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Narrow gap semiconductor Pb$_{1-x}$Sn$_{x}$Se was investigated fortopologically protected surface states in its rock-salt structural phase forx=0.45, 0.23, 0.15, and 0. Angle-resolved photoelectron spectroscopy ofintrinsically p-doped samples showed clear indication of two Dirac cones,eccentric about the time-reversal invariant point X of the surface Brillouinzone for all but the x=0 sample. Adsorption of alkalies gradually filled thesurface bands with electrons, driving the x>0 topological crystalline insulatorsystems through Lifshitz transitions, and from a hole- to electron-like Fermisurface. The electron-doped bands in x>0 samples exhibited the fullconfiguration of the Dirac cones, also confirming electron-hole symmetry of thesurface bands.

Inducing Lifshitz transition by extrinsic doping of surface bands in topological crystalline insulator Pb$_{1-x}$Sn$_{x}$Se