Electrons in free space have a well-defined mass. Recently, a new class of materials called topological insulators have been discovered, where the low energy electrons have zero mass. Amazingly, these electrons can be described by the same equation that is used to describe relativistic particles travelling close to the speed of light. These special electrons in topological insulators have the potential to be used in many applications such as quantum computation, spin-electronics and achieving disspiationless transport. In this talk I will describe our recent experimental investigations of one such class of materials called Topological Crystalline Insulators (TCIs) [1,2] where topology and crystal symmetry intertwine to create linearly dispersing Fermions. To study this material, we used a scanning tunneling microscopy (STM) which can be used to visualize quantum mechanical electron standing waves. We performed scanning tunneling microscopy (STM) studies at low temperatures and as a function of magnetic field [3,4,5] to reveal the existence of massless relativistic electrons in this system. Surprisingly, the STM data reveal the coexistence of zero mass Dirac fermions with massive Dirac fermions [3] in the same sample. Through our STM data, I will discuss the role that symmetry and topology play in these systems and I will reveal the conditions to obtain zero mass electrons as well the method to impart a controllable mass to these particles.

[1] L. Fu, Topological Crystalline Insulators. Phys. Rev. Lett. 106, 106802 (2011).

[2] T. H. Hsieh et al., Topological crystalline insulators in the SnTe material class. Nat.Commun. 3, 982 (2012).

[3] Y. Okada, et al., Observation of Dirac node formation and mass acquisition in a topological crystalline insulator, Science 341, 1496-1499 (2013)

[4] Ilija Zeljkovic, et al., Mapping the unconventional orbital texture in topological crystalline insulators, Nature Physics 10, 572–577 (2014)

[5] Ilija Zeljkovic, et al., Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators, Nature Materials 14, 318–324 (2015)