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arXiv:2403.10148 · SciPost Physics

Disordered non-Fermi liquid fixed point for two-dimensional metals at Ising-nematic quantum critical points

Kyoung-Min Kim, Ki‐Seok Kim

Published Aug 23, 2024• 1 citation
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Abstract

Understanding the influence of quenched random potential is crucial for comprehending the exotic electronic transport of non-Fermi liquid metals near metallic quantum critical points. In this study, we identify a stable fixed point governing the quantum critical behavior of two-dimensional non-Fermi liquid metals in the presence of a random potential disorder. By performing renormalization group analysis on a dimensional-regularized field theory for Ising-nematic quantum critical points, we systematically investigate the interplay between random potential disorder for electrons and Yukawa-type interactions between electrons and bosonic order-parameter fluctuations in a perturbative epsilon expansion. At the one-loop order, the effective field theory lacks stable fixed points, instead exhibiting a runaway flow toward infinite disorder strength. However, at the two-loop order, the effective field theory converges to a stable fixed point characterized by finite disorder strength, termed the “disordered non-Fermi liquid (DNFL) fixed point”. Our investigation reveals that two-loop vertex corrections induced by Yukawa couplings are pivotal in the emergence of the DNFL fixed point, primarily through screening disorder scattering. Additionally, the DNFL fixed point is distinguished by a substantial anomalous scaling dimension of fermion fields, resulting in pseudogap-like behavior in the electron’s density of states. These findings shed light on the quantum critical behavior of disordered non-Fermi liquid metals, emphasizing the indispensable role of higher-order loop corrections in such comprehension.

DOI
10.21468/scipostphys.17.2.059

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Understanding the influence of quenched random potential is crucial for comprehending the exotic electronic transport of non-Fermi liquid metals near metallic quantum critical points. In this study, we identify a stable fixed point governing the quantum critical behavior of two-dimensional non-Fermi liquid metals in the presence of a random potential disorder. By performing renormalization group analysis on a dimensional-regularized field theory for Ising-nematic quantum critical points, we systematically investigate the interplay between random potential disorder for electrons and Yukawa-type interactions between electrons and bosonic order-parameter fluctuations in a perturbative epsilon expansion. At the one-loop order, the effective field theory lacks stable fixed points, instead exhibiting a runaway flow toward infinite disorder strength. However, at the two-loop order, the effective field theory converges to a stable fixed point characterized by finite disorder strength, termed the “disordered non-Fermi liquid (DNFL) fixed point”. Our investigation reveals that two-loop vertex corrections induced by Yukawa couplings are pivotal in the emergence of the DNFL fixed point, primarily through screening disorder scattering. Additionally, the DNFL fixed point is distinguished by a substantial anomalous scaling dimension of fermion fields, resulting in pseudogap-like behavior in the electron’s density of states. These findings shed light on the quantum critical behavior of disordered non-Fermi liquid metals, emphasizing the indispensable role of higher-order loop corrections in such comprehension.
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In metals, low-energy effective theories are characterized by a set of coupling functions. Among them, the angle-dependent Fermi momentum specifies the size and shape of Fermi surface. Since the Fermi momentum grows incessantly under the renormalization group flow, a metallic fixed point is defined only modulo a rescaling of Fermi momentum. In this paper, we discuss the physical consequences of this projective nature of fixed points for non-Fermi liquids with hot Fermi surfaces. The first is the absence of a unique dynamical critical exponent that dictates the relative scaling between energy and momentum. The second is mismatches between the scaling dimensions of couplings and their relevancy. Nonetheless, each projective fixed point is characterized by a few marginal and relevant coupling functions, and the notion of universality survives. We illustrate our findings by charting the space of projective fixed points and extracting their universal properties for the Ising-nematic quantum critical metal beyond the patch theory. To control the theory, we use the dimensional regularization scheme that tunes the co-dimension of Fermi surface. Near the upper critical dimension, two exactly marginal coupling functions span the space of stable projective fixed points: functions that specify the shape of the Fermi surface and the angle-dependent Fermi velocity. All other coupling functions, including the Landau functions and the universal pairing interaction, are fixed by those two marginal functions. With decreasing dimensions, the forward scattering remains irrelevant while the pairing interaction becomes relevant near two dimensions. In two dimensions, it is expected that the universal superconducting fluctuations lower the symmetry of the non-Fermi liquid realized above the superconducting transition temperatures from the loop U(1) group to a proper subgroup.