ARPES Studies of Topological Materials

A review of spin- and angle-resolved photoemission on topological materials is presented, with a specific focus on results obtained by the author. This work is aimed at readers who are new to the field or those who wish to obtain an overview of the activities in the field with respect to spin-resolved measurements. The main focus lies on topological insulators, but also Weyl and other semimetals are discussed. Further it will be explained why the measured spin polarisation from a spin polarised state should always add up to 100% and how spin interference effects influence the measured spin texture.

Currently, there is a flurry of research interest on materials with an unconventional electronic structure, and we have already seen significant progress in their understanding and engineering towards real-life applications. The interest erupted with the discovery of graphene and topological insulators in the previous decade. The electrons in graphene simulate massless Dirac Fermions with a linearly dispersing Dirac cone in their band structure, while in topological insulators, the electronic bands wind non-trivially in momentum space giving rise to gapless surface states and bulk bandgap. Weyl semimetals in condensed matter systems are the latest addition to this growing family of topological materials. Weyl Fermions are known in the context of high energy physics since almost the beginning of quantum mechanics. They apparently violate charge conservation rules, displaying the 'chiral anomaly', with such remarkable properties recently theoretically predicted and experimentally verified to exist as low energy quasiparticle states in certain condensed matter systems. Not only are these new materials extremely important for our fundamental understanding of quantum phenomena, but also they exhibit completely different transport phenomena. For example, massless Fermions are susceptible to scattering from non-magnetic impurities. Dirac semimetals exhibit non-saturating extremely large magnetoresistance as a consequence of their robust electronic bands being protected by time reversal symmetry. These open up whole new possibilities for materials engineering and applications including quantum computing. In this review, we recapitulate some of the outstanding properties of WTe₂, namely, its non-saturating titanic magnetoresistance due to perfect electron and hole carrier balance up to a very high magnetic field observed for the very first time. It also indicative of hosting Lorentz violating type-II Weyl Fermions in its bandstructure, again first predicted candidate material to host such a remarkable phase. We primarily focus on the findings of our ARPES, spin-ARPES, and time-resolved ARPES studies complemented by first-principles calculations.

The band inversions that generate the topologically non-trivial band gaps of topological insulators and the isolated Dirac touching points of three-dimensional Dirac semimetals generally arise from the crossings of electronic states derived from different orbital manifolds. Recently, the concept of single orbital-manifold band inversions occurring along high-symmetry lines has been demonstrated, stabilising multiple bulk and surface Dirac fermions. Here, we discuss the underlying ingredients necessary to achieve such phases, and discuss their existence within the family of transition metal dichalcogenides. We show how their three-dimensional band structures naturally produce only small k_z projected band gaps, and demonstrate how these play a significant role in shaping the surface electronic structure of these materials. We demonstrate, through spin- and angle-resolved photoemission and density functional theory calculations, how the surface electronic structures of the group-X TMDs PtSe₂ and PdTe₂ are host to up to five distinct surface states, each with complex band dispersions and spin textures. Finally, we discuss how the origin of several recently-realised instances of topological phenomena in systems outside of the TMDs, including the iron-based superconductors, can be understood as a consequence of the same underlying mechanism driving k_z-mediated band inversions in the TMDs.

Nodal-line Dirac semimetals are a novel class of quantum materials, where valence and conduction bands form linearly dispersing cones that are degenerate along a closed line in the Brillouin zone. Recently, single-layer Cu₂Si was proposed as the first two-dimensional nodal-line semimetal. Here we demonstrate the formation of Cu₂Si encapsulated between a graphene layer and a Cu(1 1 1) substrate, and investigate the electronic states of this heterostructure. We find that the Cu₂Si-graphene interaction is negligible and show that, as a result, the graphene layer is electronically decoupled from the substrate.