Renormalization Group Theory of Nematic Ordering 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.