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At the nematic quantum critical point that exists in the $d_{x^2-y^2}$-wavesuperconducting dome of cuprates, the massless nodal fermions interact stronglywith the quantum critical fluctuation of nematic order. We study this problemby means of renormalization group approach and show that, the fermion dampingrate $\left|\mathrm{Im}\Sigma^R(\omega)\right|$ vanishes more rapidly than theenergy $\omega$ and the quasiparticle residue $Z_f\rightarrow 0$ in the limit$\omega \rightarrow 0$. The nodal fermions thus constitute an unconventionalnon-Fermi liquid that represents an even weaker violation of Fermi liquidtheory than a marginal Fermi liquid. We also investigate the interplay ofquantum nematic critical fluctuation and gauge-potential-like disorder, andfind that the effective disorder strength flows to the strong coupling regimeat low energies. Therefore, even an arbitrarily weak disorder can drive thesystem to become a disorder controlled diffusive state. Based on thesetheoretical results, we are able to understand a number of interestingexperimental facts observed in curpate superconductors.

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