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Interdimensional effects in systems of fermions


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Over the past decade, new materials have been theoretically predicted and experimentally verified which are favourable candidates in the field of spintronics. These materials include topological insulators, graphene, and heterostructure materials with large Rashba spin-orbit coupling along an interface. In all of these materials, the electron's spin is responsible for exotic behaviour along either a surface or an interface. Interdimensional models have previously been used to analyze systems which contain low-dimensional substructures which affect the propagation properties of particles. In the case of a thin interface which affects propagation properties through a change in effective mass, and two-dimensional quantum well, analytic models allow for the calculation of the density of states inside the low-dimensional substructure. The density of states describes the availability of charge carriers in a given material, and is a fundamental quantity used to derive many other thermodynamic quantities of interest. Our principal focus is to extend the use of interdimensional models to study materials favourable for spintronics, and calculate analytic density of states for particles inside the low-dimensional substructure. We have analyzed nonrelativistic interdimensional models with Rashba spin-orbit coupling along an interface. We have extended these interdimensional models with the addition of a change in effective mass as well as attractive potential terms for motion in the interface. Topological crystalline insulators host linearly dispersing topological surface states, and present a system to construct a first quasirelativistic interdimensional fermion model. We have calculated the density of states at the location of the interface analytically in all models except the Rashba spin-orbit coupling plus effective mass system, in which numerical techniques are used. We report that in all systems with an effective mass term in the interface, the density of states has three-dimensional behaviour for low-energies transitioning to two-dimensional behaviour for high energies. Interdimensional models with Rashba spin-orbit coupling along the interface host both free and bound states contributions to the density of states. Bound states contribute terms proportional to the free two-dimensional density of states and free states contribute terms proportional to the free three-dimensional density of states. We have used experimental values from Bi/Ag heterostructure systems for our Rashba spin-orbit coupling models and PbTe in our quasirelativistic fermion model.



Fermion, quasirelativistic, density of states, interdimensional



Doctor of Philosophy (Ph.D.)


Physics and Engineering Physics




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