Electronic Correlations, Topology, and Unconventional Superconductivity in Twisted Bilayer Graphene

Abstract

Contemporary quantum materials research is guided by themes of topology - the idea that some material properties can be protected against continuous deformation - and of electronic correlations - the idea that the emergent behavior of a collection of electrons is complex and cannot be reduced to the sum of its parts. A natural confluence of these two themes can be engineered in so-called “moir´e materials”, an emerging class of two-dimensional (2D) materials produced by the rotational or lattice misalignment of atomically thin crystals. The prototypical example of this new paradigm is magic-angle twisted bilayer graphene (MATBG), where two atomically thin sheets of carbon, twisted to exactly 1.1 degrees relative to one another, hosts correlated insulating, magnetic topological, and unconventional superconducting states, none of which are found in graphene itself. In this thesis, I discuss a series of experiments that leverage the unparalleled capabilities of scanning tunneling microscopy / spectroscopy (STM / STS) to elucidate the microscopic underpinnings of MATBG. STM / STS is a powerful tool that can probe electronic dynamics with subatomic spatial resolution and unmatched energy resolution. We use STS as a novel thermodynamic sensor to identify a cascade of electronic transitions among correlated metallic phases, and as a novel probe of many-body topology to detect magnetic topological insulators in MATBG. We combine STS with point-contact spectroscopy to establish the unconventional nature of superconductivity in MATBG. Finally, we use the high-resolution imaging capabilities of the STM to probe the many-body wavefunctions of the correlated phases in MATBG, uncovering intricate atomic-scale patterns that encode important information about the origins of these phases.