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Recently, two stacked sheets of graphene with a slight relative twist, called twisted bilayer graphene, emerged as a promising system for the study of electron-electron interactions. At an angle of about 1.1°, the twist induced long-range Moiré pattern was found to result in a suppression of the kinetic energy of the electrons, which enhances the formation of correlated phases. Such correlated behavior of electrons is believed to be responsible for the observed high-temperature superconductivity in cuprates and holds out the possibility for exotic electronic behavior required for novel applications like quantum information processing. Thus, the acquisition of an understanding and the characterization of such materials is of great importance for future developments in this field. We perform an extensive exact diagonalization study of interaction driven insulators in the twisted bilayer graphene on hexagonal boron nitride Moiré heterostructure. Contrary to previous studies, we can not only confirm the formation of a fractional Chern insulator but also reveal translational symmetry breaking charge-density-waves to prevail in the thermodynamic limit at multiple fractional fillings of a realistic single-band model. A thorough analysis at different interlayer hopping parameters, motivated by experimental variability, and the role of kinetic energy at various Coulomb interaction strengths highlight the competition between these phases. The interplay of the single-particle and the interaction induced hole dispersion with the inherent Berry curvature of the Chern bands is intuitively understood to be the driving mechanism for the ground-state selection., Author: Patrick Wilhelm, B.Sc., Masterarbeit University of Innsbruck 2020

Recently, two stacked sheets of graphene with a slight relative twist, called twisted bilayer graphene, emerged as a promising system for the study of electron-electron interactions. At an angle of about 1.1°, the twist induced long-range Moiré pattern was found to result in a suppression of the kinetic energy of the electrons, which enhances the formation of correlated phases. Such correlated behavior of electrons is believed to be responsible for the observed high-temperature superconductivity in cuprates and holds out the possibility for exotic electronic behavior required for novel applications like quantum information processing. Thus, the acquisition of an understanding and the characterization of such materials is of great importance for future developments in this field. We perform an extensive exact diagonalization study of interaction driven insulators in the twisted bilayer graphene on hexagonal boron nitride Moiré heterostructure. Contrary to previous studies, we can not only confirm the formation of a fractional Chern insulator but also reveal translational symmetry breaking charge-density-waves to prevail in the thermodynamic limit at multiple fractional fillings of a realistic single-band model. A thorough analysis at different interlayer hopping parameters, motivated by experimental variability, and the role of kinetic energy at various Coulomb interaction strengths highlight the competition between these phases. The interplay of the single-particle and the interaction induced hole dispersion with the inherent Berry curvature of the Chern bands is intuitively understood to be the driving mechanism for the ground-state selection., Author: Patrick Wilhelm, B.Sc., Masterarbeit University of Innsbruck 2020