  In newly discovered topological crystalline insulators (TCIs), the unique
crystalline protection of the surface state (SS) band structure has led to a
series of intriguing predictions of strain generated phenomena, from the
appearance of pseudo-magnetic fields and helical flat bands, to the tunability
of the Dirac SS by strain that may be used to construct "straintronic"
nanoswitches. However, practical realization of this exotic phenomenology via
strain engineering is experimentally challenging and is yet to be achieved. In
this work, we have designed an experiment to not only generate and measure
strain locally, but to also directly measure the resulting effects on the Dirac
SS. We grow heteroepitaxial thin films of TCI SnTe in-situ and measure them by
using high-resolution scanning tunneling microscopy (STM). Large STM images
were analyzed to determine picoscale changes in the atomic positions which
reveal regions of both tensile and compressive strain. Simultaneous
Fourier-transform STM was then used to determine the effects of strain on the
Dirac electrons. We find that strain continuously tunes the momentum space
position of the Dirac points, consistent with theoretical predictions. Our work
demonstrates the fundamental mechanism necessary for using TCIs in strain-based
applications, and establishes these systems as highly tunable platforms for
nanodevices.
