How to construct effective Hamiltonians for moiré materials

Johannes Lischner

Imperial College London



Since the discovery of correlated insulator states and unconventional superconductivity in twisted bilayer graphene in 2018, there has been an intense effort to understand the electronic properties of moiré materials. However, the combination of large supercells (containing more than 10,000 atoms for magic-angle twisted bilayer graphene) and strong electron correlations makes the theoretical description of this new class of materials highly challenging. Standard strong correlation techniques for real materials are often based on downfolded effective Hamiltonians where the number of degrees of freedom is greatly reduced compared to full first-principles models. Generating accurate effective Hamiltonians, however, is a difficult task even for materials with few atoms in the unit cell. In this talk, I will try to give a pedagogical introduction into procedures for developing effective Hamiltonians from first-principles techniques and describe how these methods must be extended for the description of moiré materials.

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