UC Santa Barbara

Topological materials are an exciting new area of inquiry. These materials exhibit fundamentally new and nonlocal phenomena including spin-polarized surface states. More tantalizing is the prediction that an intrinsic topological superconductor could exhibit quasi-particles called Majorana anyons and provide the materials platform for building a quantum computer robust to many of the decoherence effects that plague competing quantum computation technologies. A scalable quantum computer would be able to solve many problems that are fundamentally intractable with current computing technologies and is hoped to provide a path towards understanding some of the most difficult contemporary physics questions such as the interaction of electrons in correlated systems.

While new topological materials---especially topological superconductors---are desired, design rules for predicting new topological metals are far from understood. Electronic materials discovery, especially in the laboratory, is largely driven by chemical understanding of the atomic bonding motifs in the crystalline structure that generate relevant electronic structure features. By modifying these motifs via chemical substitution and comparing with carefully constructed simulations, new topological materials are discovered and understood. Here, we present computational studies on five families of topological metals with varying functional properties, ranging from catalytic activity to complex magnetic ordering and superconductivity. In each study, emphasis is placed on the orbital origins of the predicted topological electronic structure.

The first part of the dissertation explores bonding interactions and electronic structure in three cubic metals: Na(Pd,Pt)3O4, Mn3ZnC, and LaIn3. Chapter 2 describes the bonding of palladium and platinum d orbitals with square-planar coordinating O p orbitals in NaPd3O4 and NaPt3O4. This unusual geometry generates an inversion of dx^2-y^2 and dz^2 bands, yielding an exotic nodal cube state that is a higher-degeneracy analog of a Dirac semimetal. Spin-orbit coupling effects partially fragment this cube, with stronger fragmentation in the Pt containing compound. Chapter 3 follows the electronic structure progression of antiperovskite Mn3ZnC, which transitions from a ferromagnetic room temperature phase to a distorted non-collinear magnetic structure at low temperatures. The electronic structure of this material can largely be understood in terms of Mn d bonding and magnetism. The ferromagnetic phase is shown to host topological Weyl nodes and surface states. The Weyl nodes are largely gapped and eliminated in the low temperature phase. The removal of Weyl nodes via structural distortion and antiferromagnetic ordering is likely common to a wider variety of Weyl metals. In chapter 4, the Fermi surface of auricupride LaIn3 is simulated and compared to experimental quantum oscillation measurements. The electronic structure is explained in terms of a simple tight-binding model involving only In p orbital interactions with close similarity to prior work on the ZrSiS family of square-net semimetals. While further experimental verification is needed, an initial survey suggests that LaIn3 hosts a wide variety of topological surface states.

The second part of the dissertation examines the electronic structure of three compounds, CsV3Sb5, GdV6Sn6, and YV6Sn6, in which the relevant electronic properties derive largely from the bonding of d orbitals on 2D kagome planes of vanadium atoms. Chapter 5 offers a careful comparison of simulation results to experimental X-ray diffraction and quantum oscillation measurements that track the charge density wave and electronic structure transitions that occur upon cooling crystals of CsV3Sb5. The charge density wave is shown to derive primarily from breathing-mode distortions of the vanadium kagome net, which are energetically favored in the DFT and qualitatively agree with the experimental structural solution and low frequency quantum oscillation signals. The predicted band reconstruction, combined with an earlier prediction of Z2 topological surface states in CsV3Sb5, suggest that surface states may be active at the Fermi level at the superconducting transition temperature, indicating that CsV3Sb5 is a promising intrinsic topological superconductor candidate. Chapter 6 details the synthesis of GdV6Sn6 and YV6Sn6 crystals, electronic structure predictions and initial comparison of the simulated electronic structure to experimental ARPES measurements. Like CsV3Sb5, these kagome metals are predicted to host Z2 topological surface states. The relevant electronic structure of these materials derives from V-V, V-Sn, and Sn-Sn bonding interactions. Substitution on the Gd/Y site provides additional magnetic tunability.