Interactions between the microscopic constituents of many-body quantum systems are a fundamental challenge in condensed matter physics. The inconceivable complexity associated with the mutual attraction and repulsion among the myriad of particles necessitates formulations of effective models capturing a minuscule, yet determining, fraction of the dynamics. However, the intricacy of the microscopic interactions also leads to fascinating many-body quantum phases of matter.

This thesis will investigate a variety of phenomena arising in electronic ground states driven by microscopic interactions. A study of the novel compound magic-angle twisted bilayer graphene will examine the topic from a fundamental perspective, where purely interaction-induced ordered phases will be identified in an effective superlattice model of the twist-angle-generated moiré pattern. The results will be obtained by unrestricted selfconsistent solutions to the Hartree-Fock approximated interactions of the effective low-energy Wannier orbitals exhibiting fragile topology. The fragile topology causes non-negligible hopping-like interaction terms to appear in the effective model and induces non-trivial topological Chern insulators at all integer filling factors of the low-energy bands. It will be shown that these Chern insulating phases are in excellent agreement with results obtained by quantum Monte Carlo and density matrix renormalization group simulations justifying the applicability of the Hartree-Fock approach. Additional charge, spin, or valley density wave orders will be presented, the latter being reminiscent of the Kekulé spiral reported in other magic-angle twisted bilayer graphene studies.

Furthermore, this thesis will provide insight into effects arising from the presence of defects in microscopically ordered states. In particular, the response to defects, both in the form of multiple atomic impurities and dislocation-induced lattice relaxation, in unconventional superconductors will be investigated. The studies will assume an attractive nearest-neighbor superconducting pairing mechanism to be present and compute selfconsistent mean-field simulations of the bond-pairings on the imperfection-modified lattice. The results provide evidence for a general notion of defect-induced spontaneous time-reversal symmetry breaking generated by local loop currents in an otherwise timereversal symmetric superconductor. The notion questions the current interpretation of experimental evidence for time-reversal symmetry breaking as a global order in unconventional superconductors. Finally, a study on impurity-assisted detection of global symmetry-preserving anti-ferro-orbital order in an unconventional superconductor will be presented. Employing a T -matrix approach, theoretical computations will predict an interesting superconductivity-enhanced response in the quasiparticle interference anisotropy originating from the local orbital order and emerging in the vicinity of singleatom impurities. The predictions are corroborated by scanning tunneling microscopy measurements on Co-terminated CeCoIn5. The findings suggest that the method could be utilized to detect other, thus far, hidden orders in unconventional superconductors.