Theory of the nodal nematic quantum phase transition in superconductors

TL;DR

This paper analyzes the nature of an Ising nematic quantum phase transition within a d-wave superconductor, revealing continuous transition characteristics and effects on quasiparticle behavior, with implications for cuprate superconductors.

Contribution

It provides a theoretical framework for understanding the nematic quantum phase transition in superconductors, including effects of quantum fluctuations and disorder.

Findings

Transition is continuous within 1/N expansion.

Quantum fluctuations enhance dispersion anisotropy.

Quasiparticle peaks are critically broadened except near the Fermi surface.

Abstract

We study the character of an Ising nematic quantum phase transition (QPT) deep inside a d-wave superconducting state with nodal quasiparticles in a two-dimensional tetragonal crystal. We find that, within a 1/N expansion, the transition is continuous. To leading order in 1/N, quantum fluctuations enhance the dispersion anisotropy of the nodal excitations, and cause strong scattering which critically broadens the quasiparticle (qp) peaks in the spectral function, except in a narrow wedge in momentum space near the Fermi surface where the qp's remain sharp. We also consider the possible existence of a nematic glass phase in the presence of weak disorder. Some possible implications for cuprate physics are also discussed.