Cubic Rashba Effect in the Surface Spin Structure of Rare-Earth Ternary Materials.

Spin-orbit interaction and structure inversion asymmetry in combination with magnetic ordering is a promising route to novel materials with highly mobile spin-polarized carriers at the surface. Spin-resolved measurements of the photoemission current from the Si-terminated surface of the antiferromagnet TbRh_{2}Si_{2} and their analysis within an ab initio one-step theory unveil an unusual triple winding of the electron spin along the fourfold-symmetric constant energy contours of the surface states. A two-band k·p model is presented that yields the triple winding as a cubic Rashba effect. The curious in-plane spin-momentum locking is remarkably robust and remains intact across a paramagnetic-antiferromagnetic transition in spite of spin-orbit interaction on Rh atoms being considerably weaker than the out-of-plane exchange field due to the Tb 4f moments.

Nonuniversal Transverse Electron Mean Free Path through Few-layer Graphene.

In contrast to the in-plane transport electron mean-free path in graphene, the transverse mean-free path has received little attention and is often assumed to follow the "universal" mean-free path (MFP) curve broadly adopted in surface and interface science. Here we directly measure transverse electron scattering through graphene from 0 to 25 eV above the vacuum level both in reflection using low energy electron microscopy and in transmission using electronvolt transmission electron microscopy. From these data, we obtain quantitative MFPs for both elastic and inelastic scattering. Even at the lowest energies, the total MFP is just a few graphene layers and the elastic MFP oscillates with graphene layer number, both refuting the universal curve. A full theoretical calculation taking the graphene band structure into consideration agrees well with experiment, while the key experimental results are reproduced even by a simple optical toy model.

Strong Linear Dichroism in Spin-Polarized Photoemission from Spin-Orbit-Coupled Surface States.

A comprehensive understanding of spin-polarized photoemission is crucial for accessing the electronic structure of spin-orbit coupled materials. Yet, the impact of the final state in the photoemission process on the photoelectron spin has been difficult to assess in these systems. We present experiments for the spin-orbit split states in a Bi-Ag surface alloy showing that the alteration of the final state with energy may cause a complete reversal of the photoelectron spin polarization. We explain the effect on the basis of ab initio one-step photoemission theory and describe how it originates from linear dichroism in the angular distribution of photoelectrons. Our analysis shows that the modulated photoelectron spin polarization reflects the intrinsic spin density of the surface state being sampled differently depending on the final state, and it indicates linear dichroism as a natural probe of spin-orbit coupling at surfaces.

Nanoscale analysis of the oxidation state and surface termination of praseodymium oxide ultrathin films on ruthenium(0001).

The complex structure and morphology of ultrathin praseodymia films deposited on a ruthenium(0001) single crystal substrate by reactive molecular beam epitaxy is analyzed by intensity-voltage low-energy electron microscopy in combination with theoretical calculations within an ab initio scattering theory. A rich coexistence of various nanoscale crystalline surface structures is identified for the as-grown samples, notably comprising two distinct oxygen-terminated hexagonal Pr2O3(0001) surface phases as well as a cubic Pr2O3(111) and a fluorite PrO2(111) surface component. Furthermore, scattering theory reveals a striking similarity between the electron reflectivity spectra of praseodymia and ceria due to very efficient screening of the nuclear charge by the extra 4f electron in the former case.

Quantum spin Hall insulators in centrosymmetric thin films composed from topologically trivial BiTeI trilayers.

The quantum spin Hall insulators predicted ten years ago and now experimentally observed are instrumental for a break- through in nanoelectronics due to non-dissipative spin-polarized electron transport through their edges. For this transport to persist at normal conditions, the insulators should possess a sufficiently large band gap in a stable topological phase. Here, we theoretically show that quantum spin Hall insulators can be realized in ultra-thin films constructed from a trivial band insulator with strong spin-orbit coupling. The thinnest film with an inverted gap large enough for practical applications is a centrosymmetric sextuple layer built out of two inversely stacked non-centrosymmetric BiTeI trilayers. This nontrivial sextuple layer turns out to be the structure element of an artificially designed strong three-dimensional topological insulator Bi2Te2I2. We reveal general principles of how a topological insulator can be composed from the structure elements of the BiTeX family (X = I, Br, Cl), which opens new perspectives towards engineering of topological phases.

Spin-orbit coupling at surfaces and 2D materials.

Spin-orbit interaction gives rise to a splitting of surface states via the Rashba effect, and in topological insulators it leads to the existence of topological surface states. The resulting k(//) momentum separation between states with the opposite spin underlies a wide range of new phenomena at surfaces and interfaces, such as spin transfer, spin accumulation, spin-to-charge current conversion, which are interesting for fundamental science and may become the basis for a breakthrough in the spintronic technology. The present review summarizes recent theoretical and experimental efforts to reveal the microscopic structure and mechanisms of spin-orbit driven phenomena with the focus on angle and spin-resolved photoemission and scanning tunneling microscopy.

Spin-Flip and Element-Sensitive Electron Scattering in the BiAg2 Surface Alloy.

Heavy metal surface alloys represent model systems to study the correlation between electron scattering, spin-orbit interaction, and atomic structure. Here, we investigate the electron scattering from the atomic steps of monolayer BiAg_{2} on Ag(111) using quasiparticle interference measurements and density functional theory. We find that intraband transitions between states of opposite spin projection can occur via a spin-flip backward scattering mechanism driven by the spin-orbit interaction. The spin-flip scattering amplitude depends on the chemical composition of the steps, leading to total confinement for pure Bi step edges, and considerable leakage for mixed Bi-Ag step edges. Additionally, the different localization of the occupied and unoccupied surface bands at Ag and Bi sites leads to a spatial shift of the scattering potential barrier at pure Bi step edges.

Surface resonances in electron reflection from overlayers.

Electron scattering by oxygen monolayers on the Ru(0 0 0 1) surface is studied both experimentally and theoretically. Sharp transmission resonances at low energies are revealed and established to originate from critical points of a special kind in the complex band structure of the substrate. Electron reflection from the clean and oxidized Ru(0 0 0 1) is measured for kinetic energies up to 40 eV at normal incidence for oxygen coverages of 1/4, 1/2, 3/4, and one monolayer. The reflection spectra R(E) are analyzed using a Bloch-waves based ab initio scattering theory. In addition to the substrate-induced resonances the reconstructed (2 × 1) and (2 × 2) surfaces show surface resonances due to pre-emergent secondary diffraction beams. The R(E) spectra are shown to give unambiguous evidence of the hcp stacking of the oxygen layer.

Experimental verification of PbBi2Te4 as a 3D topological insulator.

The experimental evidence is presented of the topological insulator state in PbBi2Te4. A single surface Dirac cone is observed by angle-resolved photoemission spectroscopy with synchrotron radiation. Topological invariants Z2 are calculated from the ab initio band structure to be 1;(111). The observed two-dimensional isoenergy contours in the bulk energy gap are found to be the largest among the known three-dimensional topological insulators. This opens a pathway to achieving a sufficiently large spin current density in future spintronic devices.

Surface scattering via bulk continuum states in the 3D topological insulator Bi2Se3.

We have performed scanning tunneling microscopy and differential tunneling conductance (dI/dV) mapping for the surface of the three-dimensional topological insulator Bi(2)Se(3). The fast Fourier transformation applied to the dI/dV image shows an electron interference pattern near Dirac node despite the general belief that the backscattering is well suppressed in the bulk energy gap region. The comparison of the present experimental result with theoretical surface and bulk band structures shows that the electron interference occurs through the scattering between the surface states near the Dirac node and the bulk continuum states.

Hexagonally deformed Fermi surface of the 3D topological insulator Bi2Se3.

A hexagonal deformation of the Fermi surface of Bi2Se3 has been for the first time observed by angle-resolved photoemission spectroscopy. This is in contrast to the general belief that Bi2Se3 possesses an ideal Dirac cone. The hexagonal shape is found to disappear near the Dirac node, which would protect the surface state electrons from backscattering. It is also demonstrated that the Fermi energy of naturally electron-doped Bi2Se3 can be tuned by 1% Mg doping in order to realize the quantum topological transport.

Strong rashba-type spin polarization of the photocurrent from bulk continuum States: experiment and theory for Bi(111).

Strong spin polarization of the photocurrent from bulk continuum states of Bi(111) is experimentally observed. On the basis of ab initio one-step photoemission theory the effect is shown to originate from the strong polarization of the initial states at the surface and to be the result of the surface sensitivity of photoemission. Final state effects cause deviations of the k{∥} dependence of polarization from strictly antisymmetric relative to Γ.

Experimental realization of a three-dimensional topological insulator phase in ternary chalcogenide TlBiSe2.

We report the first observation of a topological surface state on the (111) surface of the ternary chalcogenide TlBiSe2 by angle-resolved photoemission spectroscopy. By tuning the synchrotron radiation energy we reveal that it features an almost ideal Dirac cone with the Dirac point well isolated from bulk continuum states. This suggests that TlBiSe2 is a promising material for realizing quantum topological transport.

Very-low-energy electron diffraction from TiS(2): experiment and ab initio theory.

An experimental and theoretical study of very-low-energy electron diffraction from the (0001) surface of 1T TiS(2) is presented. The normal incidence electron transmission spectrum is measured up to 37 eV above the Fermi level. Ab initio calculations of the spectra are performed with the full-potential extended linear augmented plane wave [Formula: see text] method. The experimental spectrum is interpreted in terms of the unoccupied complex band structure (CBS) of the semi-infinite crystal. Three CBS branches responsible for the electron transmission at normal incidence are determined. The role of inelastic scattering is discussed. The energy dependence of the optical potential V(i) is determined from the shape of the experimental spectral structures. A sharp increase of V(i) at 21.5 eV is detected, which is associated with a plasmon peak in the electron energy-loss function.

Determination of the hole lifetime from photoemission: Ti 3d states in TiTe2.

The electron hole spectral width Gamma(h) of Ti 3d states in layered TiTe2 and the inverse lifetime V(i) of the photoelectron final states are determined from experiment within the one-step theory of photoemission. The condition for the possibility of separating the effects of Gamma(h) and V(i) is a strongly non-free-electron character of the final states. The resulting drastic changes of the line shape with photon energy are experimentally observed and explained by an ab initio theory. A nonmonotonic dependence of V(i) on the final-state energy is observed; it is shown to reveal the real space structure of the complex electron self-energy.

Spectral line shape variations in time-resolved photoemission from a solid.

Laser assisted photoemission by a subfemtosecond ultraviolet pulse is studied by solving the time-dependent Schrödinger equation for a one-dimensional model crystal. Without the laser field, the shape and the energy location of the spectrum are determined by the energy dependence of the photoemission cross section. In the presence of the laser field, the time growth of the population of the final state is predicted to cause extremely sharp variations of spectral width as a function of release time. This can help enhance time resolution of the measurements. A simple phenomenological model to describe the line shape is proposed.

Angle-resolved photoemission from surface states.

The role of the evanescent part of the unoccupied complex band structure in photoemission from surface states is revealed. The frequency dependence of the emission intensity from two surface states on the (100) and (111) surfaces of Al in the photon energy range from 40 to 110 eV is explained within an ab initio one-step theory of photoemission. A novel embedding method to determine surface states is presented. A high sensitivity of surface states spectra to details of the surface potential barrier is predicted, which offers a way to efficiently monitor surface properties.