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) 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. 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.