Two-dimensional van der Waals materials grow into a hot and big field in condensed matter physics in the past decade. One particularly intriguing thing is the possibility to stack different layers together as one wish, like playing a Lego game, which can create artificial structures that do not exist in nature.
These new structures can enable rich new physics from interlayer interaction: The interaction is strong, because in low-dimension materials electrons are exposed to the interface and are susceptible to other layers; and the screening of interaction is less prominent. The consequence is rich, not only from the extensive list of two-dimensional materials available nowadays, but also from the freedom of interlayer configuration, such as displacement and twist angle, which creates a gigantic parameter space to play with.
On the other hand, however, the huge parameter space sometimes can make it challenging to describe consistently with a single picture. For example, the large periodicity or even incommensurability in van der Waals systems creates difficulty in using periodic boundary condition. Worse still, the huge superlattice unit cell and overwhelming computational efforts involved to some extent prevent the establishment of a simple physical picture to understand the evolution of system properties in the parameter space of interlayer configuration.
In the first part of the dissertation, I will focus on classification of the huge parameter space into subspaces, and introduce suitable theoretical approaches for each subspace. For each approach, I will discuss its validity, limitation, general solution, as well as a specific example of application demonstrating how one can obtain the most important effects of interlayer interaction with little computation efforts. Combining all the approaches introduced will provide an analytic solution to cover majority of the parameter space, which will be very helpful in understanding the intuitive physical picture behind the consequence of interlayer interaction, as well as its systematic evolution in the parameter space.
Experimentally, optical spectroscopy is a powerful tool to investigate properties of materials, owing to its insusceptibility to extrinsic effects like defects, capability of obtaining information in large spectral range, and the sensitivity to not only density of states but also wavefunction through transition matrix element. Following the classification of interlayer interaction, I will present optical spectroscopy studies of three van der Waals systems: Two-dimensional few layer phosphorene, one-dimensional double-walled nanotubes, and two-dimensional graphene/hexagonal Boron Nitride heterostructure. Experimental results exhibit rich and distinctively different effects of interlayer interaction in these systems, as a demonstration of the colorful physics from the large parameter space. On the other hand, all these cases can be well-described by the methods developed in the theory part, which explains experimental results quantitatively through only a few parameters each with clear physical meaning. Therefore, the formalism given here, both from theoretical and experimental aspects, offers a generally useful methodology to study, understand and design van der Waals materials for both fascinating physics and novel applications.