UC Santa Barbara

Thin films are fertile ground in the study of so-called topological materials.Electrostatic gating, quantum confinement, and strain engineering afford separate degrees of control over the bulk band structure and, as a result, the presence of topological surface states, and are candidate routes toward engineering more exotic, correlated topological states. Cadmium arsenide is a topological material that affords such possibilities. It is called a 3D Dirac semimetal because, in its electronic structure, the crossing of spin-degenerate bands generates low-energy physics resembling that of the Dirac equation, with a linear dispersion in three dimensions. These Dirac nodes, as the crossings are called, can be manipulated to realize different topological phases.

One part of this dissertation describes the growth of thin films of cadmium arsenide of a particular orientation, (001), previously unstudied, using molecular beam epitaxy.The films' morphology, crystal structure, and orientation are investigated with x-ray diffraction, x-ray reflectivity, and atomic force microscopy alongside results from scanning transmission electron microscopy. (001)-oriented films are of special interest because, in the (001) surface Brillouin zone, the 3D Dirac nodes project onto the same point, resulting in a surface state different from those on every other surface.

The rest of the dissertation focuses on studies of the quantum Hall effect in these films. Transport through the (001) surface states is observed and studied in the quantum Hall regime, where the sequences of filling factors, as a function of magnetic field and carrier density in the film, reveal the Dirac nature of these two-dimensional surface states.The picture of the cadmium arsenide (001) film, then, as a three-dimensional topological insulator, is developed with reference to its band structure, with help from an effective model of its surface states. This picture is tested experimentally via the evolution of the quantum Hall effect in films of diminishing thickness. This evolution is contrasted with the predictions of an alternative model for the film's electronic structure based on subband confinement. These growth and transport studies establish cadmium arsenide not just as a topological insulator of notably high carrier mobility, but as a versatile platform for studying and realizing topological phases in thin films.