Unconventional non-Fermi liquid state caused by nematic criticality in cuprates

TL;DR

This paper investigates the unconventional non-Fermi liquid behavior near nematic quantum critical points in cuprates, revealing weaker violations of Fermi liquid theory and the impact of disorder, supported by renormalization group analysis.

Contribution

It provides a theoretical analysis of nematic criticality in cuprates showing a novel non-Fermi liquid state and the effects of disorder, advancing understanding of quantum critical phenomena.

Findings

Nodal fermions exhibit a damping rate vanishing faster than energy

Quasiparticle residue approaches zero, indicating non-Fermi liquid behavior

Weak disorder becomes strong at low energies, leading to a diffusive state

Abstract

At the nematic quantum critical point that exists in the $d_{x^2-y^2}$-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 renormalization group approach and show that, the fermion damping rate $\left|\mathrm{Im}\Sigma^R(\omega)\right|$ vanishes more rapidly than the energy $\omega$ and the quasiparticle residue $Z_f\rightarrow 0$ in the limit $\omega \rightarrow 0$. 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.