Using highly efficient GPU-based simulations of the tight-binding Bogoliubov-de Gennes equations we solve self-consistently for the pair correlation in rhombohedral (ABC) and Bernal (ABA) multilayer graphene by considering a finite intrinsic s-wave pairing potential. We find that the two different stacking configurations have opposite bulk/surface behavior for the order parameter. Surface superconductivity is robust for ABC stacked multilayer graphene even at very low pairing potentials for which the bulk order parameter vanishes, in agreement with a recent analytical approach. In contrast, for Bernal stacked multilayer graphene, we find that the order parameter is always suppressed at the surface and that there exists a critical value for the pairing potential below which no superconducting order is achieved. We considered different doping scenarios and find that homogeneous doping strongly suppresses surface superconductivity while non-homogeneous fieldinduced doping has a much weaker effect on the superconducting order parameter. For multilayer structures with hybrid stacking (ABC and ABA) we find that when the thickness of each region is small (few layers), high-temperature surface superconductivity survives throughout the bulk due to the proximity effect between ABC/ABA interfaces where the order parameter is enhanced.

We report a multiscale modeling of electronic structure of a conducting polymer poly(3,4-ethylenedioxythiopehene) (PEDOT) based on a realistic model of its morphology. We show that when the charge carrier concentration increases, the character of the density of states (DOS) gradually evolves from the insulating to the semimetallic, exhibiting a collapse of the gap between the bipolaron and valence bands with the drastic increase of the DOS between the bands. The origin of the observed behavior is attributed to the effect of randomly located counterions giving rise to the states in the gap. These results are discussed in light of recent experiments. The method developed in this work is general and can be applied to study the electronic structure of other conducting polymers.

The spectra of conducting polymers obtained using ultraviolet photoelectron spectroscopy (UPS) exhibit a typical broadening of the tail σ ≈ 1 eV, which by an order of magnitude exceeds a commonly accepted value of the broadening of the tail of the density of states σ ≈ 0.1 eV obtained using transport measurements. In this work, an origin of this anomalous broadening of the tail of the UPS spectra in a doped conducting polymer, PEDOT (poly(3,4-ethylenedioxythiophene)), is discussed. Based on the semiempirical approach and using a realistic morphological model, the density of valence states in PEDOT doped with molecular counterions is computed. It is shown that due to a disordered character of the material with randomly distributed counterions, the localized charge carriers in PEDOT crystallites experience spatially varying electrostatic potential. This leads to spatially varying local vacuum levels and binding energies. Taking this variation into account the UPS spectrum is obtained with the broadening of the tail comparable to the experimentally observed one. The results imply that the observed broadening of the tail of the UPS spectra in PEDOT provides information about a disordered spatially varying potential in the material rather than the broadening of the DOS itself.

Using highly efficient simulations of the tight-binding Bogoliubov-de Gennes model we solved self-consistently for the pair correlation and the Josephson current in a Superconducting-Bilayer graphene-Superconducting Josephson junction. Different doping levels for the non-superconducting link are considered in the short and long junction regime. Self-consistent results for the pair correlation and superconducting current resemble those reported previously for single layer graphene except in the Dirac point where remarkable differences in the proximity effect are found as well as a suppression of the superconducting current in long junction regime. Inversion symmetry is broken by considering a potential difference between the layers and we found that the supercurrent can be switched if junction length is larger than the Fermi length.

A tight-binding approach based on the Chebyshev-Bogoliubov-de Gennes method is used to describe disordered single-layer graphene Josephson junctions. Scattering by vacancies, ripples or charged impurities is included. We compute the Josephson current and investigate the nature of multiple Andreev reflections, which induce bound states appearing as peaks in the density of states for energies below the superconducting gap. In the presence of single atom vacancies, we observe a strong suppression of the supercurrent that is a consequence of strong inter-valley scattering. Although lattice deformations should not induce inter-valley scattering, we find that the supercurrent is still suppressed, which is due to the presence of pseudo-magnetic barriers. For charged impurities, we consider two cases depending on whether the average doping is zero, i.e. existence of electron-hole puddles, or finite. In both cases, short range impurities strongly affect the supercurrent, similar to the vacancies scenario