Quasiparticle Energy and Excitons in Two-Dimensional Structures

Two-dimensional materials, such as graphene-related structures, transition metal dichalcogenides, are attracting enormous interest in nowadays condensed matter physics. They not only serve as ideal testbeds for rich physics in reduced-dimensional electron systems but are also of particular importance in nanoelectronic technology. Their electronic, transport, and optical properties are largely determined by the nature of excited states, such as quasiparticles and excitons. Understanding how these excited states emerge from a many-electron system is an intriguing intellectual process, which gives insight into experimental observation and sheds light on manipulating the materials\u27 properties. From this aspect, it is highly desirable to introduce many-body perturbation theories, which do not rely on data from experiments, to study these excited-state properties and their relations to experimental measurements.In thisthesis, I will present a comprehensive study on a variety of two-dimensional materials using first-principles calculation with many-body effects taken into account. Particular attention is given to the impact of electrical gating, stacking order, and doping on the quasiparticle and excitonic properties

Topological kink states at a tilt boundary in gated multi-layer graphene

The search for new realization of topologically protected edge states is an active area of research. We show that a tilt boundary in gated multi-layer graphene supports topologically protected gapless kink states, associated with quantum valley Hall insulator (QVH). We investigate such kink states from two perspectives: the microscopic perspective of a tight-binding model and an ab-initio calculation on bilayer, and the perspective of symmetry protected topological (SPT) states for general multi-layer. We show that a AB-BA bilayer tilt boundary supports gapless kink states that are undeterred by strain concentrated at the boundary. Further, we establish the kink states as concrete examples of edge states of {\it time-reversal symmetric} ${\mathbb Z}$-type SPT, protected by no valley mixing, electron number conservation, and time reversal $T$ symmetries. This allows us to discuss possible phase transitions upon symmetry changes from the SPT perspective. Recent experimental observations of a network of such tilt boundaries suggest that transport through these novel topological kink states might explain the long standing puzzle of sub-gap conductance. Further, recent observation of gap closing and re-opening in gated bi-layer might be the first example of a transition between two distinct SPT's: QVH and LAF.Comment: Improved a discussion of the structural aspects of the tilt boundary. Included a discussion of boundary condition dependence. Added new section on connection to experiment