Modeling the pseudogap metallic state in cuprates: Quantum disordered pair density wave

Abstract

We present a way to quantum-disorder a pair density wave and propose it to be a candidate of the effective low-energy description of the pseudogap metal which may reveal itself in a sufficiently high magnetic field that suppresses the $d$-wave pairing. The ground state we construct is a small-pocket Fermi liquid with a bosonic Mott insulator in the density-wave-enlarged unit cell. At low energy, the charge density is mainly carried by charge $2e$ bosons, which develop a small insulating gap. As an intermediate step, we discuss the quantum disordering of a fully gapped superconductor and its excitation spectrum. A simplified 1D model, which we solve numerically, is used to illustrate the introduced concepts. We discuss a number of experimental consequences. The interplay between the electron and the small-gap boson results in a step-function background in the electron spectral function which may be consistent with existing angle-resolved photoemission spectroscopy data. Optical excitation across the boson gap can explain the onset and the magnitude of the mid infrared absorption reported long ago.