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arXiv:cond-mat/0307446 · Physical Review B

Roton Fermi liquid: A metallic phase of two-dimensional electrons

Leon Balents, Matthew P. A. Fisher

Published Feb 28, 2005• 13 citations
arXivHTMLPDF

Abstract

We introduce and analyze a metallic phase of two-dimensional $(2\mathrm{D})$ electrons, the roton Fermi liquid (RFL), which, in contrast to the Landau--Fermi liquid, supports both gapless fermionic and bosonic quasiparticle excitations. The RFL is accessed using a reformulation of $2\mathrm{D}$ electrons consisting of fermionic quasiparticles and $hc∕2e$ vortices interacting with a mutual long-ranged statistical interaction. In the presence of a strong vortex-antivortex (i.e., roton) hopping term, the RFL phase emerges as an exotic yet eminently tractable quantum ground state. The RFL phase exhibits a ``Bose surface'' of gapless roton excitations describing transverse current fluctuations, has off-diagonal quasi-long-ranged order at zero temperature $(T=0)$, but is not superconducting, having zero superfluid density and no Meissner effect. The electrical resistance vanishes as $T\ensuremath{\rightarrow}0$ with a power of temperature (and frequency), $R(T)\ensuremath{\sim}{T}^{\ensuremath{\gamma}}$ (with $\ensuremath{\gamma}>1$), independent of the impurity concentration. The RFL phase also has a full Fermi surface of quasiparticle excitations just as in a Landau--Fermi liquid. Electrons can, however, scatter anomalously from rotonic ``current fluctuations'' and ``superconducting fluctuations.'' Current fluctuations induced by the gapless rotons scatter anomalously only at ``hot spots'' on the Fermi surface (with tangents parallel to the crystalline axes), while superconducting fluctuations give rise to an anomalous lifetime over the entire Fermi surface except near the (incipient) nodal points (``cold spots''). Fermionic quasiparticles dominate the Hall electrical transport. We also find three dominant instabilities of the RFL phase: an instability to a conventional Fermi-liquid phase driven by vortex condensation, a BCS-type instability toward fermion pairing, and a (nonpairing) superconducting instability. Precisely at the instability into the Fermi-liquid state, the exponent $\ensuremath{\gamma}$ saturates the bound, $\ensuremath{\gamma}=1$, so that $R(T)\ensuremath{\sim}T$. Upon entering the superconducting state the rotons are gapped out, and the anomalous quasiparticle scattering is strongly suppressed. We discuss how the RFL phase might underlie the strange metallic state of the cuprates near optimal doping, and outline a phenomenological picture to accommodate the underdoped pseudogap regime and the overdoped Landau--Fermi-liquid phase.

DOI
10.1103/physrevb.71.085119

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We introduce and analyze a metallic phase of two-dimensional (2D)(2\mathrm{D})(2D) electrons, the roton Fermi liquid (RFL), which, in contrast to the Landau--Fermi liquid, supports both gapless fermionic and bosonic quasiparticle excitations. The RFL is accessed using a reformulation of 2D2\mathrm{D}2D electrons consisting of fermionic quasiparticles and hc∕2ehc∕2ehc∕2e vortices interacting with a mutual long-ranged statistical interaction. In the presence of a strong vortex-antivortex (i.e., roton) hopping term, the RFL phase emerges as an exotic yet eminently tractable quantum ground state. The RFL phase exhibits a Bose surface'' of gapless roton excitations describing transverse current fluctuations, has off-diagonal quasi-long-ranged order at zero temperature $(T=0)$, but is not superconducting, having zero superfluid density and no Meissner effect. The electrical resistance vanishes as $T\ensuremath{\rightarrow}0$ with a power of temperature (and frequency), $R(T)\ensuremath{\sim}{T}^{\ensuremath{\gamma}}$ (with $\ensuremath{\gamma}>1$), independent of the impurity concentration. The RFL phase also has a full Fermi surface of quasiparticle excitations just as in a Landau--Fermi liquid. Electrons can, however, scatter anomalously from rotonic current fluctuations'' and superconducting fluctuations.'' Current fluctuations induced by the gapless rotons scatter anomalously only at hot spots'' on the Fermi surface (with tangents parallel to the crystalline axes), while superconducting fluctuations give rise to an anomalous lifetime over the entire Fermi surface except near the (incipient) nodal points (``cold spots''). Fermionic quasiparticles dominate the Hall electrical transport. We also find three dominant instabilities of the RFL phase: an instability to a conventional Fermi-liquid phase driven by vortex condensation, a BCS-type instability toward fermion pairing, and a (nonpairing) superconducting instability. Precisely at the instability into the Fermi-liquid state, the exponent \ensuremathγ\ensuremath{\gamma}\ensuremathγ saturates the bound, \ensuremathγ=1\ensuremath{\gamma}=1\ensuremathγ=1, so that R(T)\ensuremath∼TR(T)\ensuremath{\sim}TR(T)\ensuremath∼T. Upon entering the superconducting state the rotons are gapped out, and the anomalous quasiparticle scattering is strongly suppressed. We discuss how the RFL phase might underlie the strange metallic state of the cuprates near optimal doping, and outline a phenomenological picture to accommodate the underdoped pseudogap regime and the overdoped Landau--Fermi-liquid phase.
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We consider systems of nonrelativistic, interacting electrons at finite density and zero temperature in d=2,3,ldots dimensions. Our main concern is to characterize those systems that, under the renormalization flow, are driven away from the Landau Fermi-liquid (LFL) renormalization-group fixed point. We are especially interested in understanding under what circumstances such a system is a marginal Fermi-liquid (MFL) when the dimension of space is d\ensuremath{\geqslant}2. The interacting electron system is analyzed by combining renormalization-group (RG) methods with so called 'Luther-Haldane' bosonization techniques. The RG calculations are organized as a double expansion in the inverse scale parameter ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$ , which is proportional to the width of the effective momentum space around the Fermi surface and in the running coupling constant ${\mathrm{g}}_{\ensuremath{\lambda}}$ , which measures the strength of electron interactions at energy scales \ensuremath{\sim}vF{\mathrm{v}}_{\mathrm{F}}vF​ kF{\mathrm{k}}_{\mathrm{F}}kF​ /\ensuremath{\lambda}. For systems with a strictly convex Fermi surface, superconductivity is the only symmetry-breaking instability. Excluding such an instability, the system can be analyzed by means of bosonization. The RG and the underlying perturbation expansion in powers of ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$ serve to characterize the approximations involved by bosonizing the system. We argue that systems with short-range interactions flow to the LFL fixed point. Within the approximations involved by bosonization, the same holds for systems with long-range, longitudinal, density-density interactions. For electron systems interacting via long-range, transverse, current-current interactions, a deviation from LFL behavior is possible: if the exponent \ensuremath{\alpha} parametrizing the singularity of the interaction potential in momentum space by V-hat(|p|)\ensuremath{\sim}1/|p${\mathrm{|}}^{\mathrm{\ensuremath{\alpha}}}$ is greater than or equal to d-1, the results of the bosonization calculation are consistent with a MFL.
In this paper, the sixth in series, we continue our analysis of the interplay between non-Fermi liquid and pairing in the effective low-energy model of fermions with singular dynamical interaction $V({\mathrm{\ensuremath{\Omega}}}_{m})={\overline{g}}^{\ensuremath{\gamma}}/{|{\mathrm{\ensuremath{\Omega}}}_{m}|}^{\ensuremath{\gamma}}$ (the $\ensuremath{\gamma}$ model). The model describes low-energy physics of various quantum-critical metallic systems at the verge of an instability towards density or spin order, pairing of fermions at the half-filled Landau level, color superconductivity, and pairing in SYK-type models. In previous papers I--V, we analyzed the $\ensuremath{\gamma}$ model for $\ensuremath{\gamma}\ensuremath{\le}2$ and argued that the ground state is an ordinary superconductor, but there is an infinite number of local minima of the condensation energy. We further argued that the condensation energy spectrum becomes continuous and gapless, and superconducting Tc{T}_{c}Tc​ vanishes due to critical longitudinal gap fluctuations. In this paper, we consider larger $2<\ensuremath{\gamma}<3$. We show that the system moves away from criticality in that the condensation energy spectrum again becomes discrete and gapless, and Tc{T}_{c}Tc​ becomes finite. Yet, we show that the gap functions for $\ensuremath{\gamma}>2$ and $\ensuremath{\gamma}<2$ are topologically different as they live on different sheets of the Riemann surface. This makes $\ensuremath{\gamma}=2$ a topological quantum-critical point. We further show that the fermionic excitation spectrum for $\ensuremath{\gamma}>2$ acquires a new feature---a bound state at the edge of a continuum, with a macroscopic degeneracy, which is a fraction of the total number of states in the system. We obtain the phase diagram on the $({\ensuremath{\omega}}_{D},\ensuremath{\gamma})$ plane, where ${\ensuremath{\omega}}_{D}$ is a mass of a pairing boson, and on the $(T,\ensuremath{\gamma})$ plane. The latter consists of two distinct superconducting phases at $\ensuremath{\gamma}<2$ and $\ensuremath{\gamma}>2$ and the intermediate pseudogap state of preformed pairs in between.
Understanding non-Landau Fermi liquids in dimensions higher than one, has been a subject of great interest. Such phases may serve as parent states for other unconventional phases of quantum matter, in a similar manner that conventional broken symmetry states can be understood as instabilities of the Landau Fermi liquid. In this work, we investigate the emergence of a novel non-Landau Fermi liquid in two dimensions, where the fermions with quadratic band-touching dispersion interact with a Bose metal. The bosonic excitations in the Bose metal possess an extended nodal-line spectrum in momentum space, which arises due to the subsystem symmetry or the restricted motion of bosons. Using renormalization group analysis and direct computations, we show that the extended infrared (IR) singularity of the Bose metal leads to a line of interacting fixed points of novel non-Landau Fermi liquids, where the anomalous dimension of the fermions varies continuously, akin to the Luttinger liquid in one dimension. Further, the multi-patch generalization of the model is used to explore other unusual features of the resulting ground state.
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.