Robust Platforms for Superconductivity : Disorder Robustness and Topological Density of States Peaks

Abstract: We explore the connection between robust material platforms for superconductivity and the modern condensed matter physics paradigms of two-dimensional materials, topological states of matter, and odd-frequency superconductivity. Specifically, the recent discoveries of gapless topological matter and truly two-dimensional materials with graphene have greatly expanded the class of materials for which topology produces large, robust, even singular, density of states (DOS) peaks in the electronic structure that in turn are highly susceptible to new ordered states of matter, including superconductivity. In this thesis, we address the crucial question of superconductivity and competing orders near such DOS peaks, in addition to the stability of unconventional superconducting orders towards disorder. We show that DOS peaks are not only highly conducive to ordered states, but also that they are particularly favorable for superconductivity. We show that superconducting domes are especially likely to appear near DOS peaks. The result is fundamental, and stems from an inherent difference between the ordering susceptibilities towards superconductivity and all competing orders, providing a distinctive advantage for superconductivity. The result has relevance for several concrete material platforms that we consider further, including graphene doped to the van Hove singularity, magic angle twisted bilayer graphene, and rhombohedral graphite with its topological protected flat bands surface states. In both single layer and in magic angle twisted bilayer graphene, the symmetry of the lattice promotes unconventional d-wave superconductivity with either a time-reversal-breaking d+id chiral or a nematic symmetry. In the single graphene sheet, the chiral state is ubiquitously favored, while as we show, using full-scale atomistic modeling capturing the long-ranged moiré patterns, a nematic ordering is unexpectedly dominant in twisted bilayer graphene. Furthermore, we show that that d+id-wave state in graphene close to the van Hove doping is remarkably disorder robust, despite the unconventional pairing, with a robustness that is comparable to a conventional superconducting state. Likewise, we show that a proximity induced odd-frequency p-wave pairing in a normal-superconducting junction is not only robust to disorder, but is in fact generated by such disorder, demonstrating again an unexpected interplay between order symmetry and robustness. Alongside with method development for finite time-correlations in superconductors, our results points towards new and unconventional platforms for realizing robust superconductivity.