171 research outputs found
Gap equation with pairing correlations beyond mean field and its equivalence to a Hugenholtz-Pines condition for fermion pairs
The equation for the gap parameter represents the main equation of the
pairing theory of superconductivity. Although it is formally defined through a
single-particle property, physically it reflects the pairing correlations
between opposite-spin fermions. Here, we exploit this physical connection and
cast the gap equation in an alternative form which explicitly highlights these
two-particle correlations, by showing that it is equivalent to a
Hugenholtz-Pines condition for fermion pairs. At a formal level, a direct
connection is established in this way between the treatment of the condensate
fraction in condensate systems of fermions and bosons. At a practical level,
the use of this alternative form of the gap equation is expected to make easier
the inclusion of pairing fluctuations beyond mean field. As a proof-of-concept
of the new method, we apply the modified form of the gap equation to the
long-pending problem about the inclusion of the Gorkov-Melik-Barkhudarov
correction across the whole BCS-BEC crossover, from the BCS limit of strongly
overlapping Cooper pairs to the BEC limit of dilute composite bosons, and for
all temperatures in the superfluid phase. Our numerical calculations yield
excellent agreement with the recently determined experimental values of the gap
parameter for an ultra-cold Fermi gas in the intermediate regime between BCS
and BEC, as well as with the available quantum Monte Carlo data in the same
regime.Comment: 24 pages, 13 figure
Entanglement between pairing and screening in the Gorkov-Melik-Barkhudarov correction to the critical temperature throughout the BCS-BEC crossover
The theoretical description of the critical temperature Tc of a Fermi
superfluid dates back to the work by Gor'kov and Melik-Barkhudarov (GMB), who
addressed it for a weakly-coupled (dilute) superfluid in the BCS
(weak-coupling) limit of the BCS-BEC crossover. The point made by GMB was that
particle-particle (pairing) excitations, which are responsible for
superfluidity to occur below Tc, and particle-hole excitations, which give rise
to screening also in a normal system, get effectively disentangled from each
other in the BCS limit, thus yielding a reduction by a factor 2.2 of the value
of Tc obtained when neglecting screening effects. Subsequent work on this
topic, aimed at extending the original GMB argument away from the BCS limit
with diagrammatic methods, has kept this disentangling between pairing and
screening throughout the BCS-BEC crossover, without realising that the
conditions for it to be valid are soon violated away from the BCS limit. Here,
we reconsider this problem from a more general perspective and argue that
pairing and screening are intrinsically entangled with each other along the
whole BCS-BEC crossover but for the BCS limit considered by GMB. We perform a
detailed numerical calculation of the GMB diagrammatic contribution extended to
the whole BCS-BEC crossover, where the full wave-vector and frequency
dependence occurring in the repeated in-medium two-particle scattering is duly
taken into account. Our numerical calculations are tested against analytic
results available in both the BCS and BEC limits, and the contribution of the
GMB diagrammatic term to the scattering length of composite bosons in the BEC
limit is highlighted. We calculate Tc throughout the BCS-BEC crossover and find
that it agrees quite well with Quantum Monte Carlo calculations and
experimental data available in the unitarity regime.Comment: 21 pages, 11 figure
Pairing fluctuation effects on the single-particle spectra for the superconducting state
Single-particle spectra are calculated in the superconducting state for a
fermionic system with an attractive interaction, as functions of temperature
and coupling strength from weak to strong. The fermionic system is described by
a single-particle self-energy that includes pairing-fluctuation effects in the
superconducting state. The theory reduces to the ordinary BCS approximation in
weak coupling and to the Bogoliubov approximation for the composite bosons in
strong coupling. Several features of the single-particle spectral function are
shown to compare favorably with experimental data for cuprate superconductors.Comment: 4 pages, 4 figure
BCS-BEC crossover at finite temperature in the broken-symmetry phase
The BCS-BEC crossover is studied in a systematic way in the broken-symmetry
phase between zero temperature and the critical temperature. This study bridges
two regimes where quantum and thermal fluctuations are, respectively,
important. The theory is implemented on physical grounds, by adopting a
fermionic self-energy in the broken-symmetry phase that represents fermions
coupled to superconducting fluctuations in weak coupling and to bosons
described by the Bogoliubov theory in strong coupling. This extension of the
theory beyond mean field proves important at finite temperature, to connect
with the results in the normal phase. The order parameter, the chemical
potential, and the single-particle spectral function are calculated numerically
for a wide range of coupling and temperature. This enables us to assess the
quantitative importance of superconducting fluctuations in the broken-symmetry
phase over the whole BCS-BEC crossover. Our results are relevant to the
possible realizations of this crossover with high-temperature cuprate
superconductors and with ultracold fermionic atoms in a trap.Comment: 21 pages, 15 figure
Spatial emergence of off-diagonal long-range order throughout the BCS-BEC crossover
In a superfluid system, off-diagonal long-range order is expected to be exhibited in the appropriate reduced
density matrices when the relevant particles (either bosons or fermion pairs) are considered to recede sufficiently
far apart from each other. This concept is usually exploited to identify the value of the condensate density,
without explicit concern, however, as to the spatial range over which this asymptotic condition can effectively be
achieved. Here, based on a diagrammatic approach that includes beyond-mean-field pairing fluctuations in the
broken-symmetry phase at the level of the t-matrix also with the inclusion of the Gorkov-Melik-Barkhudarov
(GMB) correction, we present a systematic study of the two-particle reduced density matrix for a superfluid
fermionic system undergoing the BCS-BEC crossover, when the entities to recede far apart from each other
evolve with continuity from largely overlapping Cooper pairs in the BCS limit to dilute composite bosons in the
BEC limit. By this approach, we not only provide the coupling and temperature dependence of the condensate
density at the level of our diagrammatic approach, which includes the GMB correction, but we also obtain
the evolution of the spatial dependence of the two-particle reduced density matrix, from a power law at low
temperature to an exponential dependence at high temperature in the superfluid phase, when the interparticle
coupling spans the BCS-BEC crossover. Our results put limitations on the minimum spatial extent of a finite-size
system for which superfluid correlations can effectively be established
Competition between final-state and pairing-gap effects in the radio-frequency spectra of ultracold Fermi atoms
The radio-frequency spectra of ultracold Fermi atoms are calculated by
including final-state interactions affecting the excited level of the
transition, and compared with the experimental data. A competition is revealed
between pairing-gap effects which tend to push the oscillator strength toward
high frequencies away from threshold, and final-state effects which tend
instead to pull the oscillator strength toward threshold. As a result of this
competition, the position of the peak of the spectra cannot be simply related
to the value of the pairing gap, whose extraction thus requires support from
theoretical calculations.Comment: 4 pages, 3 figures, final version published in Phys. Rev. Let
Critical current throughout the BCS-BEC crossover with the inclusion of pairing fluctuations
The present work aims at providing a systematic analysis of the current density versus momentum characteristics for a fermionic superfluid throughout the BCS-BEC crossover, even in the fully homogeneous case. At low
temperatures, where pairing fluctuations are not strong enough to invalidate a quasiparticle approach, a sharp
threshold for the inception of a back-flow current is found, which sets the onset of dissipation and identifies the
critical momentum according to Landau. This momentum is seen to smoothly evolve from the BCS to the BEC
regimes, whereby a single expression for the single-particle current density that includes pairing fluctuations
enables us to incorporate on equal footing two quite distinct dissipative mechanisms, namely, pair breaking
and phonon excitations in the two sides of the BCS-BEC crossover, respectively. At finite temperature, where
thermal fluctuations broaden the excitation spectrum and make the dissipative (kinetic and thermal) mechanisms
intertwined with each other, an alternative criterion due to Bardeen is instead employed to signal the loss of
superfluid behavior. In this way, detailed comparison with available experimental data in linear and annular
geometries is significantly improved with respect to previous approaches, thereby demonstrating the crucial role
played by quantum fluctuations in renormalizing the single-particle excitation spectrum
Magnetic Field Effect on the Pseudogap Temperature within Precursor Superconductivity
We determine the magnetic field dependence of the pseudogap closing
temperature T* within a precursor superconductivity scenario. Detailed
calculations with an anisotropic attractive Hubbard model account for a
recently determined experimental relation in BSCCO between the pseudogap
closing field and the pseudogap temperature at zero field, as well as for the
weak initial dependence of T* at low fields. Our results indicate that the
available experimental data are fully compatible with a superconducting origin
of the pseudogap in cuprate superconductors.Comment: 4 pages, 3 figure
Comparison between a diagrammatic theory for the BCS-BEC crossover and Quantum Monte Carlo results
Predictions for the chemical potential and the excitation gap recently
obtained by our diagrammatic theory for the BCS-BEC crossover in the superfluid
phase are compared with novel Quantum Monte Carlo results at zero temperature
now available in the literature. A remarkable agreement is found between the
results obtained by the two approachesComment: 3 pages, 2 figure
BCS-BEC crossover at finite temperature for superfluid trapped Fermi atoms
We consider the BCS-BEC crossover for a system of trapped Fermi atoms at
finite temperature, both below and above the superfluid critical temperature,
by including fluctuations beyond mean field. We determine the superfluid
critical temperature and the pair-breaking temperature as functions of the
attractive interaction between Fermi atoms, from the weak- to the
strong-coupling limit (where bosonic molecules form as bound-fermion pairs).
Density profiles in the trap are also obtained for all temperatures and
couplings.Comment: revised version, to be published in Phys. Rev. Let
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