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Physics-Uspekhi

Non-Fermi-liquid metals

L. B. Ioffe, Andrew J. Millis

Published Jun 30, 1998• 15 citations
Publisher

Abstract

The experimental discovery of a number of 'strange metals' has reopened the question of the low temperature behavior of interacting Fermi systems. Here we provide a subjective overview of some aspects of the resulting theoretical work. It seems to us that from a theoretical standpoint Landau's Fermi-liquid theory has proven to be a remarkably robust description of clean Fermi systems. The only well documented theoretical examples of non-Fermi-liquid behavior are metals subject to gauge interactions or at quantum critical points. The experimental anomalies which prompted the reexamination of Fermi-liquid theory remain in many cases mysterious.

DOI
10.1070/pu1998v041n06abeh000410

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The experimental discovery of a number of 'strange metals' has reopened the question of the low temperature behavior of interacting Fermi systems. Here we provide a subjective overview of some aspects of the resulting theoretical work. It seems to us that from a theoretical standpoint Landau's Fermi-liquid theory has proven to be a remarkably robust description of clean Fermi systems. The only well documented theoretical examples of non-Fermi-liquid behavior are metals subject to gauge interactions or at quantum critical points. The experimental anomalies which prompted the reexamination of Fermi-liquid theory remain in many cases mysterious.
An introductory survey of the theoretical ideas and calculations and experimental results which depart from Landau Fermi liquids is presented. The common themes and possible routes to the singularities leading to breakdown of Landau Fermi liquids are categorized following an elementary discussion of the theory. Soluble examples of singular or Non Fermi‐liquids include models of impurities in metals with special symmetries and one‐dimensional interacting fermions. A review of these is followed by a discussion of singular Fermi liquids in a wide variety of experimental situations and theoretical models. These include the effects of low energy collective fluctuations, gauge fields, fluctuations around quantum critical points, the normal state of high temperature superconductors and the two dimensional metallic state.
This article is aimed at a pedagogical introduction to the physics of quantum phase transitions that is unique to metallic systems. It has been recognized for some time that quantum criticality can result in a breakdown of Landau's Fermi liquid theory. Its converse, however, has not been appreciated until very recently: non-Fermi liquid behavior can in turn lead to new classes of quantum phase transition. A concrete example is provided by ``local quantum critical points''. I summarize the theoretical reasoning and experimental evidence for local quantum criticality, in the context of heavy fermion metals. The underlying physics is likely to be relevant to other correlated electron systems including doped Mott insulators.
Non-Fermi liquids are unconventional metals whose physical properties deviate qualitatively from those of noninteracting fermions due to strong quantum fluctuations near Fermi surfaces. They arise when metals are subject to singular interactions mediated by soft collective modes. In the absence of well-defined quasiparticles, universal physics of non-Fermi liquids is captured by interacting field theories which replace Landau Fermi liquid theory. However, it has been difficult to understand their universal low-energy physics due to a lack of theoretical methods that take into account strong quantum fluctuations in the presence of abundant low-energy degrees of freedom. In this review, we discuss two approaches that have been recently developed for non-Fermi liquid theory with emphasis on two space dimensions. The first is a perturbative scheme based on a dimensional regularization, which achieves a controlled access to the low-energy physics by tuning the codimension of Fermi surface. The second is a nonperturbative approach which treats the interaction ahead of the kinetic term through a non-Gaussian scaling called interaction-driven scaling. Examples of strongly coupled non-Fermi liquids amenable to exact treatments through the interaction-driven scaling are discussed.
The paradigm of Landau Fermi liquid theory has successfully described the low-energy behavior of numerous metallic systems. However, a growing number of experimental observations in strongly correlated electron materials, such as high-temperature superconductors and heavy fermion compounds, defy this conventional description, exhibiting what is known as non-Fermi liquid (NFL) behavior. These exotic states lack well-defined quasiparticle excitations, displaying anomalous scaling laws and transport properties. Ultracold atomic gases have emerged as highly controllable quantum simulators for strongly correlated matter, offering unprecedented access to tunable interaction strengths, dimensionality, and lattice geometries. This paper explores the potential of ultracold fermionic gases to unveil and characterize NFL behavior. We review the theoretical underpinnings of Landau Fermi liquid theory and its breakdown, survey prominent theoretical models for NFL states, and highlight experimental techniques in ultracold atomic systems pertinent to their detection. Specific attention is given to phenomena such as the BCS-BEC crossover, quantum criticality, and pseudogap phases in ultracold fermions, where strong interactions are expected to lead to deviations from quasiparticle descriptions. We discuss experimental signatures like anomalous spectral functions, linear-in-temperature resistivity analogs, and deviations in thermodynamic properties, proposing how these could be observed and analyzed in current and future ultracold atom platforms. This research aims to leverage the purity and tunability of atomic gases to gain fundamental insights into the nature of NFL states, contributing to a broader understanding of quantum many-body physics beyond the conventional quasiparticle picture.
A long-standing mystery of fundamental importance in correlated electron physics is to understand strange non-Fermi liquid metals that are seen in diverse quantum materials. A striking experimental feature of these metals is a resistivity that is linear in temperature (T). In this Letter we ask what it takes to obtain such non-Fermi liquid physics down to zero temperature in a translation invariant metal. If in addition the full frequency (ω) dependent conductivity satisfies ω/T scaling, we argue that the T-linear resistivity must come from the intrinsic physics of the low energy fixed point. Combining with earlier arguments that compressible translation invariant metals are "ersatz Fermi liquids" with an infinite number of emergent conserved quantities, we obtain powerful and practical conclusions. We show that there is necessarily a diverging susceptibility for an operator that is odd under inversion and time reversal symmetries, and has zero crystal momentum. We discuss a few other experimental consequences of our arguments, as well as potential loopholes, which necessarily imply other exotic phenomena.
Since the mid-eighties there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory. Examples of these so-called non-Fermi liquids include the strange metal phase of high transition temperature cuprates, and heavy fermion systems near a quantum phase transition. We report on a class of non-Fermi liquids discovered using gauge/gravity duality. The low energy behavior of these non-Fermi liquids is shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling behavior only in the temporal direction. Within this class we find examples whose single-particle spectral function and transport behavior resemble those of strange metals. In particular, the contribution from the Fermi surface to the conductivity is inversely proportional to the temperature. In our treatment these properties can be understood as being controlled by the scaling dimension of the fermion operator in the emergent IR fixed point.