Multi-patch model for transport properties of cuprate superconductors

A number of normal state transport properties of cuprate superconductors are analyzed in detail using the Boltzmann equation. The momentum dependence of the electronic structure and the strong momentum anisotropy of the electronic scattering are included in a phenomenological way via a multi-patch model. The Brillouin zone and the Fermi surface are divided in regions where scattering between the electrons is strong and the Fermi velocity is low (hot patches) and in regions where the scattering is weak and the Fermi velocity is large (cold patches). We present several motivations for this phenomenology starting from various microscopic approaches. A solution of the Boltzmann equation in the case of N patches is obtained and an expression for the distribution function away from equilibrium is given. Within this framework, and limiting our analysis to the two patches case, the temperature dependence of resistivity, thermoelectric power, Hall angle, magnetoresistance and thermal Hall conductivity are studied in a systematic way analyzing the role of the patch geometry and the temperature dependence of the scattering rates. In the case of Bi-based cuprates, using ARPES data for the electronic structure, and assuming an inter-patch scattering between hot and cold states with a linear temperature dependence, a reasonable agreement with the available experiments is obtained.Comment: 18 pages, 18 figures, to be published on Eur. Phys. J.

Extracting the condensate density from projection experiments with Fermi gases

A debated issue in the physics of the BCS-BEC crossover with trapped Fermi atoms is to identify characteristic properties of the superfluid phase. Recently, a condensate fraction was measured on the BCS side of the crossover by sweeping the system in a fast (nonadiabatic) way from the BCS to the BEC sides, thus ``projecting'' the initial many-body state onto a molecular condensate. We analyze here the theoretical implications of these projection experiments, by identifying the appropriate quantum-mechanical operator associated with the measured quantities and relating them to the many-body correlations occurring in the BCS-BEC crossover. Calculations are presented over wide temperature and coupling ranges, by including pairing fluctuations on top of mean field.Comment: 4 pages, 4 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

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

Pairing effects in the normal phase of a two-dimensional Fermi gas

In a recent experiment [M. Feld et al., Nature 480, 75 (2011); B. Froehlich et al., Phys. Rev. Lett. 109,130403 (2012)], a pairing gap was detected in a two-dimensional (2D) Fermi gas with attractive interaction at temperatures where superfluidity does not occur. The question remains open as to whether this gap is a pseudogap phenomenon or is due to a molecular state. In this paper, by using a t-matrix approach, we reproduce quite well the experimental data for a 2D Fermi gas, and set the boundary between the pseudogap and molecular regimes. We also show that pseudogap phenomena occurring in 2D and 3D can be related through a variable spanning the BCS-BEC crossover in a universal way.Comment: 10 pages, 9 figures; final versio

Temperature and coupling dependence of the universal contact intensity for an ultracold Fermi gas

Physical properties of an ultracold Fermi gas in the temperature-coupling phase diagram can be characterized by the contact intensity C, which enters the pair-correlation function at short distances and describes how the two-body problem merges into its surrounding. We show that the local order established by pairing fluctuations about the critical temperature Tc of the superfluid transition considerably enhances the contact C in a temperature range where pseudogap phenomena are maximal. Our ab initio results for C in a trap compare well with recently available experimental data over a wide coupling range. An analysis is also provided for the effects of trap averaging on C.Comment: 5 pages, 5 figure

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

Dispersions, weights, and widths of the single-particle spectral function in the normal phase of a Fermi gas

The dispersions, weights, and widths of the peaks of the single-particle spectral function in the presence of pair correlations, for a Fermi gas with either attractive or repulsive short-range inter-particle interaction, are determined in the normal phase over a wide range of wave vectors, with a twofold purpose. The first one is to determine how these dispersions identify both an energy scale known as the pseudo-gap near the Fermi wave vector, as well as an additional energy scale related to the contact C at large wave vectors. The second one is to differentiate the behaviors of the repulsive gas from the attractive one in terms of crossing versus avoided crossing of the dispersions near the Fermi wave vector. An analogy will also be drawn between the occurrence of the pseudo-gap physics in a Fermi gas subject to pair fluctuations and the persistence of local spin waves in the normal phase of magnetic materials.Comment: 18 pages, 21 figure

Evolution of the Normal State of a Strongly Interacting Fermi Gas from a Pseudogap Phase to a Molecular Bose Gas

Wave-vector resolved radio frequency (rf) spectroscopy data for an ultracold trapped Fermi gas are reported for several couplings at Tc, and extensively analyzed in terms of a pairing-fluctuation theory. We map the evolution of a strongly interacting Fermi gas from the pseudogap phase into a fully gapped molecular Bose gas as a function of the interaction strength, which is marked by a rapid disappearance of a remnant Fermi surface in the single-particle dispersion. We also show that our theory of a pseudogap phase is consistent with a recent experimental observation as well as with Quantum Monte Carlo data of thermodynamic quantities of a unitary Fermi gas above Tc.Comment: 9 pages, 9 figures. Substantially revised version (to appear in Phys. Rev. Lett.

Stability of fermionic Feshbach molecules in a Bose-Fermi mixture

In the wake of successful experiments in Fermi condensates, experimental attention is broadening to study resonant interactions in degenerate Bose-Fermi mixtures. Here we consider the properties and stability of the fermionic molecules that can be created in such a mixture near a Feshbach resonance (FR). To do this, we consider the two-body scattering matrix in the many-body environment, and assess its complex poles. The stability properties of these molecules strongly depend on their centre-of-mass motion, because they must satisfy Fermi statistics. At low centre-of-mass momenta the molecules are more stable than in the absence of the environment (due to Pauli-blocking effects), while at high centre-of-mass momenta nontrivial many body effects render them somewhat less stable