# Final PhD Oral Examination (Thesis Title: “Scanning Tunnelling Microscopy of Topological Materials”)

**Abstract: **

Topological materials have been at the forefront of condensed matter physics research over the past few decades. Characterised by electronic bands with non-trivial topological invariants, topological materials exhibit a number of interesting electronic properties, such as conducting chiral boundary states and linear electronic dispersions, and have been theorised for use in a variety of applications ranging from spintronic devices to quantum computing. Recently, topological semimetals were discovered, where the bulk electronic bands are understood in the framework of the high-energy relativistic Dirac equation and its conditional variations, the Weyl and Majorana equations. Furthermore, the vast permutations of material compounds available results in a nearly infinite sandbox for researchers to study, which has resulted in topological semimetals that have no high-energy analogue. One of such material classifications is the nodal-line semimetal, characterised by linear electronic band crossings that form lines or loops in momentum space. These nodal-line semimetals also exhibit exotic surface states, named drumhead states, which are an interesting and exciting new state with promises in high-temperature superconductivity and quantum computation. A large effort is being placed to find materials that can be used to study the fundamental properties of these materials and their resultant surface states.

Scanning tunnelling microscopy (STM) provides a perfect tool to study the topological properties of materials, able to atomically resolve the surface structure and also provide insight into scattering selection rules, which are deeply dependent on the band topology. Two topological materials were studied using STM in this thesis: the topological nodal-line semimetal ZrSiTe and the topological insulator (Bi$_x$Sb$_{1-x}$)$_2$Te$_3$. ZrSiTe was studied with an emphasis on the quasiparticle scattering characteristics, measured using Fourier-transform scanning tunnelling spectroscopy. Two main scattering features are examined, one relating to the nodal line, and the other arising from the drumhead surface state. These studies mark the first time a drumhead state has been observed using a real space measurement. (Bi$_x$Sb$_{1-x}$)$_2$Te$_3$ was studied with an emphasis on the nano-scale transport characteristics, measured using 4-probe STM and scanning tunnelling potentiometry. Effects of step edges and domain boundaries on the local resistance are studied for a fractional substitution of $x = 0.19$.