Shape-resonant superconductivity in nanofilms: from weak to strong coupling

Ultrathin superconductors of different materials are becoming a powerful platform to find mechanisms for enhancement of superconductivity, exploiting shape resonances in different superconducting properties. Here we evaluate the superconducting gap and its spatial profile, the multiple gap components, and the chemical potential, of generic superconducting nanofilms, considering the pairing attraction and its energy scale as tunable parameters, from weak to strong coupling, at fixed electron density. Superconducting properties are evaluated at mean field level as a function of the thickness of the nanofilm, in order to characterize the shape resonances in the superconducting gap. We find that the most pronounced shape resonances are generated for weakly coupled superconductors, while approaching the strong coupling regime the shape resonances are rounded by a mixing of the subbands due to the large energy gaps extending over large energy scales. Finally, we find that the spatial profile, transverse to the nanofilm, of the superconducting gap acquires a flat behavior in the shape resonance region, indicating that a robust and uniform multigap superconducting state can arise at resonance.Comment: 7 pages, 4 figures. Submitted to the Proceedings of the Superstripes 2016 conferenc

Resonant and crossover phenomena in a multiband superconductor tuning the chemical potential near a band edge

Resonances in the superconducting properties, in a regime of crossover from BCS to mixed Bose-Fermi superconductivity, are investigated in a two-band superconductor where the chemical potential is tuned near the band edge of the second mini-band generated by quantum confinement effects. The shape resonances at T=0 in the superconducting gaps (belonging to the class of Feshbach-like resonances) is manifested by interference effects in the superconducting gap at the first large Fermi surface when the chemical potential is in the proximity of the band edge of the second mini-band. The case of a superlattice of quantum wells is considered and the amplification of the superperconducting gaps at the 3D-2D Fermi surface topological transition is clearly shown. The results are found to be in good agreement with available experimental data on a superlattice of honeycomb boron layers intercalated by Al and Mg spacer layers.Comment: 13 pages, 9 image

Pseudogap in fermionic density of states in the BCS-BEC crossover of atomic Fermi gases

We study pseudogap behaviors of ultracold Fermi gases in the BCS-BEC crossover region. We calculate the density of states (DOS), as well as the single-particle spectral weight, above the superfluid transition temperature $T_{\rm c}$ including pairing fluctuations within a $T$-matrix approximation. We find that DOS exhibits a pseudogap structure in the BCS-BEC crossover region, which is most remarkable near the unitarity limit. We determine the pseudogap temperature $T^*$ at which the pseudogap structure in DOS disappears. We also introduce another temperature $T^{**}$ at which the BCS-like double-peak structure disappears in the spectral weight. While one finds $T^*>T^{**}$ in the BCS regime, $T^{**}$ becomes higher than $T^*$ in the crossover and BEC regime. We also determine the pseudogap region in the phase diagram in terms of temperature and pairing interaction.Comment: 6 pages, 4 figures, Proceedings of QFS 200

Superfluid phase transition and strong-coupling effects in an ultracold Fermi gas with mass imbalance

We investigate the superfluid phase transition and effects of mass imbalance in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an cold Fermi gas. We point out that the Gaussian fluctuation theory developed by Nozi\`eres and Schmitt-Rink and the $T$-matrix theory, that are now widely used to study strong-coupling physics of cold Fermi gases, give unphysical results in the presence of mass imbalance. To overcome this problem, we extend the $T$-matrix theory to include higher-order pairing fluctuations. Using this, we examine how the mass imbalance affects the superfluid phase transition. Since the mass imbalance is an important key in various Fermi superfluids, such as $^{40}$K-$^6$Li Fermi gas mixture, exciton condensate, and color superconductivity in a dense quark matter, our results would be useful for the study of these recently developing superfluid systems.Comment: 7 pages, 4 figures, Proceedings of QFS-201

Incommensurate Charge Density Waves in the adiabatic Hubbard-Holstein model

The adiabatic, Holstein-Hubbard model describes electrons on a chain with step $a$ interacting with themselves (with coupling $U$) and with a classical phonon field \f_x (with coupling \l). There is Peierls instability if the electronic ground state energy F(\f) as a functional of \f_x has a minimum which corresponds to a periodic function with period ${\pi\over p_F}$, where $p_F$ is the Fermi momentum. We consider ${p_F\over\pi a}$ irrational so that the CDW is {\it incommensurate} with the chain. We prove in a rigorous way in the spinless case, when \l,U are small and {U\over\l} large, that a)when the electronic interaction is attractive $U<0$ there is no Peierls instability b)when the interaction is repulsive $U>0$ there is Peierls instability in the sense that our convergent expansion for F(\f), truncated at the second order, has a minimum which corresponds to an analytical and ${\pi\over p_F}$ periodic \f_x. Such a minimum is found solving an infinite set of coupled self-consistent equations, one for each of the infinite Fourier modes of \f_x.Comment: 16 pages, 1 picture. To appear Phys. Rev.

An explanation for a universality of transition temperatures in families of copper oxide superconductors

A remarkable mystery of the copper oxide high-transition-temperature (Tc) superconductors is the dependence of Tc on the number of CuO2 layers, n, in the unit cell of a crystal. In a given family of these superconductors, Tc rises with the number of layers, reaching a peak at n=3, and then declines: the result is a bell-shaped curve. Despite the ubiquity of this phenomenon, it is still poorly understood and attention has instead been mainly focused on the properties of a single CuO2 plane. Here we show that the quantum tunnelling of Cooper pairs between the layers simply and naturally explains the experimental results, when combined with the recently quantified charge imbalance of the layers and the latest notion of a competing order nucleated by this charge imbalance that suppresses superconductivity. We calculate the bell-shaped curve and show that, if materials can be engineered so as to minimize the charge imbalance as n increases, Tc can be raised further.Comment: 15 pages, 3 figures. The version published in Natur

Pseudogap and spectral function from superconducting fluctuations to the bosonic limit

The crossover from weak to strong coupling for a three dimensional continuum model of fermions interacting via an attractive contact potential is studied above the superconducting critical temperature. The pair-fluctuation propagator, the one-loop self-energy, and the spectral function are investigated in a systematic way from the superconducting fluctuation regime (weak coupling) to the bosonic regime (strong coupling). Analytic and numerical results are reported. In the strong-coupling regime, where the pair fluctuation propagator has bosonic character, two quite different peaks appear in the spectral function, a broad one at negative frequencies and a narrow one at positive frequencies. By decreasing coupling, the two-peak structure evolves smoothly. In the weak-coupling regime, where the fluctuation propagator has diffusive Ginzburg-Landau character, the overall line-shape of the spectral function is more symmetric. The systematic analysis of the spectral function identifies specific features which allow one to distinguish by ARPES whether a system is in the weak- or strong-coupling regime. Connection of the results of our analysis with the phenomenology of cuprate superconductors is also attempted and rests on the recently introduced two-gap model.Comment: 19 pages, 18 figure

Pair excitations and parameters of state of imbalanced Fermi gases at finite temperatures

The spectra of low-lying pair excitations for an imbalanced two-component superfluid Fermi gas are analytically derived within the path-integral formalism taking into account Gaussian fluctuations about the saddle point. The spectra are obtained for nonzero temperatures, both with and without imbalance, and for arbitrary interaction strength. On the basis of the pair excitation spectrum, we have calculated the thermodynamic parameters of state of cold fermions and the first and second sound velocities. The parameters of pair excitations show a remarkable agreement with the Monte Carlo data and with experiment.Comment: 14 pages, 5 figure

d-wave superconductivity near charge instabilities

We investigate the symmetry of the superconducting order parameter in the proximity of a phase-separation or of an incommensurate charge-density-wave instability. The attractive effective interaction at small or intermediate transferred momenta is singular near the instability. This strongly $q$-dependent interaction, together with a residual local repulsion between the quasiparticles and an enhanced density of states for band structures appropriate for the high temperature superconducting oxides, strongly favors the formation of $d$-wave superconductivity. The relative stability with respect to superconductivity in the $s$-wave channel is discussed in detail, finding this latter hardly realized in the above conditions. The superconducting temperature is mostly determined by the closeness to the quantum critical point associated to the charge instability and displays a stronger dependence on doping with respect to the simple proximity to a Van Hove singularity. The relevance of this scenario and the generic agreement of the resulting phase diagram with the properties displayed by high temperature superconducting oxides is discussed.Comment: 1 revtex file and 12 postscript figure

From Majorana theory of atomic autoionization to Feshbach resonances in high temperature superconductors

The Ettore Majorana paper - Theory of incomplete P triplets- published in 1931, focuses on the role of selection rules for the non-radiative decay of two electron excitations in atomic spectra, involving the configuration interaction between discrete and continuum channels. This work is a key step for understanding the 1935 work of Ugo Fano on the asymmetric lineshape of two electron excitations and the 1958 Herman Feshbach paper on the shape resonances in nuclear scattering arising from configuration interaction between many different scattering channels. The Feshbach resonances are today of high scientific interest in many different fields and in particular for ultracold gases and high Tc superconductivity.Comment: 13 pages, 7 figures. Journal of Superconductivity and Novel Magnetism to be publishe