\n Electrons in free space have a well-defined mass. Recently\, a new c
lass of materials called topological insulators were discovered\, where th
e low energy electrons have *zero* mass. In fact\, these electrons
can be described by the same massless Dirac equation that is used to descr
ibe relativistic particles travelling close to the speed of light. In this
talk I will describe our recent experimental and theoretical investigatio
ns of a class of materials called Topological Crystalline Insulators (TCIs
) [1]. TCIs are recently discovered materials [2\,3] where topology and cr
ystal symmetry intertwine to create linearly dispersing Fermions similar t
o graphene. To study this material we used a scanning tunneling microscope
[3\,4\,5]. With the help of our high-resolution data\, I will show how ze
ro-mass electrons and massive electrons can coexist in the same material.
I will discuss the conditions to obtain these zero mass electrons as well
the method to impart a controllable mass to the particles and show how our
studies create a path to engineering the Dirac band gap and realizing int
eraction-driven topological quantum phenomena in TCIs.

\n \;< /p>\n

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

\n [2] T. H. Hsieh et al.\, Topolo
gical crystalline insulators in the SnTe material class. *Nat.Commun. <
/em>3\, 982 (2012).*

\n [3] Y. Okada\, et al.\, Observation of Dira
c node formation and mass acquisition in a topological crystalline insulat
or\, *Science* 341\, 1496-1499 (2013)

\n [4] Ilija Zeljkovi
c\, et al.\, Mapping the unconventional orbital texture in topological cry
stalline insulators\, *Nature Physics* 10\, 572&ndash\;577 (2014)\n

\n [5] Ilija Zeljkovic\, et al.\, Dirac mass generation from crysta
l symmetry breaking on the surfaces of topological crystalline insulators\
, *arXiv:1403.4906*