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We present a theory of SNS junctions, a normal metal sandwiched between two superconductors, along the crossover from the BCS to the BEC regime. We calculate the Josephson current as a function of the chemical potential relative to the band edge in the superconducting region, $\mu_S$, where the BEC phase is indicated by $\mu_S <0$. The chemical potential relative to the band edge in the normal metal, $\mu_N$, allows us to tune the junction between the SNS case ($\mu_N>0$) and the SIS case, where the superconductors are separated by a tunneling barrier. We find that there are Andreev levels in the BEC regime, as long as there is sufficient density of states in the normal region, i.e. when $\mu_N>\Delta$, where $\Delta$ is the amplitude of the superconducting order parameter. For 1D SNS junctions, we find the Josephson current $I_S$ carried by these Andreev levels to be a function of the ratio $\Delta/\Delta_d$, where $\Delta_d$ is the Andreev level spacing. At zero temperature, the Josephson current has a maximum on the BCS side of the transition where $\Delta$ is maximal. At finite temperature, however, we find that the maximum moves to the BEC side of the crossover. We identify the mechanism for this phenomenon to be the decrease in the number of Andreev levels at the BCS-BEC crossover, accompanied by an increase in excitation energy to the unoccupied levels, making it less likely that these states are thermally occupied. Thereby, at finite temperature, the Josephson current is more strongly reduced on the BCS side of the crossover, resulting in a maximal Josephson current at the BCS-BEC crossover., Comment: 5 pages, 6 figures

Superconductivity was recently reported in several quasicrystalline systems. These are materials which are structurally ordered, but since they are not translationally invariant, the usual BCS theory does not apply. At the present time, the underlying mechanism and the properties of the superconducting phase are insufficiently understood. To gain a better understanding of quasiperiodic superconductors, we consider the attractive Hubbard model on the Fibonacci chain, and examine its low-temperature superconducting phase in detail using the Bogoliubov-de Gennes mean-field approach. We obtain superconducting solutions as a function of the parameters controlling the physical properties of the system: the strength of the Hubbard attraction $U$, the chemical potential $\mu$, and the strength of the modulation of the Fibonacci Hamiltonian, $w$. We find that there is a bulk transition at a critical temperature that obeys a power law in $U$. The local superconducting order parameter is self-similar both in real and perpendicular space. The local densities of states vary from site to site, however, the width of the superconducting gap is the same on all sites. The interplay between the Hubbard attraction and the intrinsic gaps of the Fibonacci chain results in a complex zero-temperature $\mu$-$U$ phase diagram with insulating domes surrounded by superconducting regions. Finally, we show that tuning $w$ from weak to strong quasicrystalline modulation gives rise to qualitatively different thermodynamic behaviors as could be observed by measuring the specific heat.

In magic angle twisted bilayer graphene, transport, thermodynamic and spectroscopic experiments pinpoint at a competition between distinct low-energy states with and without electronic order. We use Dynamical Mean Field Theory (DMFT) on the topological heavy Fermion (THF) model of twisted bilayer graphene to investigate the emergence of electronic correlations and long-range order in the absence of strain. We contrast moment formation, Kondo screening and ordering on a temperature basis and explain the nature of emergent correlated states based on three central phenomena: (i) the formation of local spin and valley isospin moments around 100K, (ii) the ordering of the local isospin moments around 10K preempting Kondo screening, and (iii) a cascadic redistribution of charge between localized and delocalized electronic states upon doping. At integer fillings, we find that low energy spectral weight is depleted in the symmetric phase, while we find insulating states with gaps enhanced by exchange coupling in the zero-strain ordered phases. Doping away from integer filling results in distinct metallic states: a "bad metal" above the ordering temperature, where scattering off the disordered local moments suppresses electronic coherence, and a "good metal" in the ordered states with coherence of quasiparticles facilitated by isospin order. This finding reveals coherence from order as the microscopic mechanism behind the Pomeranchuk effect observed experimentally. Upon doping, there is a periodic charge reshuffling between localized and delocalized electronic orbitals leading to cascades of doping-induced Lifshitz transitions, local spectral weight redistributions and periodic variations of the electronic compressibility. Our findings provide a unified understanding of the most puzzling aspects of scanning tunneling spectroscopy, transport, and compressibility experiments., Comment: 22 pages, 7 figures

We consider a two-dimensional generalization of the Su-Schrieffer-Heeger model which is known to possess a non-trivial topological band structure. For this model, which is characterized by a single parameter, the hopping ratio $0 \leq r\leq 1$, the inhomogeneous superconducting phases induced by an attractive $U$ Hubbard interaction are studied using mean field theory. We show, analytically and by numerical diagonalization, that in lattices with open boundaries, phases with enhanced superconducting order on the corners or the edges can appear, depending on the filling. For finite samples at half filling, the corner site superconducting transition temperature can be much larger than that of the bulk. A novel proximity effect thus arises for $T_{c,bulk} < T

The quantum many body states in the BCS-BEC crossover regime are of long-lasting interest. Here we report direct spectroscopic evidence of BCS-BEC crossover in real-space in a FeSe monolayer thin film by using spatially resolved scanning tunneling spectra. The crossover is driven by the shift of band structure relative to the Fermi level. The theoretical calculation based on a two-band model qualitatively reproduces the measured spectra in the whole crossover range. In addition, the Zeeman splitting of the quasi-particle states is found to be consistent with the characteristics of a condensate. Our work paves the way to study the exotic states of BCS-BEC crossover in a two-dimensional crystalline material at the atomic scale.