Theory of the Nodal Nematic Quantum Phase Transition in Superconductors

Abstract

We study the character of an Ising nematic quantum phase transition 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 qps 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.