Renormalization group theory of nematic ordering in d-wave superconductors

TL;DR

This paper develops a quantum field theory framework for nematic order in d-wave superconductors, revealing critical behavior and anisotropic fermion spectral functions through a renormalization group analysis.

Contribution

It provides an all-orders renormalization group analysis of nematic ordering coupled to fermions, with exact results for the quantum critical point.

Findings

Nematic order exhibits a large anomalous dimension.

Fermion spectral functions are highly anisotropic.

The theory describes quantum critical behavior in d-wave superconductors.

Abstract

We examine the quantum theory of the spontaneous breaking of lattice rotation symmetry in d-wave superconductors on the square lattice. This is described by a field theory of an Ising nematic order parameter coupled to the gapless fermionic quasiparticles. We determine the structure of the renormalization group to all orders in a 1/N_f expansion, where N_f is the number of fermion spin components. Asymptotically exact results are obtained for the quantum critical theory in which, as in the large N_f theory, the nematic order has a large anomalous dimension, and the fermion spectral functions are highly anisotropic.