Electronic transport in SnTe based topological crystalline insulators

Tin telluride (SnTe) is a topological crystalline insulator: a variant of the well-known topological insulator class where the topological protection arises from crystal symmetries. The topological surface states (TSSs) have been experimentally observed in angle-resolved photoemission
spectroscopy and scanning tunneling microscopy measurements. Conclusive detection in electronic transport measurements remains a challenge, not in small part because of the high intrinsic bulk conductivity. This review summarizes recent progress in understanding the TCI phase in SnTe and related ternary compounds through a wide variety of electronic transport experiments, with magnetotransport as the workhorse. For example, using the Hall, weak antilocalization and Shubnikov–de Haas effects, system properties like carrier density, phase coherence, and the Fermi surface can be studied. However, disentangling contributions to the electronic transport originating from the bulk and the surface proves to be an omnipresent obstacle. Developments in transport experiments rely strongly on advances made in material engineering. Therefore, we put a spotlight on novel and improved synthesis methods, new nanostructuring approaches like selective-area growth, ultrathin films, and doping. Additionally, the interplay between the TSSs and magnetism, superconductivity and crystal perturbations can all result in nonlinear or emergent quantum phenomena or (higher-order) topological phase transitions. Especially the interplay between topology and (induced) superconductivity is of interest for anticipated applications in topological quantum computing, and is therefore a driving force behind the research on this material system. We have chosen to highlight experiments that pave the way for the exploration of
these more exotic quantum states and applications, in addition to an overview and assessment of the seminal works on the material system. Together, these findings illuminate the challenges and opportunities in surface state transport in SnTe-based topological materials.