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Motivated by recent experiments on Al nanoparticles, we have studied the effects of fixed electron number and small size in nanoscale superconductors, by applying the canonical BCS theory for the attractive Hubbard model in two and three dimensions. A negative ``gap in particles with an odd number of electrons as observed in the experiments is obtained in our canonical scheme. For particles with an even number of electrons, the energy gap exhibits shell structure as a function of electron density or system size in the weak-coupling regime: the gap is particularly large for ``magic numbers of electrons for a given system size or of atoms for a fixed electron density. The grand canonical BCS method essentially misses this feature. Possible experimental methods for observing such shell effects are discussed.
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The electronic structure near defects (such as impurities) in superconductors is explored using a new, fully self-consistent technique. This technique exploits the short-range nature of the impurity potential and the induced change in the superconducting order parameter to calculate features in the electronic structure down to the atomic scale with unprecedented spectral resolution. Magnetic and non-magnetic static impurity potentials are considered, as well as local alterations in the pairing interaction. Extensions to strong-coupling superconductors and superconductors with anisotropic order parameters are formulated.
In this paper, we review the low energy electronic structure of the kinetic energy driven d-wave cuprate superconductors. We give a general description of the charge-spin separation fermion-spin theory, where the constrained electron is decoupled as the gauge invariant dressed holon and spin. In particular, we show that under the decoupling scheme, the charge-spin separation fermion-spin representation is a natural representation of the constrained electron defined in a restricted Hilbert space without double electron occupancy. Based on the charge-spin separation fermion-spin theory, we have developed the kinetic energy driven superconducting mechanism, where the superconducting state is controlled by both superconducting gap parameter and quasiparticle coherence. Within this kinetic energy driven superconductivity, we have discussed the low energy electronic structure of the single layer and bilayer cuprate superconductors in both superconducting and normal states, and qualitatively reproduced all main features of the angle-resolved photoemission spectroscopy measurements on the single layer and bilayer cuprate superconductors. We show that the superconducting state in cuprate superconductors is the conventional Bardeen-Cooper-Schrieffer like with the d-wave symmetry, so that the basic Bardeen-Cooper-Schrieffer formalism with the d-wave gap function is still valid in discussions of the low energy electronic structure of cuprate superconductors, although the pairing mechanism is driven by the kinetic energy by exchanging spin excitations. We also show that the well pronounced peak-dip-hump structure of the bilayer cuprate superconductors in the superconducting state and double-peak structure in the normal state are mainly caused by the bilayer splitting.
The electronic structure of FeSe, the simplest iron based superconductor (Fe-SC), conceals a potential of dramatic increase of Tc that realizes under pressure or in a single layer film. This is also the system where nematicity, the phenomenon of a keen current interest, is most easy to study since it is not accompanied by the antiferomagnetic transition like in all other Fe-SCs. Here we overview recent experimental data on electronic structure of FeSe-based superconductors: isovalently doped crystals, intercalates, and single layer films, trying to clarify its topology and possible relation of this topology to superconductivity. We argue that the marked differences between the experimental and calculated band structures for all FeSe compounds can be described by a hoping selective renormalization model for a spin/orbital correlated state that may naturally explain both the evolution of the band structure with temperature and nematicity.
Within the framework of the kinetic energy driven superconductivity, the electronic structure of bilayer cuprate superconductors in the superconducting state is studied. It is shown that the electron spectrum of bilayer cuprate superconductors is split into the bonding and antibonding components by the bilayer splitting, then the observed peak-dip-hump structure around the $[pi,0]$ point is mainly caused by this bilayer splitting, with the superconducting peak being related to the antibonding component, and the hump being formed by the bonding component. The spectral weight increases with increasing the doping concentration. In analogy to the normal state case, both electron antibonding peak and bonding hump have the weak dispersions around the $[pi,0]$ point.
While the beginning decade of the high-Tc cuprates era passed under domination of local theories, Abrikosov was one of the few who took seriously the electronic band structure of cuprates, stressing the importance of an extended Van Hove singularity near the Fermi level. These ideas have not been widely accepted that time mainly because of a lack of experimental evidence for correlation between saddle point position and superconductivity. In this short contribution, based on the detailed comparison of the electronic band structures of different families of cuprates and iron based superconductors I argue that a general mechanism of the Tc enhancement in all known high-Tc superconductors is likely related with the proximity of certain Van Hove singularities to the Fermi level. While this mechanism remains to be fully understood, one may conclude that it is not related with the electron density of states but likely with some kind of resonances caused by a proximity of the Fermi surface to topological Lifshitz transition. One may also notice that the electronic correlations often shifts the electronic bands to optimal for superconductivity positions.
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