I will discuss some of our recent work aimed at understanding the electronic structure and spectroscopy of novel superconductors, topological materials, and atomically thin 2D films beyond graphene. [1-6] Illustrative examples will include: (i) How by exploiting electronic structure techniques we have been able to successfully predict and understand the characteristics of many new classes of binary, ternary and quaternary topologically interesting materials, including topological crystalline insulators and Weyl and other more exotic semi-metallic topological phases; (ii) How atomically thin ‘beyond graphene’ 2D and layered materials offer exciting new possibilities for manipulating electronic structures and provide novel platforms for fundamental science and applications; (iii) With regard to the high-Tc’s, I will discuss recent breakthroughs in modeling first-principles the insulating pristine compounds and the transition from the insulating to the metallic state with doping without invoking any free parameters such as U. A first-principles description of the competing stripe and magnetic phases in the cuprates also then becomes possible, providing a new pathway for modeling correlated materials more generally.
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