Manifestations of topological order in bulk properties

The interplay between band theory and topology has revolutionized our understanding of semiconductors. When a semiconductor has inverted orbital ordering, it was shown that relativistic Dirac states emerge at its surface. This inverted band ordering is topologically distinct from the normal ordering found in conventional semiconductors such as GaAs, Si or PbSe. The Dirac surface states have long been thought to be the only manifestation of this topologically distinct character.

In a recent article published in Physical Review Letters (Phys. Rev. Lett. 119 106602 (2017)), the infrared magnetospectroscopy group at Laboratoire Pierre Aigrain and the ENS Physics Department along with collaborators from Johannes Kepler University of Linz in Austria and BESSY-II in Berlin demonstrate manifestations of non-trivial topology in bulk 3D electron transport at high magnetic fields in Pb1-xSnxSe semiconductor alloys. They thereby challenge the long-held paradigm that surface states are the only manifestation of non-trivial band topology.

They show that a strong magnetic field can significantly impact the energy gap and electronic transport of topological materials. In relativistic terms, the energy gap is related to the mass of the electrons. The team demonstrate that as the magnetic field increases, the electron mass becomes lighter, the carrier group velocity is thus enhanced and the resistance of the material drops. This is only true in topological materials. In trivial materials, the field enhances the electron mass, and the resistance of the material increases with increasing magnetic field, as normally expected.

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This achievement complements a previous realization of the team and their collaborators, where they showed that the topological index of a material can be measured by precisely quantifying the velocity of its Dirac fermions. Nature Partner Journals Quantum Materials 2 26 (2017). Both works contribute to the teams effort to study the topological phase diagram of (Pb,Sn) based topological insulator and to identify novel quantum phases that can appear at high fields, and upon quantum confinement.

This work was highlighted by the editors among their suggestions for exceptional articles that appeared in Physical Review Letters. The work is partly supported by the LabEx ENS-ICFP.