A comprehensive mapping of the spin polarization of the electronic bands in ferroelectric α-GeTe(111) films has been performed using a time-of-flight momentum microscope equipped with an imaging spin filter that enables a simultaneous measurement of more than 10.000 data points (voxels). A Rashba type splitting of both surface and bulk bands with opposite spin helicity of the inner and outer Rashba bands is found revealing a complex spin texture at the Fermi energy. The switchable inner electric field of GeTe implies new functionalities for spintronic devices. The strong coupling of electron momentum and spin in low-dimensional structures allows an electrically controlled spin manipulation in spintronic devices [1-4], e.g. via the Rashba effect [5]. The Rashba effect has first been experimentally demonstrated in semiconductor heterostructures, where an electrical field perpendicular to the layered structure, i.e. perpendicular to the electron momentum, determines the electron spin orientation relative to its momentum [6-8]. An asymmetric interface structure causes the necessary inversion symmetry breaking and accounts for the special spin-splitting of electron states, the Rashba effect [5], the size of which can be tuned by the strength of the electrical field. For most semiconducting materials the Rashba effect causes only a quite small splitting of the order of 10 −2 ˚ A −1 and thus requires experiments at very low temperatures [9-11] and also implies large lateral dimensions for potential spintronic applications. A considerably larger splitting has been predicted theoretically [12] and was recently found experimentally for the surface states of GeTe(111) [13, 14]. GeTe is a ferroelectric semiconductor with a Curie temperature of 700 K. Thus, besides the interface induced Rashba splitting, the ferroelectric properties also imply a broken inversion symmetry within the bulk and thus would allow for the electrical tuning of the bulk Rashba splitting via switching the ferroelectric polarization [12, 15, 16]. This effect is of great interest for non-volatile spin orbitronics [10]. For GeTe a bulk Rashba splitting of 0.19Å19Å −1 has been predicted theoretically [12]. Experimentally, bulk-Rashba bands are rare and have only been found in the layered polar semiconductors BiTeCl and BiTeI [17-20] that, however, are not switchable. A characterization of the ferroelectric properties and a measurement of the spin polarization of the surface states of GeTe(111) at selected k-points has been performed previously by force microscopy [21, 22] and spin-resolved angular resolved photoemission spectroscopy, respectively [13]. A recent experimental and theoretical study revealed that at the Fermi level the hybridization of surface and bulk states causes surface-bulk resonant states resulting in unconventional spin topologies with chiral symmetry [14]. Here, we demonstrate the spin structure of surface and bulk bands of the GeTe(111) surface using the novel pho-toemission technique of spin-resolved time-of-flight momentum microsco...

Helical locking of spin and momentum and prohibited backscattering are the key properties of topologically protected states 1,2 . They are expected to enable novel types of information processing by providing pure spin currents 3,4 , or fault tolerant quantum computation by using the Majorana fermions at interfaces of topological states with superconductors 5 . So far, the required helical conduction channels used to realize Majorana fermions are generated through the application of an axial magnetic field to conventional semiconductor nanowires 6 . Avoiding the magnetic field enhances the possibilities for circuit design significantly 7 . Here, we show that subnanometre-wide electron channels with natural helicity are present at surface step edges of the weak topological insulator Bi 14 Rh 3 I 9 (ref. 8). Scanning tunneling spectroscopy reveals the electron channels to be continuous in both energy and space within a large bandgap of 200 meV, evidencing its non-trivial topology. The absence of these channels in the closely related, but topologically trivial compound Bi 13 Pt 3 I 7 corroborates the channels' topological nature. The backscatter-free electron channels are a direct consequence of Bi 14 Rh 3 I 9 's structure: a stack of two-dimensional topologically insulating, graphene-like planes separated by trivial insulators. We demonstrate that the surface of Bi 14 Rh 3 I 9 can be engraved using an atomic force microscope, allowing networks of protected channels to be patterned with nanometre precision.The compound Bi 14 Rh 3 I 9 consists of two types of layers being alternately stacked. One layer, [(Bi 4 Rh) 3 I] 2+ , exhibits a graphenelike honeycomb lattice formed by rhodium-centred bismuth cubes, as revealed by X-ray diffraction (XRD) (red layer, Fig. 1b) and is a two-dimensional topological insulator (2DTI) according to density functional theory (DFT; ref. 8). Its structure mimics the originally proposed quantum spin Hall insulator in graphene 9 , but with an inverted bandgap being four orders of magnitude larger. The other layer separating the 2DTIs is a [Bi 2 I 8 ] 2− spacer with a trivial bandgap (blue layer, Fig. 1b). Such a stack of layers has been proposed to be a weak three-dimensional topological insulator (3DTI; ref. 10), as the only alternative of time-reversal protected 3DTIs to the meanwhile intensely studied strong 3DTIs, such as, for example, Bi 2 Se 3 (refs 1,2). However, weak 3DTIs remained elusive until DFT results in good correspondence with angle-resolved photoemission spectroscopy (ARPES) data confirmed the synthesized compound Bi 14 Rh 3 I 9 to be one 8 . Theory predicts that weak 3DTIs feature helical edge states at step edges on the surface that is perpendicular to the stacking direction 11 . These edge states are topologically protected and immune to backscattering as long as time-reversal symmetry persists. Thus, perfect conduction of these channels with conductivity e 2 /h is anticipated 11,12 . Moreover, partially interfacing these channels with superconductors is predicted to in...

Using low-temperature scanning tunneling spectroscopy, we map the local density of states of graphene quantum dots supported on Ir(111). Because of a band gap in the projected Ir band structure around the graphene K point, the electronic properties of the QDs are dominantly graphenelike. Indeed, we compare the results favorably with tight binding calculations on the honeycomb lattice based on parameters derived from density functional theory. We find that the interaction with the substrate near the edge of the island gradually opens a gap in the Dirac cone, which implies soft-wall confinement. Interestingly, this confinement results in highly symmetric wave functions. Further influences of the substrate are given by the known moiré potential and a 10% penetration of an Ir surface resonance into the graphene layer.

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Using high resolution spin-and angle-resolved photoemission spectroscopy, we map the electronic structure and spin texture of the surface states of the topological insulator Sb2Te3. In combination with density functional calculations (DFT), we directly show that Sb2Te3 exhibits a partially occupied, single spin-Dirac cone around the Fermi energy EF, which is topologically protected. DFT obtains a spin polarization of the occupied Dirac cone states of 80-90 %, which is in reasonable agreement with the experimental data after careful background subtraction. Furthermore, we observe a strongly spin-orbit split surface band at lower energy. This state is found at E − EF −0.8 eV at the Γ-point, disperses upwards, and disappears at about E − EF = −0.4 eV into two different bulk bands. Along the Γ − K direction, the band is located within a spin-orbit gap. According to an argument given by Pendry and Gurman in 1975, such a gap must contain a surface state, if it is located away from the high symmetry points of the Brillouin zone. Thus, the novel spin-split state is protected by symmetry, too.