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Vigorousness of effective hydrodynamics from Anderson localization in two dimensional nematic quantum criticality

Kyoung-Min Kim, Ki‐Seok Kim

Published May 21, 2019• 0 citations
OpenAlex

Abstract

The $1994$ first discovery of a metal-insulator transition in two dimensions and series of $1997-1998$ experiments on two dimensional metal-insulator transitions in various samples of MOSFETs changed the paradigm of Anderson localization that metals cannot exist in two dimensions. Unfortunately, this delocalization physics of the diffusive regime does not apply to the effective hydrodynamic regime of quantum criticality. In the present study, we investigate effects of mutual correlations between hydrodynamic fluctuations and weak-localization corrections on Anderson localization, based on the renormalization group analysis up to the two-loop order. As a result, we find that the absence of quantum coherence in two-particle composite excitations gives rise to a novel disordered non-Fermi liquid metallic state near two dimensional nematic quantum criticality with nonmagnetic disorders. This research would be the first 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.

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The 199419941994 first discovery of a metal-insulator transition in two dimensions and series of 1997−19981997-19981997−1998 experiments on two dimensional metal-insulator transitions in various samples of MOSFETs changed the paradigm of Anderson localization that metals cannot exist in two dimensions. Unfortunately, this delocalization physics of the diffusive regime does not apply to the effective hydrodynamic regime of quantum criticality. In the present study, we investigate effects of mutual correlations between hydrodynamic fluctuations and weak-localization corrections on Anderson localization, based on the renormalization group analysis up to the two-loop order. As a result, we find that the absence of quantum coherence in two-particle composite excitations gives rise to a novel disordered non-Fermi liquid metallic state near two dimensional nematic quantum criticality with nonmagnetic disorders. This research would be the first step in understanding the T−T-T−linear electrical resistivity as a characteristic feature of non-Fermi liquids and the origin of unconventional superconductivity from effective hydrodynamics of quantum criticality.
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−T-T−linear electrical resistivity as a characteristic feature of non-Fermi liquids and the origin of unconventional superconductivity from effective hydrodynamics of quantum criticality.
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.
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.
Nematic fluctuations alter the low-energy electronic behavior and reshape the mean-field phase diagram. We study a two-dimensional nematic metal with a two-component internal degree of freedom. Near the quantum critical point (QCP), longitudinal nematic fluctuations generate the non-Fermi-liquid self-energy ∝∣ω∣2/3\propto|ω|^{2/3}∝∣ω∣2/3, whereas transverse fluctuations give a subleading logarithmic, marginal-Fermi-liquid correction. Nevertheless, the transverse sector dominates the correction to the phase diagram through a quantum order-by-disorder mechanism: the emergent nematic background reshapes the electronic spectrum, alters the decay of nematic bosons, and produces a negative singular free-energy correction. This correction reconstructs the phase diagram, drives the transition first order, and is described by a scaling function whose two asymptotic limits define two critical regimes with free-energy corrections scaling as R8/3R^{8/3}R8/3 and R3R^3R3, respectively, where RRR is the order-parameter magnitude; their powers follow from the competition between the characteristic momentum of normal-state nematic fluctuations and that of the ordered-state background. These two regimes are experimentally distinguishable through nematic-susceptibility hysteresis measurements. The corrected phase diagram shows that the enlarged nodal ααα phase masks the otherwise bare QCP, making it inaccessible; consequently, the logarithmic self-energy correction is by no means negligible at low energies.
Resorting to a recently developed theoretical device called dimensional regularization for quantum criticality with a Fermi surface, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Unfortunately, we fail to approach the spin-liquid Mott quantum critical point from the U(1) spin-liquid state within the dimensional regularization technique. Self-interactions between charge fluctuations called holons are not screened, which shows a run-away renormalization group flow, interpreted as holons remain gapped. This leads us to consider another fixed point, where the spinon Fermi surface can be destabilized across the Mott transition. Based on this conjecture, we reveal the nature of the spin-liquid Mott quantum critical point: Dimensional reduction to one dimension occurs for spin dynamics described by spinons. As a result, Landau damping for both spin and charge dynamics disappear in the vicinity of the Mott quantum critical point. When the flavor number of holons is over its critical value, an interacting fixed point appears to be identified with an inverted XYXYXY universality class, controlled within the dimensional regularization technique. On the other hand, a fluctuation-driven first order metal-insulator transition results when it is below the critical number. We propose that the destabilization of a spinon Fermi surface and the emergence of one-dimensional spin dynamics near the spin-liquid Mott quantum critical point can be checked out by spin susceptibility with a 2kF2{k}_{F}2kF​ transfer momentum, where kF{k}_{F}kF​ is a Fermi momentum in the U(1) spin-liquid state: The absence of Landau damping in U(1) gauge fluctuations gives rise to a divergent behavior at zero temperature while it vanishes in the presence of a spinon Fermi surface.
We study the superconducting instability of a two-dimensional disordered Fermi liquid weakly coupled to the soft fluctuations associated with proximity to an Ising-ferromagnetic quantum critical point. We derive interaction-induced corrections to the Usadel equation governing the superconducting gap function, and show that diffusion and localization effects drastically modify the interplay between fermionic incoherence and strong pairing interactions. In particular, we obtain the phase diagram, and demonstrate that (i) there is an intermediate range of disorder strength where superconductivity is enhanced, eventually followed by a tendency towards the superconductor-insulator transition at stronger disorder; and (ii) diffusive particle-particle modes (so-called ``Cooperons'') acquire anomalous dynamical scaling z=4z=4z=4, indicating strong non-Fermi liquid behavior.