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 the Physical Society of Japan

Pseudogap Phenomena in the BCS Pairing Model

Satoshi Fujimoto

Published May 15, 2002• 18 citations
Publisher

Abstract

We investigate pseudogap phenomena realized in the BCS pairing model with a long but finite interaction range. We calculate the single-particle self-energy in all orders exactly in the temperature range where the superconducting fluctuation propagator is Gaussian-like. It is found that vertex corrections to the self-energy, which are discarded in the previous studies, are crucially important for the pseudogap of the single-particle density of states in higher order calculations.

DOI
10.1143/jpsj.71.1230

Related papers

Superfluid density of states and pseudogap phenomenon in the BCS-BEC crossover regime of a superfluid Fermi gas

Ryota Watanabe, Shunji Tsuchiya, Yoji Ohashi

We investigate single-particle excitations and strong-coupling effects in the BCS-BEC crossover regime of a superfluid Fermi gas. Including phase and amplitude fluctuations of the superfluid order parameter within a $T$-matrix theory, we calculate the superfluid density of states (DOS), as well as single-particle spectral weight, over the entire BCS-BEC crossover region below the superfluid transition temperature ${T}_{\mathrm{c}}$. We clarify how the pseudogap in the normal state evolves into the superfluid gap, as one passes through ${T}_{\mathrm{c}}$. While the pseudogap in DOS continuously evolves into the superfluid gap in the weak-coupling BCS regime, the superfluid gap in the crossover region is shown to appear in DOS after the pseudogap disappears below ${T}_{\mathrm{c}}$. In the phase diagram with respect to the temperature and interaction strength, we determine the region where strong pairing fluctuations dominate over single-particle properties of the system. Our results would be useful for the study of strong-coupling phenomena in the BCS-BEC crossover regime of a superfluid Fermi gas.

arXiv:1007.3840•Physical Review A•Oct 28, 2010•54 citations

Interplay of the pseudogap and the BCS gap for heteropairs in 40 K- 6 Li mixture

P. Lipavský, Christophe Berthod

The description of heteropairs like 40 K- 6 Li near and in the superconducting state requires a fully self-consistent theory (see H anai R. and O hashi Y., Phys. Rev. A , 90 (2014) 043622). We derive analytic pseudogap Green's functions for the “normal” and superconducting states from the Luttinger-Ward theory with the T -matrix in the static separable approximation. The self-consistency in the closing loop of self-energy has two pronounced effects on the single-particle spectrum. First, the single-particle excitations decay before the asymptotic quasiparticle propagation is established, therefore the normal state is not a Fermi liquid. Second, the pseudogap has a V shape even for s -wave pairing. The V-shaped pseudogap and the U-shaped BCS gap interfere resulting in slope breaks of the gap walls and the in-gap states in the density of states. Various consequences of an incomplete self-consistency are demonstrated.

arXiv:1609.00240•Europhysics Letters (EPL)•Nov 1, 2016•0 citations

Dynamical Mean Field Theory of the Gutzwiller-projected BCS Hamiltonian: Phase Fluctuations and the Pseudogap

Kwon Park

One of the most prominent problems in high temperature superconductivity is the nature of the pseudogap phase in underdoped regimes; particularly important is the role of phase fluctuations. The Gutzwiller-projected BCS Hamiltonian is a useful model for high temperature superconductivity due to an exact mapping to the Heisenberg model at half filling and generally a very close connection to the t-J model at moderate doping. We develop the dynamical mean field theory for the d-wave BCS Hamiltonian with on-site repulsive interaction, $U$, physically imposing the partial Gutzwiller projection. For results, two pseudogap energy scales are identified: one associated with the bare pairing gap for the singlet formation and the other with the local phase coherence. The real superconducting gap determined from sharp coherence peaks in the density of states shows strong renormalization from the bare value due to $U$.

arXiv:cond-mat/0701588•Jan 24, 2007•0 citations

Superconductivity in the exactly solvable model of pseudogap state: The absence of self-averaging

É. Z. Kuchinskii, M. V. Sadovskii

The features of the superconducting state are studied in the simple exactly solvable model of the pseudogap state induced by fluctuations of the short-range “dielectric” order in the model of the Fermi surface with “hot” spots. The analysis is carried out for arbitrary short-range correlation lengths ξ corr . It is shown that the superconducting gap averaged over such fluctuations differs from zero in a wide temperature range above the temperature T c of the uniform superconducting transition in the entire sample, which is a consequence of non-self-averaging of the superconducting order parameter over the random fluctuation field. In the temperature range T > T c , superconductivity apparently exists in individual regions (drops). These effects become weaker with decreasing correlation length ξ corr ; in particular, the range of existence for drops becomes narrower and vanishes as ξ corr → 0, but for finite values of ξ corr , complete self-averaging does not take place.

arXiv:cond-mat/0110013•Journal of Experimental and Theoretical Physics•Mar 1, 2002•3 citations

Single-particle properties and pseudogap effects in the BCS-BEC crossover regime of an ultracold Fermi gas above Tc

Shunji Tsuchiya, Ryota Watanabe, Yoji Ohashi

We investigate strong-coupling effects on normal-state properties of an ultracold Fermi gas. Within the framework of $T$-matrix approximation in terms of pairing fluctuations, we calculate the single-particle density of states (DOS), as well as the spectral weight, over the entire BCS--Bose-Einstein condensate (BEC) crossover region above the superfluid phase-transition temperature ${T}_{\text{c}}$. Starting from the weak-coupling BCS regime, we show that the so-called pseudogap develops in DOS above ${T}_{\text{c}}$, which becomes remarkable in the crossover region. The pseudogap structure continuously changes into a fully gapped one in the strong-coupling BEC regime, where the gap energy is directly related to the binding energy of tightly bound molecules. We determine the pseudogap temperature ${T}^{\ensuremath{\ast}}$ where the dip structure in DOS vanishes. The value of ${T}^{\ensuremath{\ast}}$ is shown to be very different from another characteristic temperature ${T}^{\ensuremath{\ast}\ensuremath{\ast}}$ where a BCS-type double-peak structure disappears in the spectral weight. While one finds ${T}^{\ensuremath{\ast}}>{T}^{\ensuremath{\ast}\ensuremath{\ast}}$ in the BCS regime, ${T}^{\ensuremath{\ast}\ensuremath{\ast}}$ becomes higher than ${T}^{\ensuremath{\ast}}$ in the crossover region and BEC regime. Including this, we determine the pseudogap region in the phase diagram of ultracold Fermi gases. Our results would be useful in the search for the pseudogap region in ultracold $^{6}\text{L}\text{i}$ and $^{40}\text{K}$ Fermi gases.

arXiv:0907.4595•Physical Review A•Sep 16, 2009•140 citations

Rf spectra and pseudogap in ultracold Fermi gases across the BCS-BEC crossover from pairing fluctuation theory

Chuping Li, Lin Sun, Kaichao Zhang +5 more

The pseudogap phenomenon is a hallmark of strongly interacting Fermi systems, from high-temperature superconductors to ultracold atomic gases, yet its precise origin remains debated. Here we calculate the spectral function and rf spectra of ultracold atomic gases across the BCS-BEC crossover to quantitatively investigate the pairing mechanism of the pseudogap. We advance our pairing fluctuation theory by incorporating particle-hole fluctuations, which renormalize the effective interaction in the particle-particle channel. To achieve quantitative accuracy, we employ a full numerical convolution for the pair susceptibility and self-energy, moving beyond previous analytic pseudogap approximations. This convolution approach automatically captures two critical effects: (i) the full spectral broadening of fermions due to finite pair lifetime, and (ii) the previously neglected pair-hole scattering effect, which manifests as a substantial Hartree energy. We calculate the spectral function, and use rf spectral intensity maps and energy distribution curves to determine the quasiparticle dispersion. From these, we extract the pseudogap $Δ$, Hartree energy, and chemical potential, mapping their evolution across the crossover. Our results show that the pseudogap emerges continuously as the system moves from the BCS regime toward BEC. Furthermore, the pair spectral function reveals that pairs become diffusive at energies above 2$Δ$, indicating that the pair lifetime is governed by virtual binding and unbinding processes. Our calculations achieve quantitative agreement with recent experiments across the BCS-BEC crossover, including at unitarity, providing strong support for a pairing-based origin of the pseudogap as described by our pairing fluctuation theory.

arXiv:2604.06004•Apr 7, 2026•0 citations
We investigate pseudogap phenomena realized in the BCS pairing model with a long but finite interaction range. We calculate the single-particle self-energy in all orders exactly in the temperature range where the superconducting fluctuation propagator is Gaussian-like. It is found that vertex corrections to the self-energy, which are discarded in the previous studies, are crucially important for the pseudogap of the single-particle density of states in higher order calculations.
We investigate single-particle excitations and strong-coupling effects in the BCS-BEC crossover regime of a superfluid Fermi gas. Including phase and amplitude fluctuations of the superfluid order parameter within a TTT-matrix theory, we calculate the superfluid density of states (DOS), as well as single-particle spectral weight, over the entire BCS-BEC crossover region below the superfluid transition temperature Tc{T}_{\mathrm{c}}Tc​. We clarify how the pseudogap in the normal state evolves into the superfluid gap, as one passes through Tc{T}_{\mathrm{c}}Tc​. While the pseudogap in DOS continuously evolves into the superfluid gap in the weak-coupling BCS regime, the superfluid gap in the crossover region is shown to appear in DOS after the pseudogap disappears below Tc{T}_{\mathrm{c}}Tc​. In the phase diagram with respect to the temperature and interaction strength, we determine the region where strong pairing fluctuations dominate over single-particle properties of the system. Our results would be useful for the study of strong-coupling phenomena in the BCS-BEC crossover regime of a superfluid Fermi gas.
The description of heteropairs like 40 K- 6 Li near and in the superconducting state requires a fully self-consistent theory (see H anai R. and O hashi Y., Phys. Rev. A , 90 (2014) 043622). We derive analytic pseudogap Green's functions for the “normal” and superconducting states from the Luttinger-Ward theory with the T -matrix in the static separable approximation. The self-consistency in the closing loop of self-energy has two pronounced effects on the single-particle spectrum. First, the single-particle excitations decay before the asymptotic quasiparticle propagation is established, therefore the normal state is not a Fermi liquid. Second, the pseudogap has a V shape even for s -wave pairing. The V-shaped pseudogap and the U-shaped BCS gap interfere resulting in slope breaks of the gap walls and the in-gap states in the density of states. Various consequences of an incomplete self-consistency are demonstrated.
One of the most prominent problems in high temperature superconductivity is the nature of the pseudogap phase in underdoped regimes; particularly important is the role of phase fluctuations. The Gutzwiller-projected BCS Hamiltonian is a useful model for high temperature superconductivity due to an exact mapping to the Heisenberg model at half filling and generally a very close connection to the t-J model at moderate doping. We develop the dynamical mean field theory for the d-wave BCS Hamiltonian with on-site repulsive interaction, UUU, physically imposing the partial Gutzwiller projection. For results, two pseudogap energy scales are identified: one associated with the bare pairing gap for the singlet formation and the other with the local phase coherence. The real superconducting gap determined from sharp coherence peaks in the density of states shows strong renormalization from the bare value due to UUU.
The features of the superconducting state are studied in the simple exactly solvable model of the pseudogap state induced by fluctuations of the short-range “dielectric” order in the model of the Fermi surface with “hot” spots. The analysis is carried out for arbitrary short-range correlation lengths ξ corr . It is shown that the superconducting gap averaged over such fluctuations differs from zero in a wide temperature range above the temperature T c of the uniform superconducting transition in the entire sample, which is a consequence of non-self-averaging of the superconducting order parameter over the random fluctuation field. In the temperature range T > T c , superconductivity apparently exists in individual regions (drops). These effects become weaker with decreasing correlation length ξ corr ; in particular, the range of existence for drops becomes narrower and vanishes as ξ corr → 0, but for finite values of ξ corr , complete self-averaging does not take place.
We investigate strong-coupling effects on normal-state properties of an ultracold Fermi gas. Within the framework of TTT-matrix approximation in terms of pairing fluctuations, we calculate the single-particle density of states (DOS), as well as the spectral weight, over the entire BCS--Bose-Einstein condensate (BEC) crossover region above the superfluid phase-transition temperature Tc{T}_{\text{c}}Tc​. Starting from the weak-coupling BCS regime, we show that the so-called pseudogap develops in DOS above Tc{T}_{\text{c}}Tc​, which becomes remarkable in the crossover region. The pseudogap structure continuously changes into a fully gapped one in the strong-coupling BEC regime, where the gap energy is directly related to the binding energy of tightly bound molecules. We determine the pseudogap temperature ${T}^{\ensuremath{\ast}}$ where the dip structure in DOS vanishes. The value of ${T}^{\ensuremath{\ast}}$ is shown to be very different from another characteristic temperature ${T}^{\ensuremath{\ast}\ensuremath{\ast}}$ where a BCS-type double-peak structure disappears in the spectral weight. While one finds ${T}^{\ensuremath{\ast}}>{T}^{\ensuremath{\ast}\ensuremath{\ast}}$ in the BCS regime, ${T}^{\ensuremath{\ast}\ensuremath{\ast}}$ becomes higher than ${T}^{\ensuremath{\ast}}$ in the crossover region and BEC regime. Including this, we determine the pseudogap region in the phase diagram of ultracold Fermi gases. Our results would be useful in the search for the pseudogap region in ultracold 6Li^{6}\text{L}\text{i}6Li and 40K^{40}\text{K}40K Fermi gases.
The pseudogap phenomenon is a hallmark of strongly interacting Fermi systems, from high-temperature superconductors to ultracold atomic gases, yet its precise origin remains debated. Here we calculate the spectral function and rf spectra of ultracold atomic gases across the BCS-BEC crossover to quantitatively investigate the pairing mechanism of the pseudogap. We advance our pairing fluctuation theory by incorporating particle-hole fluctuations, which renormalize the effective interaction in the particle-particle channel. To achieve quantitative accuracy, we employ a full numerical convolution for the pair susceptibility and self-energy, moving beyond previous analytic pseudogap approximations. This convolution approach automatically captures two critical effects: (i) the full spectral broadening of fermions due to finite pair lifetime, and (ii) the previously neglected pair-hole scattering effect, which manifests as a substantial Hartree energy. We calculate the spectral function, and use rf spectral intensity maps and energy distribution curves to determine the quasiparticle dispersion. From these, we extract the pseudogap ΔΔΔ, Hartree energy, and chemical potential, mapping their evolution across the crossover. Our results show that the pseudogap emerges continuously as the system moves from the BCS regime toward BEC. Furthermore, the pair spectral function reveals that pairs become diffusive at energies above 2ΔΔΔ, indicating that the pair lifetime is governed by virtual binding and unbinding processes. Our calculations achieve quantitative agreement with recent experiments across the BCS-BEC crossover, including at unitarity, providing strong support for a pairing-based origin of the pseudogap as described by our pairing fluctuation theory.