Projected Bulk Band Gap Research Articles

One-dimensionality of the spin-polarized surface conduction and valence bands of quasi-one-dimensional Bi chains on GaSb(110)-( 2×1 )

Surface electronic structure and its one-dimensionality above and below the Fermi level ($E_{\rm F}$) were surveyed on the Bi/GaSb(110)-(2$\times$1) surface hosting quasi-one-dimensional (Q1D) Bi chains, using conventional (one-photon) and two-photon angle-resolved photoelectron spectroscopy (ARPES) and theoretical calculations. ARPES results reveal that the Q1D electronic states are within the projected bulk bandgap. Circular dichroism of two-photon ARPES and density-functional-theory calculation indicate clear spin and orbital polarization of the surface states consistent with the giant sizes of Rashba-type SOI, derived from the strong contribution of heavy Bi atoms. The surface conduction band above $E_{\rm F}$ forms a nearly straight constant-energy contour, suggesting its suitability for application in further studies of one-dimensional electronic systems with strong SOI. A tight-binding model calculation based on the obtained surface electronic structure successfully reproduces the surface band dispersions and predicts possible one- to two-dimensional crossover in the temperature range of 60--100~K.

Subpicosecond spin dynamics of excited states in the topological insulator Bi2Te3

Using time-, spin- and angle-resolved photoemission, we investigate the ultrafast spin dynamics of hot electrons on the surface of the topological insulator Bi$_2$Te$_3$ following optical excitation by fs-infrared pulses. We observe two surface-resonance states above the Fermi level coexisting with a transient population of Dirac fermions that relax in about $\sim$2 ps. One state is located below $\sim$0.4 eV just above the bulk continuum, the other one at $\sim$0.8 eV inside a projected bulk band gap. At the onset of the excitation, both states exhibit a reversed spin texture with respect to that of the transient Dirac bands, in agreement with our one-step photoemission calculations. Our data reveal that the high-energy state undergoes spin relaxation within $\sim$0.5 ps, a process that triggers the subsequent spin dynamics of both the Dirac cone and the low-energy state, which behave as two dynamically-locked electron populations. We discuss the origin of this behavior by comparing the relaxation times observed for electrons with opposite spins to the ones obtained from a microscopic Boltzmann model of ultrafast band cooling introduced into the photoemission calculations. Our results demonstrate that the nonequilibrium surface dynamics is governed by electron-electron rather than electron-phonon scattering, with a characteristic time scale unambiguously determined by the complex spin texture of excited states above the Fermi level. Our findings reveal the critical importance of detecting momentum and energy-resolved spin textures with fs resolution to fully understand the sub-ps dynamics of transient electrons on the surface of topological insulators.

Spin texture of time-reversal symmetry invariant surface states on W(110).

We find in the case of W(110) previously overlooked anomalous surface states having their spin locked at right angle to their momentum using spin-resolved momentum microscopy. In addition to the well known Dirac-like surface state with Rashba spin texture near the -point, we observe a tilted Dirac cone with circularly shaped cross section and a Dirac crossing at 0.28 × within the projected bulk band gap of tungsten. This state has eye-catching similarities to the spin-locked surface state of a topological insulator. The experiments are fortified by a one-step photoemission calculation in its density-matrix formulation.

Relationship between embedding-potential eigenvalues and topological invariants of time-reversal invariant band insulators

The embedding potential defined on the boundary surface of a semi-infinite crystal relates the value and normal derivative of generalized Bloch states propagating or decaying toward the interior of the crystal. It becomes Hermitian when the electron energy $\ensuremath{\epsilon}$ is located in a projected bulk band gap at a given wave vector $\mathbf{k}$ in the surface Brillouin zone (SBZ). If one plots the real eigenvalues of the embedding potential for a time-reversal invariant insulator in the projected bulk band gap along a path $\ensuremath{\epsilon}={\ensuremath{\epsilon}}_{0}(\mathbf{k})$ passing between two time-reversal invariant momentum (TRIM) points in the SBZ, then, they form Kramers doublets at both end points. We will demonstrate that the ${Z}_{2}$ topological invariant, $\ensuremath{\nu}$, which is either 0 or 1, depending on the product of time-reversal polarizations at the two TRIM points, can be determined from the two different ways these eigenvalues are connected between the two TRIM points. Furthermore, we will reveal a relation, $\ensuremath{\nu}=P$ mod 2, where $P$ denotes the number of poles that the embedding potential exhibits along the path. We also discuss why gapless surface states crossing the bulk band gap inevitably occur on the surface of topological band insulators from the view point of the embedding theory.

Rashba spin splitting of Shockley surface states on semi-infinite crystals

We study the Rashba spin splitting of the $L$-gap surface state on the (111) surfaces of Au, Ag, and Cu, and that of the topologically protected surface state on Sb(111) by a first-principles calculation based on the embedded Green's function technique. By taking advantage of semi-infinite surface geometry, we address several issues that are difficult to handle with the finite slab calculation. For Au(111), we investigate the nonlinear dependence on wave vector $\mathbf{k}$ of the spin-splitting energy, and also at what wave number each dispersion curve of the two spin-split bands is merged into a surface-projected bulk band. Then, we discuss why Cu(111) exhibits a larger Rashba effect than Ag(111) despite the fact that the atomic orbitals of Ag have larger spin-orbit matrix elements than those of Cu. We reveal that, while the wave function of the $L$-gap surface state has strong ${p}_{z}$ character (the $z$ axis is surface normal), the Rashba spin splitting occurs through the spin-orbit matrix element between the ${d}_{{z}^{2}}$ and ${d}_{uz}$ orbital components hybridized with ${p}_{z}$, where ${d}_{uz}$ denotes a linear combination of ${d}_{xz}$ and ${d}_{yz}$ with its orbital lobes pointing to the $\mathbf{k}$ direction (defined as the $u$ axis). Cu(111) exhibits a larger spin splitting than Ag(111), since the amount of both the ${d}_{{z}^{2}}$ and ${d}_{uz}$ components mixed in its surface-state wave function is much larger than that of Ag(111). In contrast to the (111) surfaces of noble metals, the spin splitting of the topologically protected surface state on Sb(111) arises from the spin-orbit matrix element between the ${p}_{z}$ and ${p}_{u}$ orbital components. We also discuss under what condition the energy dispersion curve of a surface state intersects the boundary line between a projected bulk band and a projected bulk band gap at a large angle, instead of gradually approaching the boundary line with increasing $|\mathbf{k}|$. Finally, we comment on a recent theoretical work of Krasovskii [Phys. Rev. B 90, 115434 (2014)] on the microscopic origin of the Rashba spin splitting.

Unconventional spin texture of a topologically nontrivial semimetal Sb(110)

The surfaces of antimony are characterized by the presence of spin-split states within the projected bulk band gap and the Fermi contour is thus expected to exhibit a spin texture. Using spin-resolved density functional theory calculations, we determine the spin polarization of the surface bands of Sb(110). The existence of the unconventional spin texture is corroborated by the investigations of the electron scattering on this surface. The charge interference patterns formed around single scattering impurities, imaged by scanning tunneling microscopy, reveal the absence of direct backscattering signal. We identify the allowed scattering vectors and analyze their bias evolution in relation to the surface-state dispersion.

Momentum-resolved electron dynamics of image-potential states on Cu and Ag surfaces

The dependence of the inelastic lifetime of electrons in the first $n=1$ image-potential state of clean and rare-gas covered Ag(111), Cu(111), and Cu(100) surfaces on their momentum parallel to the surface has been studied experimentally by means of time- and angle-resolved two-photon photoemission spectroscopy (2PPE) and theoretically by calculations based on the many-body theory within the self-energy formalism. Similar to the previously studied clean Cu(100) surface, the theoretical results are in excellent agreement with the experiment findings for Cu(111). For Ag(111), the theory overestimates the decay rate and its momentum dependence, which is attributed to the neglect of surface plasmon excitations. With increasing parallel momentum, the $n=1$ state shifts out of the projected bulk band gap on both surfaces and turns into an image-potential resonance. This opens an additional decay channel by resonant electron transfer into the bulk, which is theoretically treated by the application of the wave packet propagation approach. The expected stronger increase of the decay rate upon crossing the edge of the band gap, however, is not observed in the experiment. The decoupling of the image-potential states from the metal surface upon adsorption of rare-gas layers results in a decrease of the decay rate as well as of its momentum dependence by a similar factor, which can be successfully explained by the change of interband and intraband contributions to the total decay rate.

Image potential states as a quantum probe of graphene interfaces

Image potential states (IPSs) are electronic states localized in front of a surface in a potential well, formed by the surface projected bulk band gap on one side and the image potential barrier on the other. In the limit of a two-dimensional solid, a double Rydberg series of IPSs has been predicted, which is in contrast to a single series present in three-dimensional solids. Here, we confirm this prediction experimentally for mono- and bilayer graphene. The IPSs of epitaxial graphene on SiC are measured by scanning tunneling spectroscopy and the results are compared with ab-initio band structure calculations. Despite the presence of the substrate, both calculations and experimental measurements show that the first pair of the double series of IPSs survives and eventually evolves into a single series for graphite. Thus, IPSs provide an elegant quantum probe of the interfacial coupling in graphene systems.

Theory of inelastic lifetimes of surface-state electrons and holes at metal surfaces

After the early suggestion by John Pendry (1980 Phys. Rev. Lett. 45 1356) to probeunoccupied bands at surfaces through the time reversal of the photoemission process, theinverse-photoemission technique yielded the first conclusive experimental evidence for theexistence of image-potential bound states at metal surfaces and has led, over the last twodecades, to an active area of research in condensed-matter and surface physics. Here wedescribe the current status of the many-body theory of inelastic lifetimes of theseimage-potential states and also the Shockley surface states that exist near the Fermi levelin the projected bulk band gap of simple and noble metals. New calculations of theself-energy and lifetime of surface states on Au surfaces are presented as well, using theGWΓ approximation of many-body theory.

Band structure ofTl/Ge(111)−(3×1): Angle-resolved photoemission and first-principles prediction of giant Rashba effect

We have investigated the atomic and electronic structure of the $\text{Tl}/\text{Ge}(111)\text{\ensuremath{-}}(3\ifmmode\times\else\texttimes\fi{}1)$ surface using angle-resolved photoelectron spectroscopy (ARPES) and first-principles total-energy-band calculation. The experimental surface bands exhibit semiconducting electronic structure and are well reproduced by the band calculation based on the honeycomb-chain channel structure with Tl adsorbed at ${H}_{3}$ site. Electron density maps of the surface-related states show the formation of the $\text{Ge}=\text{Ge}$ double-bond-like state as observed on the alkali-metal-induced $\text{Si}(111)\text{\ensuremath{-}}(3\ifmmode\times\else\texttimes\fi{}1)$ surfaces. In our scalar-relativistic all-electron calculation, the Tl-derived surface bands show a Rashba-type spin splitting in the projected bulk band gap, which is not clearly resolved by ARPES due to a limited energy resolution. They show complicated dispersion due to the hybridization with the bulk states in the projected bulk band region. The lowest unoccupied surface band, which is an antibonding state formed between $\text{Tl}\text{ }6p$ and Ge dangling bonds and is highly localized in the topmost surface layer, shows a large spin-orbit splitting of $\ensuremath{\sim}200\text{ }\text{meV}$.

Electronic Structure of Ultrathin Bismuth Films with A7 and Black-Phosphorus-like Structures

Using scanning tunneling spectroscopy and first-principles calculations, we have studied the electronic structure of two different ultrathin bismuth films on a Si(111)-7×7 substrate; a hexagonal film (HEX film) having a bulklike (A7-like) structure and a film having a black-phosphorus-like structure (BP film). The HEX film is metallic because of spin–orbit (SO)-split surface-state bands lying inside the projected bulk band gap near the Fermi level. Another SO-split surface state is also observed inside the SO gap. The BP film exhibits a significant reduction in metallicity in contrast to the HEX film. This is related to the formation of a very stable paired-layer structure, the mechanism of which is similar to that of the stabilization of semiconducting bulk black P. However, unlike bulk black P, a certain extent of metallicity still remains. This slight metallicity can be associated with buckling and strain in the BP film, which is analogous to the fact that shear angle distortion in bulk Bi is responsib...

Enhanced Rashba spin-orbit splitting inBi∕Ag(111)andPb∕Ag(111)surface alloys from first principles

We present first-principles calculations of a $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ $\mathrm{Bi}∕\mathrm{Ag}(111)$-ordered surface alloy, which has recently been investigated experimentally using angle-resolved photoemission spectroscopy. The surface states in the $L$-projected bulk band gap show a Rashba-type spin-orbit splitting which is three times larger than what has been observed on a clean Bi(111) surface. This large enhancement can be explained by the strong distortion of the surface-state wave function which is caused by the substantial outward buckling of the Bi atom. Also, in a similar surface alloy, $\mathrm{Pb}∕\mathrm{Ag}(111)$, a strong Rashba-type splitting was found by our calculations. The comparison to the experimental data is more difficult due to the presence of a second, close-by surface state. We discuss the dependence of the two-dimensional band structure on the surface corrugation and compare to the experimental findings.

表面に作製する磁性ナノ構造―表面スピントロニクス―

We have proposed the surface spintronics devices based on the magnetic nano-structures constructed on the solid surfaces. Because the Fe atom layer on Cu(111) has the spin polarized states in the surface projected bulk band gap, it is possible to make the spin conductor, spin switch and non-volatile spin memory. And we propose how to make the stable magnetic nano-structures on the reactive Si surfaces.

Unoccupied surface state on Pt(111) revealed by scanning tunneling spectroscopy

We measured the dispersion of an unoccupied surface state on Pt(111) by imaging scattering states at point defects and step edges using scanning tunneling spectroscopy. By comparison to first-principles electronic structure calculations the state is assigned to an $sp$-derived surface band at the lower edge of the projected bulk band gap. In $dI∕dV(V)$ curves, the onset of the surface-state band appears as a rather broad feature. Its shape results from two spin-orbit split branches with nearly linear dispersion, one of them merging into bulk states at higher energies.

Electronic structure of a bismuth bilayer

Using angle-resolved photoemission spectroscopy, we identified four two-dimensional bands within a 1 eV binding-energy region below the Fermi level. The top two bands that are part of the complex Fermi surface of Bi (111) are located in the projected bulk band gap and exhibit sixfold rotational symmetry of the top Bi bilayer. The two lower-lying bands reside inside the projected bulk band structure. The threefold rotational symmetry of these bands indicates a weak interaction with the underlying bulk bands. Our data can be explained with a tight-binding calculation of a bilayer by eliminating the second nearest-neighbor interactions that determine the coupling between bilayers in bulk Bi.

Electron–phonon coupling in W(110)-(1×1)H

Recently, we reported high resolution angle-resolved photoemission measurements that indicated unusually strong coupling between adsorbate vibrations and a surface-localized electron state in the system W(110)-(1×1)H. We have now extended these measurements to probe the electron–phonon coupling strength as a function of position on the relevant Fermi contour. We find that the strength of the coupling is strongly dependent on Fermi wave vector, with the electron–phonon coupling constant λ varying between zero and ∼0.8. Qualitatively, the strength of the coupling is related to the position of the surface band in the projected bulk band gap, and therefore to the degree of surface localization of the surface state wave function. Such effects should play an important role in all adsorbate vibronic interactions, since the vibrational modes are generally highly localized to the outermost surface layer. We discuss these results in relation to the surface phonon anomalies observed on this surface.

Electron-Lattice Interaction onα−Ga(010)

We have investigated the (010) surface of $\ensuremath{\alpha}\ensuremath{-}\mathrm{Ga}$ by angle-resolved photoemission and low energy electron diffraction. We find a surface state around the $\overline{C}$ point of the surface Brillouin zone. The electron-phonon coupling at this surface is very strong with an electron-phonon mass enhancement parameter of $\ensuremath{\lambda}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.4\ifmmode\pm\else\textpm\fi{}0.10$. Our spectra show high background intensity in a projected bulk band gap which cannot be accounted for by defect scattering and is therefore interpreted as indicating a nonquasiparticle behavior. Upon cooling the sample below 220 K we observe a phase transition accompanied by spectral changes near the Fermi level.

Unoccupied electronic states of the Cs/Cu(100) and Cs/Cu(111) adsorption systems

We have investigated the unoccupied electronic structure of submonolayer amounts of cesium on the Cu(100) and Cu(111) surfaces by inverse photoemission (IPE) and work-function measurements. At very low Cs coverages on both substrates, IPE spectra obtained at normal incidence indicate that an adsorbate-induced feature develops in the projected bulk band gap of the substrate at an energy of $\ensuremath{\sim}3\mathrm{eV}$ above the Fermi level ${(E}_{F}).$ As the Cs coverage is increased, this feature moves to lower energy. On the Cu(100) surface, the energy of the Cs feature initially follows the decrease of the work function, and levels off at $\ensuremath{\sim}0.3\mathrm{eV}$ above ${E}_{F}$ as the Cs coverage approaches 1 ML. We observed a similar effect for the Cs/Cu(111) system. Off-normal spectra obtained for 0.08 ML of Cs on Cu(111) indicate that, at low coverages, the Cs state does not disperse with ${k}_{\ensuremath{\parallel}}.$ However, on both substrates, we observed a correlation between modulations in the intensity of the Cs feature and degeneracy between this feature and the projected bulk bands of the substrate. Energy-dependent IPE spectra suggest that the adsorbate state on both Cu surfaces has predominantly $d$-like orbital character when the state is in the projected bulk band gap of the substrate. The orbital character of the Cs feature changes to $sp\ensuremath{-}$ like when the adsorbate state is degenerate with the Cu $\mathrm{sp}$-derived bulk bands. This effect was observed whether the degeneracy was achieved by varying the Cs coverage at a fixed ${k}_{\ensuremath{\parallel}},$ or by varying ${k}_{\ensuremath{\parallel}}$ at a fixed coverage. We interpret this as evidence of momentum-dependent hybridization of the adsorbate-substrate bond.

Photoemission Study of The Electronic Structure of Wurtzite Gan(0001) Surfaces

AbstractThe surface electronic structure of wurtzite GaN (0001) (1 × 1) has been investigated using angle-resolved photoemission spectroscopy. Surfaces were cleaned by repeated cycles of N2 ion bombardment and annealing in ultra-high vacuum. A well-defined surface state below the top of the valence band is clearly observed. This state is sensitive to the adsorption of both activated H2 and O2, and exists in a projected bulk band gap, below the valence band maximum. The state shows no dispersion perpendicular or parallel to the surface. The symmetry of this surface state is even with respect to the mirror planes of the surface and polarization measurements indicate that it is of spz character, consistent with a dangling bond state.

Momentum-dependent orbital character of unoccupied Cs-induced levels on Cu(100) and Cu(111)

We present inverse photoemission spectra from the Cs Cu(100) and Cs Cu(111) systems, obtained with a photon-energy dispersive grating spectrograph. On both substrates, the intensity of a Cs-derived unoccupied electronic state increased with increasing excitation energy in regions of the surface Brillouin zone (SBZ) which contained a projected bulk band gap of the substrate. However, when the Cs feature was degenerate with the substrate sp-derived bulk band, the intensity of the Cs feature decreased with increasing excitation energy. We interpret this as evidence for a change in the orbital character of a Cs-induced unoccupied electronic state from d-like in the former case to sp-like in the latter, owing to hybridization in the adsorbate/substrate bond. This effect was observed whether sampling of the SBZ was achieved by varying the Cs coverage or by probing a different value of k ‖.