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arXiv:1106.6193 · Physical Review B

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

F. Palestini, Andrea Perali, P. Pieri, Giancarlo Calvanese Strinati

Published Jan 9, 2012• 39 citations
arXivHTMLPDF

Abstract

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 pseudogap 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 pseudogap physics in a Fermi gas subject to pair fluctuations and the persistence of local spin waves in the normal phase of magnetic materials.

DOI
10.1103/physrevb.85.024517

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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 ororor 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 pseudogap near the Fermi wave vector as well as an additional energy scale related to the contact CCC 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 pseudogap physics in a Fermi gas subject to pair fluctuations and the persistence of local spin waves in the normal phase of magnetic materials.
We compute the spectral density in the normal phase of an interacting homogenous Fermi gas using a TTT-matrix approximation. We fit the quasiparticle peaks of the spectral density to BCS-like dispersion relations and extract estimates of a ``pseudogap'' energy scale and an effective Fermi wave vector as a function of interaction strength. We find that the effective Fermi wave vector of the quasiparticles vanishes when the inverse scattering length exceeds some positive threshold. We also find that, near unitarity, the quasiparticle lifetimes, estimated from the widths of the peaks in the spectral density, approach values on the order of the inverse Fermi energy. These results are consistent with the ``breakdown of Fermi-liquid theory'' observed in recent experiments.
We show that the universal 1/k41/{k}^{4}1/k4 tail in the momentum distribution of dilute Fermi gases implies that the spectral function $A(\mathbf{k},\ensuremath{\omega})$ must have weight below the chemical potential for large momentum $k\ensuremath{\gg}{k}_{F}$, with observable consequences in radio-frequency spectroscopy experiments. We find that this incoherent spectral weight is centered around $\ensuremath{\omega}\ensuremath{\simeq}\ensuremath{-}\ensuremath{\epsilon}(\mathbf{k})$ in a range of energies of order vFk{v}_{F}kvF​k. This ``bending back'' in the dispersion, while natural for superfluids, is quite surprising for normal gases. This universal structure is present in the hard-sphere gas as well as in the Fermi-liquid ground state of the highly imbalanced, attractive gas near unitarity. We argue that, even in the BCS superfluid, this bending back at large kkk is dominated by interaction effects which do not reflect the pairing gap.
We consider the two-dimensional Fermi gas at finite temperature with attractive short-range interactions. Using the virial expansion, which provides a controlled approach at high temperatures, we determine the spectral function and contact for the normal state. Our calculated spectra are in qualitative agreement with recent photoemission measurements [M. Feld et al., Nature (London) 480, 75 (2011).], thus suggesting that the observed pairing gap is a feature of the high-temperature gas rather than being evidence of a pseudogap regime just above the superfluid transition temperature. We further argue that the strong pair correlations result from the fact that the crossover to bosonic dimers occurs at weaker interactions than previously assumed.
The two-species Fermi gas with attractive short-range interactions in two spatial dimensions provides a paradigmatic system for the understanding of strongly correlated Fermi superfluids in two dimensions. It is known to exhibit a BEC to BCS crossover as a function of ln(k_{F}a), where a is the scattering length, and to undergo a Berezinskii-Kosterlitz-Thouless superfluid transition below a critical temperature T_{c}. However, the extent of a pseudogap regime in the strongly correlated regime of ln(k_{F}a)∼1, in which pairing correlations persist above T_{c}, remains largely unexplored with controlled theoretical methods. Here, we use finite-temperature auxiliary-field quantum Monte Carlo methods on discrete lattices in the canonical ensemble formalism to calculate thermodynamical observables in the strongly correlated regime. We extrapolate to continuous time and the continuum limit to eliminate systematic errors and present results for particle numbers ranging from N=42 to N=162. We estimate T_{c} by a finite-size scaling analysis, and observe clear pseudogap signatures above T_{c} and below a temperature T^{*} in both the spin susceptibility and free-energy gap. We also present results for the contact, a fundamental thermodynamic property of quantum many-body systems with short-range interactions.
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.
We study the dilute-gas expansion for a two-dimensional Fermi system with arbitrary short-range repulsive interactions. In contrast with the three-dimensional case, we find an unusual pole in the vertex part in the particle-particle channel, for all center-of-mass momenta q2kF{\mathit{k}}_{\mathit{F}}kF​. We show that this represents an excitation consisting of bound hole pairs, which disperses down to zero energy at q=2kF{\mathit{k}}_{\mathit{F}}kF​. We study the effect of these bound states on the single-particle self-energy and find that the quasiparticles are well defined. Thus in the low-density regime, there is no breakdown of Fermi-liquid theory. In the Appendix we discuss the two-particle phase shift in the dilute Fermi gas, its connection with bound states, and the analogy with the potential scattering phase shift.