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

arXiv:cond-mat/0212332 · Physical review. B, Condensed matter

From phase- to amplitude-fluctuation-driven superconductivity in systems with precursor pairing

J. Ranninger, L. Tripodi

Published May 27, 2003• 12 citations
arXivHTMLPDF

Abstract

The change-over from phase- to amplitude-fluctuation-driven superconductivity is examined for a composite system of free electrons (fermions with concentration ${n}_{F})$ and localized electron pairs (hard-core bosons with concentration ${n}_{B})$ as a function of doping---changing the total concentration of charge carriers ${(n}_{\mathrm{tot}}{=n}_{F}{+2n}_{B}).$ The coupling together of these two subsystems via a charge exchange term induces electron pairing and ultimately superconductivity in the fermionic subsystem. The difference in statistics of the two species of charge carriers has important consequences on the doping mechanism, showing an onset temperature ${T}^{*}$ of incoherent electron pairing in the fermionic subsystem (manifest in form of a pseudogap), which steadily decreases with decreasing ${n}_{\mathrm{tot}}.$ Below ${T}^{*}$ this electron pairing leads, in the normal phase, to electron-pair resonant states (Cooperons) with quasiparticle features which strongly depend on ${n}_{\mathrm{tot}}.$ For high concentrations, where ${n}_{B}\ensuremath{\simeq}0.5,$ correlation effects between the hard-core bosons lead to itinerant Cooperons having a heavy mass ${m}_{p},$ but are long lived. Upon reducing the concentration of charge carriers and consequently ${n}_{B},$ the mass as well as the lifetime of those Cooperons is considerably reduced. As a result, for high values of ${n}_{B},$ a superconducting state below ${T}^{*}$ sets in at a ${T}_{c},$ being controlled by the phase stiffness ${D}_{\ensuremath{\varphi}}={\ensuremath{\Elzxh}}^{2}{n}_{p}{/m}_{p}$ of those Cooperons, where ${n}_{p}$ denotes their density. Upon reducing ${n}_{\mathrm{tot}},$ the phase stiffness steadily increases, and eventually exceeds the pairing energy ${k}_{B}{T}^{*}.$ There, the Cooperons loose their well defined itinerant quasi-particle features and superconductivity gets controlled by amplitude fluctuations. The resulting phase diagram with doping is reminiscent of that of the phase fluctuation scenario for high-${T}_{c}$ superconductivity, except that in our scenario the determinant factors are the mass and the lifetime of the Cooperons rather than their density.

DOI
10.1103/physrevb.67.174521

Related papers

Boson-fermion model: An exact diagonalization study

Mario Cuoco, Canio Noce, J. Ranninger +1 more

The main features of a generic boson-fermion scenario for electron pairing in a many-body correlated fermionic system are (i) a crossover from a poor metal to an insulator and finally a superconductor as the temperature decreases; (ii) the buildup of a finite amplitude of local electron pairing below a certain temperature ${T}^{*},$ followed by the onset of long-range phase correlations among electron pairs below a second characteristic temperature ${T}_{\ensuremath{\varphi}};$ and (iii) the opening of a pseudogap in the density of states of the electrons below ${T}^{*},$ rendering these electrons poorer and poorer quasi-particles as the temperature decreases, with the electron transport becoming ensured by electron pairs rather than by individual electrons. A number of these features have been obtained so far on the basis of different many-body techniques, all of which have their built-in shortcomings in the intermediate coupling regime, which is of interest here. In order to substantiate these features, we investigate them on the basis of an exact diagonalization study on rings up to eight sites. Particular emphasis has been put on the possibility of having persistent currents in mesoscopic rings tracking the change-over from single- to two-particle transport as the temperature decreases and the superconducting state is approached.

arXiv:cond-mat/0305075•Physical review. B, Condensed matter•Jun 12, 2003•15 citations

From an insulating to a superfluid pair-bond liquid

Mario Cuoco, J. Ranninger

We study an exchange coupled system of itinerant electrons and localized fermion pairs resulting in a resonant pairing formation. This system inherently contains resonating fermion pairs on bonds that lead to a superconducting phase, provided that long-range phase coherence between their constituents can be established. The prerequisite is that the resonating fermion pairs can become itinerant. This is rendered possible through the emergence of two kinds of bond fermions: individual and composite fermions made of one individual electron attached to a bound pair on a bond. If the strength of the exchange coupling exceeds a certain value, then the superconducting ground state undergoes a quantum phase transition into an insulating pair-bond liquid state. The gap of the superfluid phase thereby goes over continuously into a charge gap of the insulator. The changeover from the superconducting to the insulating phase is accompanied by a corresponding qualitative modification of the dispersion of the two kinds of fermionic excitations. Using a bond operator formalism, we derive the phase diagram of such a scenario together with the elementary excitations characterizing the various phases as a function of the exchange coupling and the temperature.

arXiv:cond-mat/0610578•Physical Review B•Sep 20, 2006•14 citations

On the Superconductivity in the Induced Pairing Model

R. Micnas, S. Robaszkiewicz, Annette Bussmann‐Holder

The two component model of coexisting local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems, is discussed. The cases of isotropic s-wave and anisotropic pairing of extended s and d x 2 −y 2-wave symmetries are analyzed for a 2D square lattice within the BCS-mean field approximation and the Kosterlitz-Thouless theory. We determined the phase diagrams and superconducting characteristics as a function of the position of the local pair (LP) level and the total electron concentration. The model exhibits several types of interesting crossovers from BCS like behavior to that of LP’s. Some of our results are discussed in connection with a two-component scenario of preformed pairs and unpaired electrons for exotic superconductors. Key words: Boson-Fermion model, Phase fluctuations A system of interacting charged bosons (bound electron pairs) and electrons can show features which are intermediate between those of local pair superconductors and those of classical BCS systems. Such a two component (bosonfermion) model is of relevance for high temperature superconductors (HTS) and other exotic superconductors [1,2,3,4,5,6,7,8,9,10]. Recently, we have studied a generalization of this model to the case of anisotropic pairing [9,10]. Here, we shortly outline the study and present further results concerning the phase diagrams and superconducting properties of such a system in the case of isotropic s-wave pairing as well as for anisotropic pairings of d- and extended s-wave symmetries, for a 2D square lattice.

•Jan 1, 2002•17 citations

Interplay between single-particle and collective features in the boson fermion model

T. Domański, J. Ranninger

We study the interplay between the single-particle and fermion-pair features in the boson fermion model, both above and below the transition temperature ${T}_{c}$, using the flow equation method. Upon lowering the temperature the single-particle fermionic spectral function (a) gradually develops a depletion of the low-energy states (pseudogap) for $T*>T>{T}_{c}$ and a true superconducting gap for $T<{T}_{c}$ and (b) exhibits a considerable transfer of spectral weight between the incoherent background and the narrow coherent peak(s) signifying long-lived quasiparticle features. The Cooperon spectral function consists of a $\ensuremath{\delta}$-function peak, centered at the renormalized boson energy $\ensuremath{\omega}={\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{E}}_{\mathbf{q}}$ and a surrounding incoherent background which is spread over a wide energy range. When the temperature approaches ${T}_{c}$ from above, this peak for $\mathbf{q}=\mathbf{0}$ moves to $\ensuremath{\omega}=0$, so that the static pair susceptibility diverges (Thouless criterion for the broken symmetry phase transition). Upon decreasing the temperature below ${T}_{c}$ the Cooperon peak becomes the collective (Goldstone) mode ${E}_{\mathbf{q}}\ensuremath{\propto}\ensuremath{\mid}\mathbf{q}\ensuremath{\mid}$ in the small-momentum region and simultaneously splits off from the incoherent background states which are expelled to the high-energy sector $\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}\ensuremath{\geqslant}2{\ensuremath{\Delta}}_{sc}(T)$. We discuss the smooth evolution of these features upon approaching ${T}_{c}$ from above and consider its feedback on the single-particle spectrum where a gradual formation of damped Bogoliubov modes (above ${T}_{c}$) is observed.

arXiv:cond-mat/0406022•Physical Review B•Nov 9, 2004•21 citations

COMPETING LOCAL AND NON-LOCAL PHASE CORRELATIONS IN FERMIONIC SYSTEMS WITH RESONANT PAIRING: THE BOSON–FERMION SCENARIO

J. Ranninger

We consider systems where the amplitude and the phase of a superfluid order parameter are controlled independently by local, respectively non-local phase correlations of the internal degrees of freedom of quasi-particles which characterize the different phases of such fermionic systems. A possible realization of such a situation is when pairing into the bosonic entities occurs via resonant scattering of itinerant fermionic particles. Examples for that are the ultracold fermionic gases in optical traps and lattices, the correlated electronic systems and strongly coupled electron-phonon systems, such as seen in the high Tc cuprates. We demonstrate the occurrence of a quantum phase transition from a superfluid to a phase uncorrelated boson liquid state in such systems, which is controlled by the competing effects of long and short range phase correlations of the constituents of composite quasi-particles.

International Journal of Modern Physics B•May 30, 2007•0 citations

Superconductivity in high- Tc and related strongly correlated systems from variational perspective: Beyond mean field theory

Józef Spałek, Maciej Fidrysiak, M. Zegrodnik +1 more

The principal purpose of this topical review is to single out some of the universal features of high-temperature (high-Tc) and related strongly-correlated systems, which can be compared with experiment in a quantitative manner. The description starts with the concept of exchange-interaction-mediated (real-space) pairing, combined with strong correlations among narrow band electrons, for which the reference state is that of the Mott–Hubbard insulator. The physical discussion of concrete properties relies on variational approach, starting from generalized renormalized mean-field theory (RMFT) in the form of statistically-consistent Gutzwiller approximation (SGA), and its subsequent generalization, i.e., a systematic Diagrammatic Expansion of the Variational (Gutzwiller-type) Wave Function (DE-GWF). The solution leads to the two energy scales, one involving unconventional quasiparticles close to the Fermi energy, and the other reflecting the fully correlated state, involving electrons deeper below the Fermi surface. Those two regimes are separated by a kink in the dispersion relation, which is observed in photoemission. As a result, one obtains both the doping dependent properties in the correlated state, and effective renormalized quasiparticles. The reviewed ground-state characteristics for high-Tc systems encompass high-Tc superconductivity, nematicity, charge- (and pair-) density-wave effects, as well as non-BCS kinetic energy gain in the paired state. The calculated dynamic properties are: the universal Fermi velocity, the Fermi wave-vector, the effective mass enhancement, the pseudogap; and the d-wave gap magnitude. We discuss that, within the variational approach, the minimal realistic model is represented by the so-called t-J-U Hamiltonian. Inadequacy of the t-J and Hubbard models, particularly of their RMFT versions, is discussed explicitly. For heavy fermion systems, modeled by the Anderson lattice model and with the DE-GWF approach, we discuss the phase diagram, encompassing superconducting, Kondo insulating, ferro- and anti-ferromagnetic states. The superconducting state is then a two-d-wave gap system. If the orbital degeneracy of f-electrons is included, the coexistent ferromagnetic- (spin–triplet) superconducting phases appear and match those observed for UGe2 in a semiquantitative manner. Finally, in the second part, we generalize our approach to the collective spin and charge fluctuations in high-Tc systems, starting from variational approach, defining the saddle-point state, and combining it with 1/N expansion. The present scheme differs essentially from that starting from the saddle-point Hartree–Fock approximation, and incorporating the fluctuations in the random phase approximation (RPA). The spectrum of collective spin and charge excitations is determined for the Hubbard and t-J-U models, and subsequently compared quantitatively with recent experiments. The Appendices provide formal details to make this review self-contained.

arXiv:2202.05113•Physics Reports•Mar 17, 2022•46 citations
The change-over from phase- to amplitude-fluctuation-driven superconductivity is examined for a composite system of free electrons (fermions with concentration nF){n}_{F})nF​) and localized electron pairs (hard-core bosons with concentration nB){n}_{B})nB​) as a function of doping---changing the total concentration of charge carriers (ntot=nF+2nB).{(n}_{\mathrm{tot}}{=n}_{F}{+2n}_{B}).(ntot​=nF​+2nB​). The coupling together of these two subsystems via a charge exchange term induces electron pairing and ultimately superconductivity in the fermionic subsystem. The difference in statistics of the two species of charge carriers has important consequences on the doping mechanism, showing an onset temperature T∗{T}^{*}T∗ of incoherent electron pairing in the fermionic subsystem (manifest in form of a pseudogap), which steadily decreases with decreasing ntot.{n}_{\mathrm{tot}}.ntot​. Below T∗{T}^{*}T∗ this electron pairing leads, in the normal phase, to electron-pair resonant states (Cooperons) with quasiparticle features which strongly depend on ntot.{n}_{\mathrm{tot}}.ntot​. For high concentrations, where nB\ensuremath≃0.5,{n}_{B}\ensuremath{\simeq}0.5,nB​\ensuremath≃0.5, correlation effects between the hard-core bosons lead to itinerant Cooperons having a heavy mass mp,{m}_{p},mp​, but are long lived. Upon reducing the concentration of charge carriers and consequently nB,{n}_{B},nB​, the mass as well as the lifetime of those Cooperons is considerably reduced. As a result, for high values of nB,{n}_{B},nB​, a superconducting state below T∗{T}^{*}T∗ sets in at a Tc,{T}_{c},Tc​, being controlled by the phase stiffness D\ensuremathφ=\ensuremath\Elzxh2np/mp{D}_{\ensuremath{\varphi}}={\ensuremath{\Elzxh}}^{2}{n}_{p}{/m}_{p}D\ensuremathφ​=\ensuremath\Elzxh2np​/mp​ of those Cooperons, where np{n}_{p}np​ denotes their density. Upon reducing ntot,{n}_{\mathrm{tot}},ntot​, the phase stiffness steadily increases, and eventually exceeds the pairing energy kBT∗.{k}_{B}{T}^{*}.kB​T∗. There, the Cooperons loose their well defined itinerant quasi-particle features and superconductivity gets controlled by amplitude fluctuations. The resulting phase diagram with doping is reminiscent of that of the phase fluctuation scenario for high-Tc{T}_{c}Tc​ superconductivity, except that in our scenario the determinant factors are the mass and the lifetime of the Cooperons rather than their density.
The main features of a generic boson-fermion scenario for electron pairing in a many-body correlated fermionic system are (i) a crossover from a poor metal to an insulator and finally a superconductor as the temperature decreases; (ii) the buildup of a finite amplitude of local electron pairing below a certain temperature T∗,{T}^{*},T∗, followed by the onset of long-range phase correlations among electron pairs below a second characteristic temperature ${T}_{\ensuremath{\varphi}};$ and (iii) the opening of a pseudogap in the density of states of the electrons below T∗,{T}^{*},T∗, rendering these electrons poorer and poorer quasi-particles as the temperature decreases, with the electron transport becoming ensured by electron pairs rather than by individual electrons. A number of these features have been obtained so far on the basis of different many-body techniques, all of which have their built-in shortcomings in the intermediate coupling regime, which is of interest here. In order to substantiate these features, we investigate them on the basis of an exact diagonalization study on rings up to eight sites. Particular emphasis has been put on the possibility of having persistent currents in mesoscopic rings tracking the change-over from single- to two-particle transport as the temperature decreases and the superconducting state is approached.
We study an exchange coupled system of itinerant electrons and localized fermion pairs resulting in a resonant pairing formation. This system inherently contains resonating fermion pairs on bonds that lead to a superconducting phase, provided that long-range phase coherence between their constituents can be established. The prerequisite is that the resonating fermion pairs can become itinerant. This is rendered possible through the emergence of two kinds of bond fermions: individual and composite fermions made of one individual electron attached to a bound pair on a bond. If the strength of the exchange coupling exceeds a certain value, then the superconducting ground state undergoes a quantum phase transition into an insulating pair-bond liquid state. The gap of the superfluid phase thereby goes over continuously into a charge gap of the insulator. The changeover from the superconducting to the insulating phase is accompanied by a corresponding qualitative modification of the dispersion of the two kinds of fermionic excitations. Using a bond operator formalism, we derive the phase diagram of such a scenario together with the elementary excitations characterizing the various phases as a function of the exchange coupling and the temperature.
The two component model of coexisting local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems, is discussed. The cases of isotropic s-wave and anisotropic pairing of extended s and d x 2 −y 2-wave symmetries are analyzed for a 2D square lattice within the BCS-mean field approximation and the Kosterlitz-Thouless theory. We determined the phase diagrams and superconducting characteristics as a function of the position of the local pair (LP) level and the total electron concentration. The model exhibits several types of interesting crossovers from BCS like behavior to that of LP’s. Some of our results are discussed in connection with a two-component scenario of preformed pairs and unpaired electrons for exotic superconductors. Key words: Boson-Fermion model, Phase fluctuations A system of interacting charged bosons (bound electron pairs) and electrons can show features which are intermediate between those of local pair superconductors and those of classical BCS systems. Such a two component (bosonfermion) model is of relevance for high temperature superconductors (HTS) and other exotic superconductors [1,2,3,4,5,6,7,8,9,10]. Recently, we have studied a generalization of this model to the case of anisotropic pairing [9,10]. Here, we shortly outline the study and present further results concerning the phase diagrams and superconducting properties of such a system in the case of isotropic s-wave pairing as well as for anisotropic pairings of d- and extended s-wave symmetries, for a 2D square lattice.
We study the interplay between the single-particle and fermion-pair features in the boson fermion model, both above and below the transition temperature Tc{T}_{c}Tc​, using the flow equation method. Upon lowering the temperature the single-particle fermionic spectral function (a) gradually develops a depletion of the low-energy states (pseudogap) for T∗>T>TcT*>T>{T}_{c}T∗>T>Tc​ and a true superconducting gap for T<TcT<{T}_{c}T<Tc​ and (b) exhibits a considerable transfer of spectral weight between the incoherent background and the narrow coherent peak(s) signifying long-lived quasiparticle features. The Cooperon spectral function consists of a $\ensuremath{\delta}$-function peak, centered at the renormalized boson energy $\ensuremath{\omega}={\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{E}}_{\mathbf{q}}$ and a surrounding incoherent background which is spread over a wide energy range. When the temperature approaches Tc{T}_{c}Tc​ from above, this peak for q=0\mathbf{q}=\mathbf{0}q=0 moves to $\ensuremath{\omega}=0$, so that the static pair susceptibility diverges (Thouless criterion for the broken symmetry phase transition). Upon decreasing the temperature below Tc{T}_{c}Tc​ the Cooperon peak becomes the collective (Goldstone) mode ${E}_{\mathbf{q}}\ensuremath{\propto}\ensuremath{\mid}\mathbf{q}\ensuremath{\mid}$ in the small-momentum region and simultaneously splits off from the incoherent background states which are expelled to the high-energy sector $\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}\ensuremath{\geqslant}2{\ensuremath{\Delta}}_{sc}(T)$. We discuss the smooth evolution of these features upon approaching Tc{T}_{c}Tc​ from above and consider its feedback on the single-particle spectrum where a gradual formation of damped Bogoliubov modes (above Tc{T}_{c}Tc​) is observed.
We consider systems where the amplitude and the phase of a superfluid order parameter are controlled independently by local, respectively non-local phase correlations of the internal degrees of freedom of quasi-particles which characterize the different phases of such fermionic systems. A possible realization of such a situation is when pairing into the bosonic entities occurs via resonant scattering of itinerant fermionic particles. Examples for that are the ultracold fermionic gases in optical traps and lattices, the correlated electronic systems and strongly coupled electron-phonon systems, such as seen in the high Tc cuprates. We demonstrate the occurrence of a quantum phase transition from a superfluid to a phase uncorrelated boson liquid state in such systems, which is controlled by the competing effects of long and short range phase correlations of the constituents of composite quasi-particles.
The principal purpose of this topical review is to single out some of the universal features of high-temperature (high-Tc) and related strongly-correlated systems, which can be compared with experiment in a quantitative manner. The description starts with the concept of exchange-interaction-mediated (real-space) pairing, combined with strong correlations among narrow band electrons, for which the reference state is that of the Mott–Hubbard insulator. The physical discussion of concrete properties relies on variational approach, starting from generalized renormalized mean-field theory (RMFT) in the form of statistically-consistent Gutzwiller approximation (SGA), and its subsequent generalization, i.e., a systematic Diagrammatic Expansion of the Variational (Gutzwiller-type) Wave Function (DE-GWF). The solution leads to the two energy scales, one involving unconventional quasiparticles close to the Fermi energy, and the other reflecting the fully correlated state, involving electrons deeper below the Fermi surface. Those two regimes are separated by a kink in the dispersion relation, which is observed in photoemission. As a result, one obtains both the doping dependent properties in the correlated state, and effective renormalized quasiparticles. The reviewed ground-state characteristics for high-Tc systems encompass high-Tc superconductivity, nematicity, charge- (and pair-) density-wave effects, as well as non-BCS kinetic energy gain in the paired state. The calculated dynamic properties are: the universal Fermi velocity, the Fermi wave-vector, the effective mass enhancement, the pseudogap; and the d-wave gap magnitude. We discuss that, within the variational approach, the minimal realistic model is represented by the so-called t-J-U Hamiltonian. Inadequacy of the t-J and Hubbard models, particularly of their RMFT versions, is discussed explicitly. For heavy fermion systems, modeled by the Anderson lattice model and with the DE-GWF approach, we discuss the phase diagram, encompassing superconducting, Kondo insulating, ferro- and anti-ferromagnetic states. The superconducting state is then a two-d-wave gap system. If the orbital degeneracy of f-electrons is included, the coexistent ferromagnetic- (spin–triplet) superconducting phases appear and match those observed for UGe2 in a semiquantitative manner. Finally, in the second part, we generalize our approach to the collective spin and charge fluctuations in high-Tc systems, starting from variational approach, defining the saddle-point state, and combining it with 1/N expansion. The present scheme differs essentially from that starting from the saddle-point Hartree–Fock approximation, and incorporating the fluctuations in the random phase approximation (RPA). The spectrum of collective spin and charge excitations is determined for the Hubbard and t-J-U models, and subsequently compared quantitatively with recent experiments. The Appendices provide formal details to make this review self-contained.