Mirror-symmetry protected quantization of Berry phases and resulting magnetoresistance across the topological transition in Pb$_{1-x}$Sn$_{x}$Se

Alexander Kazakov, Wojciech Brzezicki, Timo Hyart, Bartłomiej Turowski, Jakub Polaczyński, Zbigniew Adamus, Marta Aleszkiewicz, Tomasz Wojciechowski, Jarosław J. Domagała, Andrei Varykhalov, Gunther Springholz, Tomasz Wojtowicz, Valentine V. Volobuev, Tomasz Dietl

Published 2020-02-18Version 1

Quantization of geometrical phases accounts for phenomena, such as the Aharonov-Bohm effect and Bohr-Sommerfeld quantization of energy levels, which are hallmarks of quantum physics. It has more recently been realized that the quantized value of the Berry phase $\varphi=\pi$, if evaluated over a proper trajectory in the Brillouin zone, points to the presence of topological surface states. Similarly, positive magnetoresistance, resulting from weak antilocalization (WAL) when the spin-orbit diffusion length is much shorter than phase breaking length, is taken as evidence that the Berry phase evaluated along the Fermi cross section is quantized as $\varphi=\pi$. Here, we consider the case of cubic lead-tin monochalcogenides and demonstrate, both theoretically and experimentally, that the quantization of $\varphi$ results from the crystalline mirror and time-reversal symmetries. We show that the observed magnetoresistance behaviour follows the theory prediction that Berry phase is quantized to $\varphi=\pi$ for both topologically trivial and non-trivial materials and becomes non-quantized by intentionally breaking the mirror symmetry with an additional amorphous layer.