Avoided level crossing at the magnetic field induced topological phase transition due to spin-orbital mixing

In 3D topological insulators, an effective closure of the bulk energy gap with increasing magnetic field expected at a critical point can yield a band crossing at a gapless Dirac node. Using high-field magnetooptical Landau level spectroscopy on the topological crystalline insulator Pb1-xSnxSe, we demonstrate that such a gap closure does not occur, and an avoided crossing is observed as the magnetic field is swept through the critical field. We attribute this anticrossing to orbital parity and spin mixing of the N=0 levels. Concurrently, we observe no gap closure at the topological phase transition versus temperature suggesting that the anticrossing is a generic property of topological phase transitions.