An efficient new method is presented to calculate the quantum transports using periodic boundary conditions. This method allows the use of conventional ground state ab initio programs without big changes. The computational effort is only a few times of a normal ground state calculations, thus is makes accurate quantum transport calculations for large systems possible.

Two-dimensional (2D) materials have drawn tremendous research interest ever since the isolation of graphene in 2004. Due to weak Van der Waals bonding between layers, 2D ma- terials can be stacked together to form synthetic heterostructures with emergent electronic and excitonic properties. Recently, there has been great research interest in controlling the twisting angle between different layers to further control the material properties. One inter- esting case is when the system forms moir ́e superlattices. In this thesis, I focus on optical studies on one of the model moir ́e superlattices—transition metal dichalcogenides (TMD) based WS2/WSe2 moir ́e superlattices. With their strong light-matter interactions and large spin-orbital splitting, this system provides a unique opportunity to optically detect and ma- nipulate the correlated quantum states of matter. Our studies show important influence from the moir ́e potential on TMD’s optical properties and illustrate how we can utilize TMD’s unique properties to study interesting phases in moir ́e superlattices.In the first chapter, I will give a brief introduction to moir ́e superlattices and exciton states in WS2/WSe2 and their heterostrcutures. Following chapters consist of a series of studies we conducted on the system. Chapter 2 focuses on interlayer exciton states in WS2/WSe2 moir ́e superlattcies and their novel selection rules. Combining senstive measurements of pump probe spectroscopy and photoluminescence excitation, we identified different components in their selection rule and uniquely determine their quasi-angular momentum. Chapter 3 shows how we can utilize the intralayer exciton states in TMDs to detect strongly correlated insulating states in moir ́e superlattcies. We observed generalized Wigner crystal states that confirms the very strong correlation in WS2/WSe2 moir ́e superlattcies. In Chapter 4, I discuss our study on intralayer exciton states near correlated phases. With doping dependent aborption spectrum, we observed sharpening of the exciton states near correlated states. This indicates the changing of dielectric environments for these exciton states and other potentially interesting interactions between the insulating states and exciton states. In Chapter 5, I describe the spin-valley current in WS2/WSe2 moir ́e superlattices. We used spatially-resolved pump probe spectroscopy to create and detect pure spin-valley current. We observed much smaller mobility in the moir ́e superlattcies than large twist angle heterostructures, indicating strong moir ́e potential might impede the motion of spin. Since the mobility stays flat near correlated insulating phases while the electron conductivity dramatically changes, the system shows spin charge separation.

We present a novel linear scaling ab initio total energy electronic structure calculation method, which is simple to implement, easily to parallelize, and produces essentially the same results as the direct ab initio method, while it could be thousands of times faster.