  We perform systematic angle-resolved photoemission spectroscopic measurements
on the lead tin telluride Pb1-xSnxTe pseudobinary alloy system. We show that
the (001) crystalline surface, which is a crystalline surface symmetric about
the (110) mirror planes of the Pb1-xSnxTe crystal, pos- sesses four metallic
surface states within its surface Brillouin zone. Our systematic Fermi surface
and band topology measurements show that the observed Dirac-like surface states
lie on the symmetric momentum-space cuts. We further show that upon going to
higher electron binding energies, the surface states' isoenergetic countours in
close vicinity of each X point are observed to hybridize with each other,
leading to a Fermi surface fractionalization and the Lifshitz transition. In
addition, systematic incident photon energy dependent measurements are
performed, which enable us to un- ambiguously identify the surface states from
the bulk bands. These systematic measurements of the surface and bulk
electronic structure on Pb1-xSnxTe, supported by our first principles
calculation results, for the first time, show that the Pb1-xSnxTe system
belongs to the topological crystalline insulator phase due to the four band
inversions at the L points in its Brillouin zone, which has been recently
theoretically predicted.
