Abstract
At the nematic quantum critical point that exists in the -wave superconducting dome of cuprates, the massless nodal fermions interact strongly with the quantum critical fluctuation of nematic order. We study this problem by means of the renormalization group approach and show that, the fermion damping rate vanishes more rapidly than the energy ω and the quasiparticle residue in the limit . The nodal fermions thus constitute an unconventional non-Fermi liquid that represents an even weaker violation of Fermi liquid theory than a marginal Fermi liquid. We also investigate the interplay of quantum nematic critical fluctuation and gauge-potential-like disorder, and find that the effective disorder strength flows to the strong coupling regime at low energies. Therefore, even an arbitrarily weak disorder can drive the system to become a disorder controlled diffusive state. Based on these theoretical results, we are able to understand a number of interesting experimental facts observed in curpate superconductors.
Highlights
A large amount of experimental and theoretical studies have been devoted to studying the unusual properties of high temperature cuprate superconductors in the past thirty years [1, 2, 3, 4, 5, 6, 7, 8, 9]
We find that Zf flows to zero in the limit l → +∞, which indicates the breakdown of normal Fermi liquid and the absence of well-defined Landau quasiparticles
We have showed in the last subsection that the nodal fermions exhibit unconventional non-Fermi liquid behaviors at the nematic quantum critical point (QCP)
Summary
A large amount of experimental and theoretical studies have been devoted to studying the unusual properties of high temperature cuprate superconductors in the past thirty years [1, 2, 3, 4, 5, 6, 7, 8, 9]. At the nematic QCP, the massless fermions excited from the dx2−y2-wave gap nodes couple strongly to the quantum critical fluctuation of nematic order parameter, which can be effectively described by a (2+1)-dimensional field theory [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31] This model was first analyzed by Vojta et al [20, 21, 22], who made an ǫ-expansion and argued that the nematic phase transition is turned to first order. We find that the effective strength of gauge potential disorders tends to diverge at the lowest energy This behavior signals the emergence of a finite zero-energy DOS ρ(0) and the happening of quantum phase transition from an unconventional non-Fermi liquid to a disorder dominated diffusive state.
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