Inversion Asymmetry, Flavortronics, and Nonlinear Optics in Two-dimensional Materials

Interests in two-dimensional (2D) materials have grown tremendously after the successful isolation of a single layer graphene. The properties of 2D materials are often very different from their 3D counterparts. They offer great flexibilities in tuning their electronic and optical properties through numerous ways. For example, electronic properties not only greatly vary with the number of layers in the materials, they can also depend strongly on the relative twists among different layers. Besides scientific advances and discoveries, these findings have led to enormous efforts being put in band gap engineering and the more recent moir ́e engineering to ensure that they fulfill their unprecedented potential in technological applications. In this dissertation, we study this emerging and exciting platform. Our era of electronics is made possible through advances in semiconductor technology based on the precise manipulation of electronic charge degree of freedom. However, there are additional degrees of freedom, such as spin, layer and valley, that electrons in materials may possess. Methods to fabricate workable devices based on the manipulation of these degrees of freedom to process and store information have been extensively studied in the literature. Here, we take a step further. We consider another degree of freedom, SU(3) flavor, that exists in the so-called Q-valleys of n-type few-layer transition metal dichalcogenides. In the quantum Hall regime, Landau levels form triplets that are each three-fold degenerate. When each Landau level triplet is one-third filled or empty, we predict that a pure flavor nematic phase and a flavorless charge-density-wave phase will occur respectively below and above a critical magnetic field. Electrons carry flavor-dependent electric dipole moments even at zero magnetic field, giving rise to a nematic ferroelectric state. We further show that the flavor degree of freedom can be manipulated by an electric field, leading to a new concept: flavortronics. The local density of states of electrons in materials will be modified when they are scattered off impurities. This results in quasiparticle interference (QPI) that can be probed by scanning tunneling spectroscopy. We then study QPI of Q-valley electrons scattering off localized non- magnetic and magnetic impurities. More importantly, we propose that QPI provides a way to observe the above predicted nematic ferroelectric state. Finally, we study a moir ́e metamaterial, namely twisted double bilayer graphene (TDBG). The electronic and optical properties in twisted multilayer systems are very different from the single layer counterpart. The highly tunable quantum geometric properties of TDBG give rise to tunable photoresponses that are closely related to the polarization states, power and wavelength of the incident light. This close relationship enables us to generate a set of photovoltage maps that can be used to train a convolutional neural network to decode the properties of an unknown incoming light from its unique photovoltage map. This enables an unprecedented intelligent light sensing in an extremely compact, on-chip manner.