Ferroelectric α-GeTe is unveiled to exhibit an intriguing multiple nontrivial topology of the electronic band structure due to the existence of triple-point and type-II Weyl fermions, which goes well beyond the giant Rashba spin splitting controlled by external fields as previously reported. Using spin- and angle-resolved photoemission spectroscopy combined with ab initio density functional theory, the unique spin texture around the triple point caused by the crossing of one spin-degenerate and two spin-split bands along the ferroelectric crystal axis is derived. This consistently reveals spin winding numbers that are coupled with time-reversal symmetry and Lorentz invariance, which are found to be equal for both triple-point pairs in the Brillouin zone. The rich manifold of effects opens up promising perspectives for studying nontrivial phenomena and multicomponent fermions in condensed matter systems.

Department of Condensed Matter Physics Masaryk University Kotlářská 267 2 61137 Brno Czech Republic

Department of Physics Tsinghua University Beijing 100084 China

Institut de Physique École Polytechnique Fédérale de Lausanne CH 1015 Lausanne Switzerland

Institut für Halbleiter und Festkörperphysik Johannes Kepler Universität A 4040 Linz Austria

Institute of Physics P J Šafárik University in Košice Park Angelinum 9 040 01 Košice Slovakia

International Research Centre MagTop Institute of Physics Polish Academy of Sciences Aleja Lotnikow 32 46 PL 02668 Warsaw Poland

Laboratoire de Physique des Matériaux et Surfaces CY Cergy Paris Université 95031 Cergy Pontoise France

National Technical University KhPI Kyrpychova Street 2 61002 Kharkiv Ukraine

New Technologies Research Center University of West Bohemia 301 00 Plzeň 3 Czech Republic

Photon Science Division Paul Scherrer Institut CH 5232 Villigen Switzerland

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Field-induced ultrafast modulation of Rashba coupling at room temperature in ferroelectric α-GeTe(111)