Existence of a weak-disorder non-Fermi liquid fixed point in the hydrodynamic regime of two-dimensional nematic quantum criticality

TL;DR

This paper demonstrates the existence of a weak-disorder non-Fermi liquid fixed point in the hydrodynamic regime of two-dimensional nematic quantum critical metals, providing insights into non-Fermi liquid behavior and unconventional superconductivity.

Contribution

It introduces a two-loop RG analysis showing a weak-disorder non-Fermi liquid fixed point in the hydrodynamic regime, differing from the diffusive regime where perturbation fails.

Findings

Existence of a weak-disorder non-Fermi liquid fixed point.

Weak localization corrections are suppressed in the hydrodynamic regime.

This fixed point governs intermediate energy scales in nematic quantum critical metals.

Abstract

Role of quenched randomness in metallic quantum criticality is one of the long standing problems in condensed matter physics. An aspect of the fundamental difficulties lies in the fact that such nonmagnetic disorders lead effective interactions between abundant soft modes near the Fermi surface to be drastically enhanced particularly in the diffusive regime, where the perturbative framework does not work. Here, we revisit the problem of dirty quantum critical metals in a different angle, focusing on the hydrodynamic regime instead of the diffusive regime near the non-Fermi liquid quantum critical point. More concretely, we study effects of mutual correlations between quantum critical nematic fluctuations and weak localization corrections, and show the existence of a weak-disorder non-Fermi liquid fixed point, based on the renormalization group (RG) analysis up to the two-loop order. The two-loop order RG analysis suggests that the absence of quantum coherence in two-particle composite excitations weakens the role of weak localization corrections and allows a weakly disordered non-Fermi liquid metallic state in the hydrodynamic regime of the nematic quantum critical point. Although this dirty non-Fermi liquid metallic state may not be the true infrared stable fixed point at zero temperature, expected to be characterized by the diffusive Ohmic regime, we argue that this weak-disorder non-Fermi liquid metallic fixed point would govern the region of an intermediate energy scale, described by effective hydrodynamics of nematic quantum criticality. In this respect we believe that this research would be an important step in understanding the $T-$linear electrical resistivity as a characteristic feature of non-Fermi liquids and the origin of unconventional superconductivity from effective hydrodynamics of quantum criticality.