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We demonstrate the existence of a collective excitation branch in the pair-breaking continuum of superfluid Fermi gases and BCS superconductors, as suggested by Littlewood and Varma in 1982. We analytically continue the RPA equation on the collective mode energy through its branch cut associated with the continuum, and obtain the full complex dispersion relation, including in the strong coupling regime. For ∆/µ > 1.210 (very close to unitarity in a superfluid Fermi gas), where ∆ is the order parameter and µ the chemical potential, the real part of the branch is wholly within the band gap [0, 2∆]. In the long wavelength limit, the branch varies quadratically with the wave number, with a complex effective mass that we compute analytically. This contradicts the result of Littlewood and Varma that prevailed so far.

Recent experimental data on the optical conductivity of niobium doped SrTiO3 are interpreted in terms of a gas of large polarons with effective coupling constant α ef f ≈ 2. The theoretical approach takes into account many-body effects, the electron-phonon interaction with multiple LOphonon branches, and the degeneracy and the anisotropy of the Ti t2g conduction band. Based on the Fröhlich interaction, the many-body large-polaron theory provides an interpretation for the essential characteristics, except -interestingly -for the unexpectedly large intensity of a peak at ∼ 130 meV, of the observed optical conductivity spectra of SrTi1−xNbxO3 without any adjustment of material parameters.

The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes the breakdown of superfluidity in a two-dimensional Bose gas or a two-dimensional gas of paired fermions. In the latter case, a population imbalance between the two pairing partners in the Fermi mixture is known to influence pairing characteristics. Here, we investigate the effects of imbalance on the two-dimensional BKT superfluid transition, and show that superfluidity is even more sensitive to imbalance than for three dimensional systems. Finite-temperature phase diagrams are derived using the functional integral formalism in combination with a hydrodynamic action functional for the phase fluctuations. This allow to identify a phase separation region and tricritical points due to imbalance. In contrast to superfluidity in the three-dimensional case, the effect of imbalance is also pronounced in the strong-coupling regime. * On leave of absence from: Department of Theoretical Physics, State University of Moldova, str. A. Mateevici 60, MD-2009 Kishinev, Republic of Moldova.

We develop a description of fermionic superfluids in terms of an effective field theory for the pairing order parameter. Our effective field theory improves on the existing Ginzburg -Landau theory for superfluid Fermi gases in that it is not restricted to temperatures close to the critical temperature. This is achieved by taking into account long-range fluctuations to all orders. The results of the present effective field theory compare well with the results obtained in the framework of the Bogoliubov -de Gennes method. The advantage of an effective field theory over Bogoliubov -de Gennes calculations is that much less computation time is required. In the second part of the paper, we extend the effective field theory to the case of a two-band superfluid. The present theory allows us to reveal the presence of two healing lengths in the two-band superfluids, to analyze the finite-temperature vortex structure in the BEC-BCS crossover, and to obtain the ground state parameters and spectra of collective excitations. For the Leggett mode our treatment provides an interpretation of the observation of this mode in two-band superconductors.

Citation for published version (APA):Fomin, V. M., Gladilin, V. N., Klimin, S. N., Devreese, J. T., Kleemans, N. A. J. M., & Koenraad, P. M. (2007). Theory of electron energy spectrum and Aharonov-Bohm effect in self-assembled Inx Ga1-x As quantum rings in GaAs. Physical Review B, 76(23) Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. Theory of electron energy spectrum and Aharonov-Bohm effect in self-assembled In x Ga 1−x As quantum rings in GaAs We analyze theoretically the electron energy spectrum and the magnetization of an electron in a strained In x Ga 1−x As/ GaAs self-assembled quantum ring ͑SAQR͒ with realistic parameters, determined from the crosssectional scanning-tunneling microscopy characterization of that nanostructure. The SAQRs have an asymmetric indium-rich craterlike shape with a depression rather than an opening at the center. Although the real SAQR shape differs strongly from an idealized circular-symmetric open ring structure, the Aharonov-Bohm oscillations of the magnetization survive.

We study the phononic collective modes of the pairing field ∆ in a superfluid Fermi gas at all temperatures below T c . We deal with the coupling of these modes to the fermionic continuum of quasiparticle-quasihole excitations by performing a non-perturbative analytic continuation of the pairing field propagator. At low temperature, we recover the know exponential temperature dependence of the damping rate and velocity shift of the Anderson-Bogoliubov branch. In the vicinity of T c , and in the BCS regime, our calculations reveal two phononic branches; the first one has a velocity that tends to a finite non-zero value at T c , while the second one has a velocity that vanishes with a critical exponent of 1/2 (in contradiction with Ohashi et al., J. Phys. Soc. Jap. 66, 2437), and a quality factor that diverges logarithmically with T c − T . At temperatures close to T c , this results in a double peak structure in the response function of the phase of ∆, well resolved in the BCS regime. Away from T = 0 and T c , we develop a semi-numerical method to perform the analytic continuation. This confirms the existence of two branches, and allows us to follow the disappearance of the second branch as the temperature is lowered. Our results generalize to pure fermionic condensates the double peak structure observed by Carlson and Goldman in dirty superconductors (Phys. Rev. Lett. 31, 880).

The physics of the pseudogap state is intimately linked with the pairing mechanism that gives rise to superfluidity in quantum gases and to superconductivity in high-T c cuprates, and therefore, both in quantum gases and in superconductors, the pseudogap state and preformed pairs have been under intensive experimental scrutiny. Here, we develop a path integral treatment that provides a divergence-free description of the paired state in two-dimensional Fermi gases. Within this formalism, we derive the pseudogap temperature and the pair fluctuation spectral function, and compare these results with a recent experimental measurement of the pairing in the two-dimensional Fermi gas. The removal of the infrared divergence in the number equations is shown both numerically and analytically, through a study of the long-wavelength and lowenergy limit of the pair fluctuation density. Besides the pseudogap temperature, the pair formation temperature and the critical temperature for superfluidity are also derived. The latter corresponds to the Berezinski-Kosterlitz-Thouless (BKT) temperature. The pseudogap temperature, which coincides with the pair formation temperature in the mean field, is found to be suppressed with respect to