The discovery of quantum Hall effect has motivated the use of topology instead of broken symmetry to classify the states of matter. Quantum spin Hall effect has been proposed to have a separation of spin currents as an analogue of the charge currents separation in quantum Hall effect, leading us to the era of topological insulators. Three-dimensional analogue of the Dirac state in graphene has brought us the three-dimensional Dirac states. Materials with three dimensional Dirac states could potentially be the parent compounds for Weyl semimetals and topological insulators when time-reversal or space inversion symmetry is broken. In addition to the single Dirac point linking the two dispersion cones in the Dirac/Weyl semimetals, Dirac points can form a line in the momentum space, resulting in a topological node line semimetal. These fascinating novel topological quantum materials could provide us platforms for studying the relativistic physics in condensed matter systems and potentially lead to design of new electronic devices that run faster and consume less power than traditional, silicon based transistors.

In this thesis, we present the electronic properties of novel topological quantum materials studied by angle-resolved photoemission spectroscopy (ARPES). In Chapter 1, we will lay the ground for understanding the topological quantum states in these materials. Chapter 2 will provide an introduction to the ARPES used in research presented in this thesis. ARPES results of unpublished projects such as Bi2Rh3S2, unpublished data such as PtSn4, and other materials such as CrAuTe4 will be discussed along with the description of the ARPES systems in Chapter 2. In Chapter 3, we will present the study of topological insulator (semimetal) candidate LaBi, where the Dirac cone at the Γ point is buried deeply inside the bulk spectrum and asymmetric massive states are acquired for top and bottom Dirac cones. Chapter 4 elucidates the three-dimensional Dirac state in Cd3As2 using fine tuning incident photon energies with energy step ∼ 0.15 eV, which provides kz dispersion with ultrahigh energy and momentum resolutions. Type-II Weyl semimetal candidate WTe2 displays a surprising temperature-induced Lifshitz transition. Furthermore, both “normal” and “topological” states have been observed in this material due to the fact that the electronic structure is very sensitive to strain and pressure. Detailed electronic structure of WTe2 including the surface Fermi arcs and three-dimensional bulk states will be discussed in detail in Chapter 5. In the last chapter (Chapter 6), we will present an unusual Dirac node arc structure in PtSn4 showing arcs instead of closed loops of Dirac nodes. The materials presented in this thesis are just a fraction of the known novel topological quantum materials, and more are yet to be discovered.