Ph.D. (Doctor of Philosophy)
Department of Physics
Due to their extraordinary mechanical, and fascinating electronic properties, atomically flat two-dimensional materials are attractive avenues in the search for new and interesting physical phenomena. Symmetry is a powerful tool in studying the dynamics of Bloch electrons in these crystalline solids. Here, using a tight binding description, a systematic scheme is developed to derive the symmetry labels, called irreducible representations (IRs), characterizing the Bloch eigenstates in a crystal, including an extensive discussion on the possibility that these IRs are not always unique. This theory is illustrated using monolayer MoS$_2$ and few-layer graphene as examples. Using this symmetry analysis in conjunction with the theory of invariants, a generic multiband Hamiltonian for monolayer MoS$_2$ is constructed, which incorporates the effects of spin-orbit coupling, strain and external electric and magnetic fields. In a two-band model, and restricting the system to one dimension, the spin-dependent effective Hamiltonian is found to be applicable to other quasi one-dimensional systems, i.e.\ all of these systems can be described by the same Dirac-like Hamiltonian. Hence, spin-dependent observable effects in one of these systems have counterparts in each of the other systems. Effects discussed in more detail include equilibrium spin currents, current-induced spin polarization (Edelstein effect), and spin currents generated via adiabatic spin pumping.
Fajardo, Edward Aris Diaz, "Two-Dimensional Bloch Electrons in Electric and Magnetic Fields" (2019). Graduate Research Theses & Dissertations. 7021.
Northern Illinois University
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