Topological insulators (TI) are a new phase of matter with very exotic electronic properties on their surface. As a direct consequence of the topological order, the surface electrons of TI form bands that cross the Fermi surface odd number of times and are guaranteed to be metallic. They also have a linear energy-momentum dispersion relationship that satisfies the Dirac equation and are therefore called Dirac fermions. The surface Dirac fermions of TI are spin-polarized with the direction of the spin locked to momentum and are immune from certain scatterings. These unique properties of surface electrons provide a platform for utilizing TI in future spin-based electronics and quantum computation. The surface bands of 3D TI can be directly mapped by angle-resolved photoemission spectroscopy (ARPES) and the spin polarization can be determined by spin-resolved ARPES. These types of experiments are the first to establish the 3D topological order, which demonstrates the power of ARPES in probing the surface of strongly spin-orbit coupled materials. Extensive investigation of TI has ranged from understanding the fundamental electronic and lattice structure of various TI compounds to building TI-based devices in search of more exotic particles such as Majorana fermions and magnetic monopoles. Surface-sensitive techniques that can efficiently disentangle the charge and spin degrees of freedom have been crucially important in tackling the multi-faceted problems of TI. In this thesis, I show that laser-based ARPES in combination with a time-of-flight spectrometer is a powerful tool to study the spin structure and charge dynamics of the Dirac fermions on the surface of TI. Chapter 1 gives a brief introduction of TI. Chapter 2 describes the basic principles behind ARPES and time-resolved ARPES (TrARPES). Chapter 3 provides a detailed account of the experimental setup to perform laser-based ARPES and TrARPES. In Chapters 4 and 5, how these two techniques are effectively applied to investigate two unique electronic properties of TI is elaborated. Through these studies, I have obtained a complete mapping of the spin texture of several prototypical topological insulators and have uncovered the cooling mechanism governing the hot surface Dirac fermions. / Physics

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Quantum dots exhibit strongly size-dependent optical and electrical properties. The ability to join the dots into complex assemblies creates many opportunities for scientific discovery. This motivated our present research work on QDIPs, DWELLs, and graphene like QDs. The intention of this research was to study the size dependent achievements of QDIPs, DWELLs, and graphene like QDs with those of competitive technologies, with the emphasis on the material properties, device structure, and their impact on the device performance. In this dissertation four research studies pertaining to optical properties of quantum dot and dot-in-a-well infrared photodetectors, I-V characteristics of graphene quantum dots, and energy and spin texture of germanene quantum dots are presented. Improving self-assembled QD is a key issue in the increasing the absorption and improving the performance. In the present research work, an ideal self-assembled QD structure is analyzed theoretically with twenty-hole levels (Intraband optical transitions within the valence band) and twenty-electron energy levels (DWELL). Continuing the efforts to study self-assembled QDs we extended our work to graphene like quantum dots (graphene and germanene) to study the electronic transport properties. We study numerically the intraband optical transitions within the valence band of InxGa1-xAs/GaAs pyramidal quantum dots. We analyze the possibility of tuning of corresponding absorption spectra by varying the size and composition of the dots. Both ‘x ’ and the size of the quantum dot base are varied. We have found that the absorption spectra of such quantum dots are more sensitive to the in-plane incident light. We present numerically obtained absorption optical spectra of n-doped InAs/In0.15Ga0.85As/GaAs quantum dot-in-a-well systems. The absorption spectra are mainly determined by the size of the quantum dot and have weak dependence on the thickness of the quantum well and position of the dot in a well. The dot-in-a-well system is sensitive to both in-plane and out-of-plane polarizations of the incident light with much stronger absorption intensities for the in-plane-polarized light. We also present theoretically obtained I-V characteristics of graphene quantum dots, which are realized as a small piece of monolayer graphene. We describe graphene within the nearest-neighbor tight-binding model. The current versus the bias voltage has typical step-like shape, which is due to discrete energy spectrum of the quantum dot. The current through the dot system also depends on the position of the electrodes relative to the quantum dot. In relation to graphene quantum dots, we present our study of buckled graphene-like materials, like germanene and silicene. We consider theoretically germanene quantum dot, consisting of 13, 27, and 35 germanium atoms. Due to strong spin-orbit interaction and buckled structure of the germanene layer, the direction of the spin of an electron in the quantum dot depends on both the electron energy and external perpendicular electric field. With variation of energy, the direction of spin changes by approximately 4.50. Application of external electric field results in rotation of electron spin by approximately 0.50, where the direction of rotation depends on the electron energy.