  Orbital degrees of freedom can have pronounced effects on the fundamental
properties of electrons in solids. In addition to influencing bandwidths, gaps,
correlation strength and dispersion, orbital effects have also been implicated
in generating novel electronic and structural phases, such as Jahn-Teller
effect and colossal magnetoresistance. In this work, we show for the first time
how the orbital nature of bands can result in non-trivial effects of strain on
the band structure. We use scanning tunneling microscopy and quasiparticle
interference imaging to study the effects of strain on the electronic structure
of a heteroepitaxial thin film of a topological crystalline insulator, SnTe. We
find a surprising effect where strain applied in one direction affects the band
structure in the perpendicular direction. Our theoretical calculations indicate
that this effect directly arises from the orbital nature of the conduction and
valance bands. Our results imply that a microscopic model capturing strain
effects on the band structure must include a consideration of the orbital
nature of the bands.
