase in underdoped high-$T_c$ cuprates. The antinodal Fermi surface sections are gapped out, giving rise to a normal state Fermi arc whose length shrinks with underdoping. Below $T_c$, the superexchange interaction induces a $d$-wave superconducting gap that coexists with the VBG pseudogap. The evolution of the local and momentum-space spectroscopy with doping and temperature captures the salient properties of the pseudogap phenomena and the electronic disorder.

• Received 1 August 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.107001