# The Transformation of the Superconducting Gap to an Insulating Pseudogap at a Critical Hole Density in the Cuprates

## TL;DR

This paper explains how the superconducting gap in cuprates transforms into an insulating pseudogap at a critical hole density, driven by umklapp scattering and Mott localization, using a wavepacket formalism.

## Contribution

It introduces a novel application of the wavepacket formalism to describe the pseudogap transition in cuprates, emphasizing the role of umklapp scattering in gap formation.

## Key findings

- Energy gaps can open on specific surfaces due to umklapp scattering.
- The pseudogap results from a pairing instability involving umklapp processes.
- Superconducting gap evolves into an insulating pseudogap at critical doping.

## Abstract

We apply the recent wavepacket formalism developed by Ossadnik to describe the origin of the short range ordered pseudogap state as the hole doping is lowered through a critical density in cuprates. We argue that the energy gain that drives this precursor state to Mott localization, follows from maximizing umklapp scattering near the Fermi energy. To this end we show how energy gaps driven by umklapp scattering can open on an appropriately chosen surface, as proposed earlier by Yang, Rice and Zhang. The key feature is that the pairing instability includes umklapp scattering, leading to an energy gap not only in the single particle spectrum but also in the pair spectrum. As a result the superconducting gap at overdoping is turned into an insulating pseudogap, in the antinodal parts of the Fermi surface.