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

Shape resonance for the anisotropic superconducting gaps near a Lifshitz transition: the effect of electron hopping between layers

The multigap superconductivity modulated by quantum confinement effects in a superlattice of quantum wells is presented. Our theoretical BCS approach captures the low-energy physics of a shape resonance in the superconducting gaps when the chemical potential is tuned near a Lifshitz transition. We focus on the case of weak Cooper-pairing coupling channels and strong pair exchange interaction driven by repulsive Coulomb interaction that allows to use the BCS theory in the weak-coupling regime neglecting retardation effects like in quantum condensates of ultracold gases. The calculated matrix element effects in the pairing interaction are shown to yield a complex physics near the particular quantum critical points due to Lifshitz transitions in multigap superconductivity. Strong deviations of the ratio $2\Delta/T_c$ from the standard BCS value as a function of the position of the chemical potential relative to the Lifshitz transition point measured by the Lifshitz parameter are found. The response of the condensate phase to the tuning of the Lifshitz parameter is compared with the response of ultracold gases in the BCS-BEC crossover tuned by an external magnetic field. The results provide the description of the condensates in this regime where matrix element effects play a key role.Comment: 12 pages, 6 figure

A model for the phase separation controlled by doping and the internal chemical pressure in different cuprate superconductors

In the framework of a two-band model, we study the phase separation regime of different kinds of strongly correlated charge carriers as a function of the energy splitting between the two sets of bands. The narrow (wide) band simulates the more localized (more delocalized) type of charge carriers. By assuming that the internal chemical pressure on the CuO$_2$ layer due to interlayer mismatch controls the energy splitting between the two sets of states, the theoretical predictions are able to reproduce the regime of phase separation at doping higher than 1/8 in the experimental pressure-doping-$T_c$ phase diagram of cuprates at large microstrain as it appears in overoxygenated La$_2$CuO$_4$.Comment: 8 pages, 5 figures, submitted to Phys. Rev.

Emergence of weight-topology correlations in complex scale-free networks

Different weighted scale-free networks show weights-topology correlations indicated by the non linear scaling of the node strength with node connectivity. In this paper we show that networks with and without weight-topology correlations can emerge from the same simple growth dynamics of the node connectivities and of the link weights. A weighted fitness network is introduced in which both nodes and links are assigned intrinsic fitness. This model can show a local dependence of the weight-topology correlations and can undergo a phase transition to a state in which the network is dominated by few links which acquire a finite fraction of the total weight of the network.Comment: (4 pages,3 figures

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

Isotope effect on the E2g phonon and mesoscopic phase separation near the electronic topological transition in Mg1-xAlxB2

We report the boron isotope effect on the E2g phonon mode by micro-Raman spectroscopy on the ternary Mg1-xAlxB2 system, synthesized with pure isotopes 10B and 11B. The isotope coefficient on the phonon frequency is near 0.5 in the full range decreasing near x = 0. The intraband electron-phonon (e-ph) coupling, for the electrons in the sigma band, has been extracted from the E2g line-width and frequency softening. Tuning the Fermi energy near the electronic topological transition (ETT), where the sigma Fermi surface changes from 2D to 3D topology the E2g mode, shows the known Kohn anomaly on the 2D side of the ETT and a splitting of the E2g phonon frequency into a hard and soft component from x = 0 to x = 0.28. The results suggest a minor role of the intraband phonon mediated pairing in the control of the high critical temperature in Mg1-xAlxB2. The common physical features of diborides with the novel multigap FeAs-based superconductors and cuprates is discussed.Comment: 19 pages, 6 figure

Cliques and duplication-divergence network growth

A population of complete subgraphs or cliques in a network evolving via duplication-divergence is considered. We find that a number of cliques of each size scales linearly with the size of the network. We also derive a clique population distribution that is in perfect agreement with both the simulation results and the clique statistic of the protein-protein binding network of the fruit fly. In addition, we show that such features as fat-tail degree distribution, various rates of average degree growth and non-averaging, revealed recently for only the particular case of a completely asymmetric divergence, are present in a general case of arbitrary divergence.Comment: 7 pages, 6 figure

The entropy of randomized network ensembles

Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same degree-correlations or the same community structure of any given real network. We characterize these randomized network ensembles by their entropy, i.e. the normalized logarithm of the total number of networks which are part of these ensembles. We estimate the entropy of randomized ensembles starting from a large set of real directed and undirected networks. We propose entropy as an indicator to assess the role of each structural feature in a given real network.We observe that the ensembles with fixed scale-free degree distribution have smaller entropy than the ensembles with homogeneous degree distribution indicating a higher level of order in scale-free networks.Comment: (6 pages,1 figure,2 tables

Enhancing the robustness of a multiplex network leads to multiple discontinuous percolation transitions

Determining design principles that boost robustness of interdependent networks is a fundamental question of engineering, economics, and biology. It is known that maximizing the degree correlation between replicas of the same node leads to optimal robustness. Here we show that increased robustness might also come at the expense of introducing multiple phase transitions. These results reveal yet another possible source of fragility of multiplex networks that has to be taken into the account during network optimisation and design