Electronic structure studies on p-type Pb$_{1-x}$Sn$_x$Te system above and below the band inversion topological transition*

We present systematic ARPES studies on p-type Pb$_{1-x}$Sn$_x$Te samples at three different compositions with x = 0.26, 0.5, and 1.0. This material has been predicted as a topological crystalline insulator (TCI) upon band inversion at $x\simeq0.3$. We show that the observed bulk valence band is a single hole-like band in the vicinity of the $\mathrm{\overline{\textit{X}}}$ points of the surface Brillouin zone, and reveal the 3D dispersive nature of the valence band with a clear $k_z$ dispersion. We further show that despite the predicted band inversion and topological phase transition, the observed valence band electronic structure does not exhibit dramatic difference between these samples, demonstrating the critical importance of preparing in-gap or n-type samples for the realization of the TCI phase.