Electron interactions in 2D materials : excitons and quantum hall effect
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This dissertation presents studies of the electron interaction effects in two-dimensional materials. In particular, excitonic effect in transition metal dichalcogenides and quantum Hall effect in graphene have been investigated. The common thread that passes through the two topics is the interplay between electron interactions and spin and valley degrees of freedom. Chapter 1 is a brief introduction to the thesis. Chapter 2 addresses the energy and wave function of excitons in monolayer MoS$_2$. It reveals several interesting features, which can be important for exciton dynamics. Chapter 3 describes a theory of spatially indirect exciton condensates in transition metal dichalcogenide heterostructures. A systematic approach is developed to construct an effective exciton model with exciton-exciton interactions. The effective exciton model provides a useful guidance to construct the condensate phase diagram of excitons with multiple flavors. Chapter 4 identifies an SO(5) symmetry in the quantum Hall effect in graphene. The enlarged SO(5) symmetry unifies the spin antiferromagnetic order and valley $XY$ order. The physics of the SO(5) symmetry is explored using exact diagonalization and low-energy effective theory. Chapter 5 speculates about possible SU(3) and SU(4) singlet fractional quantum Hall states at a filling factor $\nu=2/3$ based on finite-size exact diagonalization study. These singlets are surprising because they are not captured by the composite fermion approach. The shift quantum number and the pair correlation function of the new states are presented.