Nanoscale four-point charge transport measurements in topological insulator thin films

Topological insulator (TI) materials, with their exotic electronic properties, cause a growing interest in modern solid state physics as promising systems for novel applications. This work presents the measurement and the analysis of characteristic transport properties of topological insulator films on the nanometer scale. The use of a multi-tip scanning tunneling microscope (STM) allows for position-dependent electrical measurements on the surface of the samples. For this purpose, the high degree of versatility of the individual tips is exploited to realize resistance measurements in dedicated configurations, even at the nanoscale. Chapter 2 presents an introduction into the operation principle of the instrument and the position-dependent four-point measurement technique. The fundamental relation between the measured resistance and the conductivity of the underlying system is derived. Furthermore, the outlined technique and its experimental capabilities are demonstrated on the example of a SrTiO$_{3}$ sample, which allows to comprehend the influence of dimensionality on the resistance. In chapter 3, a more sophisticated method of tip positioning based on overlaps of STM scans is presented. Using this method, it is possible to realize four-point measurement configurations on the nanoscale with considerable spatial precision. Chapter 4 provides an introduction into the material class of topological insulators, focusing on the origin of the associated characteristic properties. In chapters 5 – 7, nanoscale four-point resistance measurements on thin films of the strong topological insulator (Bi$_{1-x}$Sb$_{x}$)$_{2}$Te$_{3}$, enabled by the demonstrated positioning technique, are presented. Chapter 5 is focused on the electrical detection of the intrinsic spin polarization of the surface states of a TI. For this purpose, a ferromagnetic STM tip is used to extract the spin-dependent electrochemical potential of carriers during charge transport. Chapters 6 and 7 are dedicated to the topological phase transition of a 3D TI thin film into a quantum spin Hall (QSH) insulator system with reduced film thickness. In chapter 6, the necessary condition for such a phase transition, namely the interaction of the topological surface states on the two interfaces of the thin film, is studied by means of charge transport. Chapter 7 presents a measurement scheme for helical edge states, which are the sufficient condition for the formation of a QSH phase. [...