Publication Date


Document Type


First Advisor

Winkler, Roland

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

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.


229 pages




Northern Illinois University

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In Copyright

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