Emergence of topological semimetals in gap closing in semiconductors without inversion symmetry

Shuichi Murakami, Motoaki Hirayama, Ryo Okugawa, Takashi Miyake

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


Aband gap for electronic states in crystals governs various properties of solids, such as transport, optical, andmagnetic properties. Its estimation and control have been an important issue in solid-state physics. The band gap can be controlled externally by various parameters, such as pressure, atomic compositions, and external field. Sometimes, the gap even collapses by tuning some parameter. In the field of topological insulators, this closing of the gap at a time-reversal invariant momentum indicates a band inversion, that is, it leads to a topological phase transition from a normal insulator to a topological insulator. We show, through an exhaustive study on possible space groups, that the gap closing in inversion-asymmetric crystals is universal, in the sense that the gap closing always leads either to a Weyl semimetal or to a nodal-line semimetal. We consider three-dimensional spinful systems with time-reversal symmetry. The space group of the system and thewave vector at the gap closing uniquely determinewhich possibility occurs and where the gap-closing points or lines lie in the wave vector space after the closing of the gap. In particular,we show that an insulator-to-insulator transition never happens, which is in sharp contrast to inversion-symmetric systems.

Original languageEnglish
Article numbere1602680
JournalScience Advances
Issue number5
Publication statusPublished - 2017 May
Externally publishedYes

ASJC Scopus subject areas

  • General


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