Chichinadze, Dmitry2022-09-262022-09-262022-06https://hdl.handle.net/11299/241759University of Minnesota Ph.D. dissertation. 2022. Major: Physics. Advisor: Andrey Chubukov. 1 computer file (PDF); 209 pages.The topic of this dissertation is the problem of collective behavior of electrons in a particularlyinteresting quasi-two-dimensional material called twisted bilayer graphene (TBG), which is made by twisting two graphene layers with respect to each other. This materials exhibits peculiar phenomena such as superconductivity, correlated insulators, signatures of Anomalous Quantum Hall Effect, and the existence of cascade – a sequence of transitions into ordered non-superconducting states in the vicinity of integer filling of narrow bands. All those phenomena were observed in the low electron doping range, where only 8 narrow bands are filled. Small bandwidth of narrow bands puts this system in the intermediate coupling regime. This makes theoretical studies of TBG notoriously hard: neither strong-coupling, nor itinerant approach are perfect fit for the problem. The focus of this dissertation is the application of itinerant electron approach to the problem of electron correlations in TBG. This approach is valid at least away from the “magic” angle, i.e., in the region where the bandwidth of narrow bands is at least comparable to the interaction strength. We argue that electron correlation effects are stimulated by the presence of Van Hove singularities in electronic spectrum of TBG. Introducing patch models that account for electrons in the vicinity of Van Hove singularities we show that superconductivity and the cascade appear due to the unusual form of electron-electron interactions specific to TBG due to the special properties of its electronic bands. We investigate the emergent SU(4) symmetry that is crucial to the cascade and discuss the properties of superconducting state, which turns out to be nematic. We also discuss other implications of electron nematicity, as well as the relation of superconductivity and the cascade.enTBGTwisted bilayer grapheneThesis or Dissertation