In the past few decades, low dimensional materials have received extensive attention for their remarkable features and promising applications in nanoelectronics, optoelectronics, quantum computing, quantum communication, etc. To investigate the rich physics inside, abundant theoretical models were built to explore quantum effects present in low dimensional materials. The development of these theories have been far ahead the experimental realizations. Feymann[1] suggested that simulating these quantum models in controllable real systems could lead to a better understanding. In this thesis, several real systems, such as metal-organic frameworks and moiré heterostructures, are demonstrated as good quantum simulators beyond ultracold gases of bosonic and fermionic atoms. Based on first-prin...[ Read more ]

In the past few decades, low dimensional materials have received extensive attention for their remarkable features and promising applications in nanoelectronics, optoelectronics, quantum computing, quantum communication, etc. To investigate the rich physics inside, abundant theoretical models were built to explore quantum effects present in low dimensional materials. The development of these theories have been far ahead the experimental realizations. Feymann[1] suggested that simulating these quantum models in controllable real systems could lead to a better understanding. In this thesis, several real systems, such as metal-organic frameworks and moiré heterostructures, are demonstrated as good quantum simulators beyond ultracold gases of bosonic and fermionic atoms. Based on first-principles calculations, the experimental observations in such systems are explained based on various quantum models: in the first project, the structural and electronic properties of VI₃ are discussed by comparing with the experimental Raman spectra. The Dirac type magon with nontrivial bosonic topology is further investigated based on Heisenberg spin Hamiltonians. In the second project, an antiferroelastic one-dimensional spin crossover chain is demonstrated to behave collective domino-like switching. A simple 1+1 model is further proposed to fit the phase diagram. In the third project, two-dimensional metal-organic network Fe-HITP is presented to exhibit a ferromagnetic ground state with several topological nontrivial gaps opened due to the spin−orbit coupling, signifying quantum anomalous Hall features. This work implies that metal-organic frameworks could provide a versatile simulation platform to mimic topological quantum states. At last, the hourglass fermion protected by screw rotation is predicted in twisted bilayer SnS. These results would broaden the landscape of accessible physics in twisted layered systems to include the broad realm in topologic semimetals and may motivate further topology and valleytronics related researches in moiré heterostructures.

Keywords: Low dimensional materials, quantum simulators, first-principles calculations, topological materials, metal-organic frameworks, spin crossover, moiré heterostructures