Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Experimental and Theoretical Physics Letters

Dynamical nature of chaos in electron systems of high-T c superconductors

MIKHAIL V. ZVEREV, VICTOR A. KHODEL

Published Apr 1, 2002• 4 citations
Publisher

Abstract

A model of the fermion-condensation phase transition forming a plateau in the spectrum of single-particle excitations near the Fermi surface at T=0 is used to analyze those features of the spectral functions of normal states of high-T c superconductors which are inherent in a marginal Fermi liquid contaminated by impurities. With this model, such a behavior is shown to be due to the fermion condensate, which acts as an impurity subsystem because its energy spectrum at T=0 is dispersionless. The influence of the anisotropy of condensate distribution in the Brillouin zone on the spectral functions is discussed.

DOI
10.1134/1.1490008

Related papers

Quasiparticle picture of high-temperature superconductors in the frame of a Fermi liquid with the fermion condensate

M. Ya. Amusia, Vasily R. Shaginyan

A model of a Fermi liquid with the fermion condensate (FC) is applied to the consideration of quasiparticle excitations in high-temperature superconductors, in their superconducting and normal states. Within our model the appearance of the fermion condensate presents a quantum phase transition that separates the regions of normal and strongly correlated electron liquids. Beyond the phase transition point the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other---fermion condensate localized at the Fermi surface and characterized by almost dispersionless single-particle excitations. In the superconducting state the quasiparticle dispersion in systems with FC can be presented by two straight lines, characterized by effective masses ${M}_{\mathrm{FC}}^{*}$ and ${M}_{L}^{*},$ respectively, and intersecting near the binding energy, which is of the order of the superconducting gap. This same quasiparticle picture persists in the normal state, thus manifesting itself over a wide range of temperatures as new energy scales. Arguments are presented that fermion systems with FC have features of a ``quantum protectorate'' [R. B. Laughlin and D. Pines, Proc. Natl. Acad. Sci. U.S.A. 97, 28 (2000); P. W. Anderson, cond-mat/0007185 (unpublished); cond-mat/0007287 (unpublished)].

arXiv:cond-mat/0102229•Physical review. B, Condensed matter•May 21, 2001•31 citations

Fermi-condensate quantum phase transition in high-T c superconductors

M. Ya. Amusia, Vasily R. Shaginyan

The effect of a quantum phase transition associated with the appearance of fermionic condensation in an electron liquid on the properties of superconductors is considered. It is shown that the electron system in both superconducting and normal states exhibits characteristic features of a quantum protectorate after the point of this Fermi-condensate quantum phase transition. The single-particle spectrum of a superconductor can be represented by two straight lines corresponding to two effective masses M FC * and M L *. The M FC * mass characterizes the spectrum up to the binding energy E 0 , which is of the order of the superconducting gap in magnitude, and determines the spectrum at higher binding energies. Both effective masses are retained in the normal state; however, E 0 ≃4 T. These results are used to explain some remarkable properties of high-T c superconductors and are in good agreement with recent experimental data.

arXiv:cond-mat/0105477•Journal of Experimental and Theoretical Physics Letters•Mar 1, 2001•9 citations

Fermion Condensation: Theory and Experiment

VICTOR A. KHODEL, J. W. Clark, MIKHAIL V. ZVEREV

Fundamentals of fermion-condensation physics are outlined. Fermion condensation is a phase transition occurring in a strongly correlated Fermi system upon a topological reconstruction of the Landau ground state and leading to the formation of a fermion condensate that possesses the dispersionless single-particle spectrum $$\epsilon({\mathbf{p}})=0$$ in the momentum-space region adjacent to the Fermi surface and, accordingly, an anomalously enhanced density of single-particle states. A original method is developed for solving the set of nonlinear integral equations of fermion-condensation theory. This method makes it possible to analyze the problem of quantum chaos in strongly interacting multifermion systems. The computational technique used is demonstrated by applying it to superdense quark–gluon plasma, where the structure of exchange quark–quark interaction is well known. In electron systems featuring a fermion condensate, the magnitude of the gap appearing in the single-particle spectrum owing to Cooper pairing is shown to be much larger than that in Bardeen–Cooper–Schrieffer (BCS) theory. This explains both a high superconducting-transition temperature $$T_{c}$$ and, with allowance for $$C_{4}$$ crystal-lattice symmetry, the $$D$$ -wave pairing-gap structure observed in cuprates. It is found that, in addition to the BCS gap $$\Delta$$ , the spectrum of single-particle excitations of superconducting systems where a fermion condensate is present develops a nonsuperconducting gap $$\Upsilon$$ that owes its existence to the interaction of condensate particles with normal quasiparticles residing outside the condensate region in momentum space. The question of whether these results are pertinent to the two-gap structure recently unearthed in the excitation spectrum of cuprates upon analyzing ARPES data is addressed.

Physics of Atomic Nuclei•Mar 1, 2020•0 citations

Strongly Correlated Fermi Liquid and the Normal State of High Tc Superconductors

Ziqiang Wang

New insights into the strongly correlated Fermi liquid state of the SU(N) infinite-U Hubbard and t-J models are presented in connection to the metallic state of unbroken symmetry of the copper oxide planes. The nature of single particle and collective excitations is analyzed and the Landau Fermi Liquid parameters are derived. The one-particle spectral function in the Hubbard valence band is obtained with both Hubbard and Gutzwiller-like features. A simple interpretation of the large incoherent background is given in terms of a superposition of quasiparticles and a collective mode describing the propagation of a bare hole in a large U system. The spin exchange interactions produce very low lying collective modes describing the propagation of staggered spin chirality which soften at incommensurate wavevectors. The quasiparticles are strongly scattered by the low lying chirality fluctuations resulting in deviations from canonical Fermi liquid behavior at low energy scales. Of the same origin, the quasiparticle self energy is found to be strongly k-dependent. It leads to corrections to the dispersion and enhancement of the quasiparticle lifetime in the hole-like region of the interacting Fermi surface. The combined effects are sufficient to produce a sign change in the Hall coefficient evaluated for parameters relevant to the copper oxide planes. We show that these models also exhibit a zero temperature fluctuation driven transition from Fermi liquid to non Fermi liquid phase without the onset of magnetic ordering below a critical doping δc=1/4N, whereby providing a microscopic mechanism for the destruction of the Fermi liquid coherence by strong longitudinal gauge fluctuations which represent the effects of the infinite-U constraint.

International Journal of Modern Physics B•Mar 1, 1992•18 citations

Non-Fermi Liquid Behavior from Critical Fermi Surface Fluctuations

Walter Metzner, Luca Dell’Anna

Interactions in Fermi systems can generate a Pomeranchuk instability leading to orientational symmetry breaking, that is, nematic order. In a metallic system close to such an instability the Fermi surface is easily deformed by anisotropic perturbations and exhibits enhanced collective fluctuations. We analyze fluctuation effects in the quantum critical regime near a d-wave Pomeranchuk instability in two dimensions. Density correlations with a d-wave form factor and the dynamical forward scattering interaction diverge near the instability. The singular forward scattering leads to large self-energy contributions, which destroy Fermi liquid behavior over the whole Fermi surface except at “cold spots” on the Brillouin zone diagonal. The decay rate of single-particle excitations, which is related to the width of the peaks in the spectral function, exceeds the excitation energy in the low-energy limit. The dispersion of the spectra flattens strongly near those portions of the Fermi surface which are remote from the zone diagonal. The decay rate for DC transport is linear in temperature except at the cold spots. We discuss the possible relevance of d-wave Fermi surface fluctuations for the “strange metal” behavior observed in the normal phase of cuprates.

Progress of Theoretical Physics Supplement•Jan 1, 2008•0 citations

The interplay between flattening and damping of single particle spectra in strongly correlated Fermi systems

VICTOR A. KHODEL, MIKHAIL V. ZVEREV

The self-consistent theory of the fermion condensation, a specific phase transition which results in a rearrangement of the single particle degrees of freedom in strongly correlated Fermi systems is developed. Beyond the phase transition point, the single particle spectra are shown to be flat. The interplay between the flattening and the damping of the single particle spectra at $T\to 0$ is investigated. The width $γ(ε)$ of the single particle states is found to grow up linearly with $ε$ over a wide range of energy as in a marginal Fermi liquid. Our results gain insight into the success of the phenomenological theory of the normal states of high-temperature superconductors by Varma et al.

arXiv:cond-mat/9907061•Jul 5, 1999•0 citations
A model of the fermion-condensation phase transition forming a plateau in the spectrum of single-particle excitations near the Fermi surface at T=0 is used to analyze those features of the spectral functions of normal states of high-T c superconductors which are inherent in a marginal Fermi liquid contaminated by impurities. With this model, such a behavior is shown to be due to the fermion condensate, which acts as an impurity subsystem because its energy spectrum at T=0 is dispersionless. The influence of the anisotropy of condensate distribution in the Brillouin zone on the spectral functions is discussed.
A model of a Fermi liquid with the fermion condensate (FC) is applied to the consideration of quasiparticle excitations in high-temperature superconductors, in their superconducting and normal states. Within our model the appearance of the fermion condensate presents a quantum phase transition that separates the regions of normal and strongly correlated electron liquids. Beyond the phase transition point the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other---fermion condensate localized at the Fermi surface and characterized by almost dispersionless single-particle excitations. In the superconducting state the quasiparticle dispersion in systems with FC can be presented by two straight lines, characterized by effective masses MFC∗{M}_{\mathrm{FC}}^{*}MFC∗​ and ML∗,{M}_{L}^{*},ML∗​, respectively, and intersecting near the binding energy, which is of the order of the superconducting gap. This same quasiparticle picture persists in the normal state, thus manifesting itself over a wide range of temperatures as new energy scales. Arguments are presented that fermion systems with FC have features of a ``quantum protectorate'' [R. B. Laughlin and D. Pines, Proc. Natl. Acad. Sci. U.S.A. 97, 28 (2000); P. W. Anderson, cond-mat/0007185 (unpublished); cond-mat/0007287 (unpublished)].
The effect of a quantum phase transition associated with the appearance of fermionic condensation in an electron liquid on the properties of superconductors is considered. It is shown that the electron system in both superconducting and normal states exhibits characteristic features of a quantum protectorate after the point of this Fermi-condensate quantum phase transition. The single-particle spectrum of a superconductor can be represented by two straight lines corresponding to two effective masses M FC * and M L *. The M FC * mass characterizes the spectrum up to the binding energy E 0 , which is of the order of the superconducting gap in magnitude, and determines the spectrum at higher binding energies. Both effective masses are retained in the normal state; however, E 0 ≃4 T. These results are used to explain some remarkable properties of high-T c superconductors and are in good agreement with recent experimental data.
Fundamentals of fermion-condensation physics are outlined. Fermion condensation is a phase transition occurring in a strongly correlated Fermi system upon a topological reconstruction of the Landau ground state and leading to the formation of a fermion condensate that possesses the dispersionless single-particle spectrum ϵ(p)=0\epsilon({\mathbf{p}})=0ϵ(p)=0 in the momentum-space region adjacent to the Fermi surface and, accordingly, an anomalously enhanced density of single-particle states. A original method is developed for solving the set of nonlinear integral equations of fermion-condensation theory. This method makes it possible to analyze the problem of quantum chaos in strongly interacting multifermion systems. The computational technique used is demonstrated by applying it to superdense quark–gluon plasma, where the structure of exchange quark–quark interaction is well known. In electron systems featuring a fermion condensate, the magnitude of the gap appearing in the single-particle spectrum owing to Cooper pairing is shown to be much larger than that in Bardeen–Cooper–Schrieffer (BCS) theory. This explains both a high superconducting-transition temperature TcT_{c}Tc​ and, with allowance for C4C_{4}C4​ crystal-lattice symmetry, the DDD -wave pairing-gap structure observed in cuprates. It is found that, in addition to the BCS gap Δ\DeltaΔ , the spectrum of single-particle excitations of superconducting systems where a fermion condensate is present develops a nonsuperconducting gap Υ\UpsilonΥ that owes its existence to the interaction of condensate particles with normal quasiparticles residing outside the condensate region in momentum space. The question of whether these results are pertinent to the two-gap structure recently unearthed in the excitation spectrum of cuprates upon analyzing ARPES data is addressed.
New insights into the strongly correlated Fermi liquid state of the SU(N) infinite-U Hubbard and t-J models are presented in connection to the metallic state of unbroken symmetry of the copper oxide planes. The nature of single particle and collective excitations is analyzed and the Landau Fermi Liquid parameters are derived. The one-particle spectral function in the Hubbard valence band is obtained with both Hubbard and Gutzwiller-like features. A simple interpretation of the large incoherent background is given in terms of a superposition of quasiparticles and a collective mode describing the propagation of a bare hole in a large U system. The spin exchange interactions produce very low lying collective modes describing the propagation of staggered spin chirality which soften at incommensurate wavevectors. The quasiparticles are strongly scattered by the low lying chirality fluctuations resulting in deviations from canonical Fermi liquid behavior at low energy scales. Of the same origin, the quasiparticle self energy is found to be strongly k-dependent. It leads to corrections to the dispersion and enhancement of the quasiparticle lifetime in the hole-like region of the interacting Fermi surface. The combined effects are sufficient to produce a sign change in the Hall coefficient evaluated for parameters relevant to the copper oxide planes. We show that these models also exhibit a zero temperature fluctuation driven transition from Fermi liquid to non Fermi liquid phase without the onset of magnetic ordering below a critical doping δc=1/4N, whereby providing a microscopic mechanism for the destruction of the Fermi liquid coherence by strong longitudinal gauge fluctuations which represent the effects of the infinite-U constraint.
Interactions in Fermi systems can generate a Pomeranchuk instability leading to orientational symmetry breaking, that is, nematic order. In a metallic system close to such an instability the Fermi surface is easily deformed by anisotropic perturbations and exhibits enhanced collective fluctuations. We analyze fluctuation effects in the quantum critical regime near a d-wave Pomeranchuk instability in two dimensions. Density correlations with a d-wave form factor and the dynamical forward scattering interaction diverge near the instability. The singular forward scattering leads to large self-energy contributions, which destroy Fermi liquid behavior over the whole Fermi surface except at “cold spots” on the Brillouin zone diagonal. The decay rate of single-particle excitations, which is related to the width of the peaks in the spectral function, exceeds the excitation energy in the low-energy limit. The dispersion of the spectra flattens strongly near those portions of the Fermi surface which are remote from the zone diagonal. The decay rate for DC transport is linear in temperature except at the cold spots. We discuss the possible relevance of d-wave Fermi surface fluctuations for the “strange metal” behavior observed in the normal phase of cuprates.
The self-consistent theory of the fermion condensation, a specific phase transition which results in a rearrangement of the single particle degrees of freedom in strongly correlated Fermi systems is developed. Beyond the phase transition point, the single particle spectra are shown to be flat. The interplay between the flattening and the damping of the single particle spectra at T→0T\to 0T→0 is investigated. The width γ(ε)γ(ε)γ(ε) of the single particle states is found to grow up linearly with εεε over a wide range of energy as in a marginal Fermi liquid. Our results gain insight into the success of the phenomenological theory of the normal states of high-temperature superconductors by Varma et al.