Site-Specific Contributions to the Band Inversion in a Topological Crystalline Insulator

In a topological crystalline insulator (TCI) the inversion of the bulk valence and conduction bands is a necessary condition to observe surface metallic states. Solid solutions of Pb$_{1-x}$Sn$_x$Te have been shown to be TCI, where band inversion occurs as a result of the band gap evolution upon alloying with Sn. The origins of this band inversion remain unclear. Herein the role of Sn insertion into the PbTe matrix is investigated for the $p$-type Pb$_{1-x}$Sn$_x$Te series with $x$ = 0, 0.35, 0.60, and 1.00 via nuclear magnetic resonance (NMR) and transport measurements. $^{207}$Pb, $^{119}$Sn, and $^{125}$Te line shapes, spin-lattice relaxation rates, and Knight shifts provide site-specific characterization of the electronic band structure. This probe of the electronic band structure shows that the band inversion is unaffected by lattice distortions but related to spatial electronic inhomogeneities formed by Sn incorporation into the PbTe matrix. Strong relativistic effects are found to be responsible for the band inversion, regardless of carrier type and concentration, suggesting a novel interpretation of the band gap evolution with composition. The temperature dependences of the NMR parameters reveal a negative temperature coefficient of the direct gap for SnTe and positive coefficient for PbTe.