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arXiv:1103.1942 · Physical Review A

Formation of magnetic impurities and pair-breaking effect in a superfluid Fermi gas

Yoji Ohashi

Published Jun 10, 2011• 12 citations
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Abstract

We theoretically investigate the introduction of magnetic impurities into a superfluid Fermi gas. In the presence of a population imbalance (${N}_{\ensuremath{\uparrow}}>{N}_{\ensuremath{\downarrow}}$, where ${N}_{\ensuremath{\sigma}}$ is the number of Fermi atoms with pseudospin $\ensuremath{\sigma}=\ensuremath{\uparrow},\ensuremath{\downarrow}$), we show that nonmagnetic potential scatterers embedded in the system are magnetized in the sense that some of the excess spin-$\ensuremath{\uparrow}$ atoms are localized around them. They destroy the superfluid order parameter around them, as in the case of the magnetic impurity effect discussed in the superconductivity literature. This pair-breaking effect naturally leads to localized excited states below the superfluid excitation gap. To confirm our idea in a simple manner, we consider an attractive Fermi-Hubbard model within the mean-field theory at $T=0$. We determine consistent superfluid properties around a nonmagnetic impurity, such as the superfluid order parameter, local population imbalance, as well as the single-particle density of states, in the presence of a population imbalance. Since competition between superconductivity and magnetism is one of the most fundamental problems in condensed-matter physics, our results would be useful for the study of this important issue in cold Fermi gases.

DOI
10.1103/physreva.83.063611

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We theoretically investigate the introduction of magnetic impurities into a superfluid Fermi gas. In the presence of a population imbalance (N\ensuremath↑>N\ensuremath↓{N}_{\ensuremath{\uparrow}}>{N}_{\ensuremath{\downarrow}}N\ensuremath↑​>N\ensuremath↓​, where N\ensuremathσ{N}_{\ensuremath{\sigma}}N\ensuremathσ​ is the number of Fermi atoms with pseudospin \ensuremathσ=\ensuremath↑,\ensuremath↓\ensuremath{\sigma}=\ensuremath{\uparrow},\ensuremath{\downarrow}\ensuremathσ=\ensuremath↑,\ensuremath↓), we show that nonmagnetic potential scatterers embedded in the system are magnetized in the sense that some of the excess spin-\ensuremath↑\ensuremath{\uparrow}\ensuremath↑ atoms are localized around them. They destroy the superfluid order parameter around them, as in the case of the magnetic impurity effect discussed in the superconductivity literature. This pair-breaking effect naturally leads to localized excited states below the superfluid excitation gap. To confirm our idea in a simple manner, we consider an attractive Fermi-Hubbard model within the mean-field theory at T=0T=0T=0. We determine consistent superfluid properties around a nonmagnetic impurity, such as the superfluid order parameter, local population imbalance, as well as the single-particle density of states, in the presence of a population imbalance. Since competition between superconductivity and magnetism is one of the most fundamental problems in condensed-matter physics, our results would be useful for the study of this important issue in cold Fermi gases.
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In cold atom experiments, we have tools to create spin dependent optical potential, which gives us the possibility to achieve classical magnetic impurity in cold atom systems. Here we study the physics of magnetic impurity. A localized magnetic impurity can induce a mid-gap bound state, the Yu-Shiba state, in superfluid Fermi gas. We propose a modified RF spectroscopy to measure the local density of states, as a cold-atom analog of STM, which may be used to detect Yu-Shiba state. In addition, magnetic impurity can locally induce population imbalance in the system, potentially providing a method to realize FFLO-like state in a controlled way. We demonstrate such a possibility by solving the self-consist Bogoliubov-de Gennes equations.
A spin-imbalanced superfluid Fermi gas harmonically trapped in a two-dimensional optical lattice with a single classical magnetic impurity is investigated by Bogoliubov-de Gennes equations. In both the spin-balanced and weak spin-imbalanced cases, we show that a strong magnetic impurity can change the sign of the pairing order parameter. The amplitude of the sign-changed order parameter caused by impurity is affected by the strength of the impurity potential, temperature, and particle density. Compared to the spin-balanced case, we find that an additional in-gap bound state can be induced by a strong magnetic impurity in the weak spin-imbalanced case. In the strong spin-imbalanced case where the Fulde-Ferrell-Larkin-Ovchinnikov state is established as the ground state, the impurity induces wide spatial oscillations of pairing order parameters and can enhance the order parameters by suppressing the local spin imbalance.
A spin-imbalanced superfluid Fermi gas harmonically trapped in a two-dimensional optical lattice with a single classical magnetic impurity is investigated by Bogoliubov-de Gennes equations. In both the spin-balanced and weak spin-imbalanced cases, we show that a strong magnetic impurity can change the sign of the pairing order parameter. The amplitude of the sign-changed order parameter caused by impurity is affected by the strength of the impurity potential, temperature, and particle density. Compared to the spin-balanced case, we find that an additional in-gap bound state can be induced by a strong magnetic impurity in the weak spin-imbalanced case. In the strong spin-imbalanced case where the Fulde-Ferrell-Larkin-Ovchinnikov state is established as the ground state, the impurity induces wide spatial oscillations of pairing order parameters and can enhance the order parameters by suppressing the local spin imbalance.
We present a systematic investigation of the effects of ``nonmagnetic'' impurities on the sss-wave BCS-BEC crossover in atomic Fermi gases within a pairing fluctuation theory. Both pairing and impurity scattering TTT matrices are treated self-consistently at the same time. While the system is less sensitive to impurity scattering in the Born limit, for strong impurity scatterers, both the frequency and the gap function are highly renormalized, leading to significant suppression of the superfluid Tc{T}_{c}Tc​, the order parameter, and the superfluid density. We also find the formation of impurity bands and smearing of coherence peak in the fermion density of states, leading to a spectrum weight transfer and finite lifetime of Bogoliubov quasiparticles. In the BCS regime, the superfluidity may be readily destroyed by the impurity of high density, leading to a superfluid-insulator quantum phase transition at zero temperature. In comparison, the superfluidity in unitary and BEC regimes is relatively more robust.
We consider imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mix-tures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species both occupying only a single hyperfine state. In both cases, the number of atoms for each component is allowed to be differ-ent, which leads to a spin imbalance, or spin polarization. Two different atomic species also lead to a mass imbalance. Imbalanced Fermi gases are relevant to condensed-matter physics, nuclear physics and astroparticle physics. They have been studied intensively in recent years, following their experimental realization in ultracold atomic Fermi gases. The experimental control in such a system allows for a systematic study of the equation of state and the phase diagram as a function of temperature, spin polarization and interaction strength. In this re-view, we discuss the progress in understanding strongly-interacting imbalanced Fermi gases, where a main goal is to describe the results of the highly controlled experiments. We start by discussing Feshbach resonances, after which we treat the imbalanced Fermi gas in mean-field theory to give an introduction to the relevant physics. We encounter several unusual superfluid phases, including phase-separation, gapless Sarma superfluidity, and supersolidity. To obtain a more quantitative description of the experiments, we review also more sophisti-cated techniques, such as diagrammatic methods and the renormalization-group theory. We end the review by discussing two theoretical approaches to treat the inhomogeneous imbalanced Fermi gas, namely the Landau-Ginzburg theory and the Bogoliubov-de Gennes approach. Key words: