  The newly discovered topological crystalline insulators (TCIs) harbor a
complex band structure involving multiple Dirac cones. These materials are
potentially highly tunable by external electric field, temperature or strain
and could find future applications in field-effect transistors, photodetectors,
and nano-mechanical systems. Theoretically, it has been predicted that
different Dirac cones, offset in energy and momentum-space, might harbor vastly
different orbital character, a unique property which if experimentally
realized, would present an ideal platform for accomplishing new spintronic
devices. However, the orbital texture of the Dirac cones, which is of immense
importance in determining a variety of materials properties, still remains
elusive in TCIs. Here, we unveil the orbital texture in a prototypical TCI
Pb$_{1-x}$Sn$_x$Se. By using Fourier-transform (FT) scanning tunneling
spectroscopy (STS) we measure the interference patterns produced by the
scattering of surface state electrons. We discover that the intensity and
energy dependences of FTs show distinct characteristics, which can directly be
attributed to orbital effects. Our experiments reveal the complex band topology
involving two Lifshitz transitions and establish the orbital nature of the
Dirac bands in this new class of topological materials, which could provide a
different pathway towards future quantum applications.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics;Materials Science