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Abstract

The topological character of a semiconductor is governed by the parity of the conduction and valence band. In topological insulators, band topology is non-trivial, since the parity of the conduction and valence bands appears to be inverted compared to commonly known semiconductors. Under certain symmetry consideration, this inverted band parity leads to topological surface states (TSS).¹ No experimental assessment of this band inversion can be made using conventional experimental probes, apart from the observation of topological surface states, upon its occurrence. We tackle this problem and study the topological phase transition in (111)-Pb_1-xSn_xSe films grown by MBE having a high mobility (10⁴cm²/Vs) and low carrier density (<2x10¹⁸cm^-3) using magnetooptical IR Landau level spectroscopy. We show that in the massive Dirac system Pb_1-xSn_xSe, the topological character of the system, or equivalently the sign of its band-gap, can be experimentally determined by a precise measurement of the bulk Fermi velocity.² This is corroborated by the observation of a cyclotron resonance from topological surface states in the non-trivial regime and its suppression in the trivial regime. I will argue that our findings are likely to be universal to all material classes described by an effective Hamiltonian³ similar to that of Pb_1-xSn_xSe, and can be extended to other systems that host topological phase transitions, such as Pb_1-xSnxTe,⁴ Hg_1-xCd_xTe, Bi_2-xIn_xSe₃, Heusler topological insulators, and novel 3D Dirac semimetals. Our work paves the way to experimentally study the thermodynamics of topological phase transitions. 
 

1. B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006). 
2. B. A. Assaf, T. Phuphachong, V. V. Volobuev, G. Bauer, G. Springholz, L.-A. De Vaulchier, and Y. Guldner, arXiv 1608.08912.  
3. C. X. Liu, X. L. Qi, H. Zhang, X. Dai, Z. Fang, and S. C. Zhang, Phys. Rev. B 82, 045122 (2010).
4. B. A. Assaf, T. Phuphachong, V. V. Volobuev, A. Inhofer, G. Bauer, G. Springholz, L. A. de Vaulchier, and Y. Guldner, Sci. Rep. 6, 20323 (2016), T. Phuphachong, B.A. Assaf, V. V. Volobuev, A. Inhofer, G. Bauer, G. Springholz, L. A. de Vaulchier, and Y. Guldner ICPS proceedings, Beijing, China (2016).  
    

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