Electronic Structure and Transport in Correlated and Complex Materials

This dissertation has two parts. The first part provides studies on superconducting systems. The electronic structure and superconducting gaps have been investigated in detail in the multi-orbital iron-based superconducting system with the help of experimental scanning tunneling microscopy results. The results provide quantitative information about the magnitude of the superconducting gaps and hence give important insight to the electron pairing mechanism in these materials. This work also shows that the Josephson current calculation provides a unique pathway to map the spatial variation of the magnitude and phase of the superconducting order parameter in iron-based superconductors in absence of magnetic field and in simple s-wave superconductors in presence of magnetic field. The second part of the dissertation contains study of nano-scale transport networks. This work shows the concept of equivalent resistor in coherent quantum regime through the establishment of Transport Equivalent Networks for various classes of transport networks. This work presents a unique direction for future nano electronics in terms of miniaturization of electronic-circuits.