Triple-Point Fermions in Ferroelectric GeTe

Abstract

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 angleresolved 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.

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

“…Figure 1 b presents the band structure of thin films of α-GeTe(111) along the Γ À K high-symmetry direction, revealed by static ARPES measurements using only the probe pulses, in agreement with existing literature [6][7][8][14][15][16] . The observed band structure is in excellent agreement with calculations using the one-step model of photoemission 17 (Fig.…”

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

“…Figure 1b presents the band structure of thin films of α-GeTe(111) along the Γ − K highsymmetry direction, revealed by static ARPES measurements using only the probe pulses, in agreement with existing literature. [3][4][5]7,8,17 The observed band structure is in excellent agreement with Bloch spectral function (BSF) calculations (Fig. 1c) performed for a Te terminated surface with short bonds between the last two atomic lattice planes of the top Te surface and the next subsurface Ge plane (right part of Fig.…”

Triple nodal points characterized by their nodal-line structure in all magnetic space groups

“…Initially, TPs were considered within the context of spin-orbit-coupled (SOC) systems, where flavor-(2) TPs were classified into type A vs type B according to the absence or presence of attached nodal-line (NL) arcs [29,39]. Using photoemission spectroscopy, TPs were shown to exist in the band structure of various materials, including MoP [33], WC [37], and ferroelectric GeTe [44].…”