Triple point fermions in ferroelectric GeTe.

Ferroelectric GeTe is unveiled to exhibit an intriguing multiple non-trivial 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 non-trivial phenomena and multi-component fermions in condensed matter systems.