Spin-orbit splitting of the<i>L</i>-gap surface state on Au(111) and Ag(111)

Nicolay, G.; Reinert, F.; Hüfner, S.; Blaha, Peter

doi:10.1103/physrevb.65.033407

Cited by 259 publications

(277 citation statements)

References 13 publications

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“…The most recent results for the G states on the noble metals have been obtained with unprecedented resolution and quality by Hüfner and co-workers [100,121,122]. The breakthrough is due to the advent of ''third-generation'' electron energy analyzers, which allow ultra-high-resolution photoelectron spectroscopy with resolution parameters DE ¼ 2:5 meV and Dy ¼ AE0:15 as verified experimentally after excitation with monochromatized HeI radiation (ho ¼ 21:22 eV).…”

Section: Shockley States On Noble-metal Surfacesmentioning

confidence: 99%

“…The observed splitting is a consequence of the lack of inversion symmetry at the surface and should therefore also be expected on Ag (1 1 1) and Cu (1 1 1). However, the calculation [122] shows the effects to be too small to be detected despite the available resolution in DE and Dy. The middle panel in Fig.…”

Section: Shockley States On Noble-metal Surfacesmentioning

confidence: 99%

“…The top panel gives the 2D Fermi surface map. The bottom panel shows a gray scale plot of the dispersion Eðk k Þ along the GM-direction of the surface Brillouin zone, including (thin lines) the theoretical result from a fully relativistic density-functional calculation [122]. The observed splitting is a consequence of the lack of inversion symmetry at the surface and should therefore also be expected on Ag (1 1 1) and Cu (1 1 1).…”

Section: Shockley States On Noble-metal Surfacesmentioning

confidence: 99%

See 2 more Smart Citations

Decay of electronic excitations at metal surfaces

Echenique

Berndt

Chulkov

et al. 2004

Surface Science Reports

438

403

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Section: Shockley States On Noble-metal Surfacesmentioning

confidence: 99%

Section: Shockley States On Noble-metal Surfacesmentioning

confidence: 99%

Section: Shockley States On Noble-metal Surfacesmentioning

confidence: 99%

See 1 more Smart Citation

Decay of electronic excitations at metal surfaces

Echenique

Berndt

Chulkov

et al. 2004

Surface Science Reports

438

403

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“…Previous experimental work has been conducted for quantum corrals on either the Cu(111) surface 16,17 or on the Ag(111) surface 18 , where the neglect of spin-orbit coupling, as stated above, is completely justified 3,6 . However, this would not be the case for quantum corrals formed on the Au(111) surface.…”

mentioning

confidence: 99%

Spin−Orbit Coupling Induced Interference in Quantum Corrals

Walls

Heller

2007

Nano Lett.

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Lack of inversion symmetry at a metallic surface can lead to an observable spin-orbit interaction. For certain metal surfaces, such as the Au(111) surface, the experimentally observed spin-orbit coupling results in spin rotation lengths on the order of tens of nanometers, which is the typical length scale associated with quantum corral structures formed on metal surfaces. In this work, multiple scattering theory is used to calculate the local density of states (LDOS) of quantum corral structures comprised of nonmagnetic adatoms in the presence of spin-orbit coupling. Contrary to previous theoretical predictions, spin-orbit coupling induced modulations are observed in the theoretical LDOS, which should be observable using scanning tunneling microscopy.In the presence of time reversal symmetry [E(k, ↑) = E(−k, ↓)] and spatial inversion symmetry [E(k, ↑) = E(−k, ↑)], no spin splitting can exist since E(k, ↑) = E(k, ↓). At a metal surface, however, spatial inversion symmetry is violated, and a spin splitting can therefore occur, i.e., E(k, ↑) = E(k, ↓). The spin-orbit coupling in surface states was first observed by LaShell et al. 1 on the Au(111) surface using photoemission spectroscopy. The form of the spin-orbit interaction was found to be similar to the Rashba spin-orbit coupling 2 , which has been heavily studied in semiconductor heterostructures and quantum wells. Additional experimental 3,4 and theoretical 5,6,7 evidence have confirmed the presence of significant spin-orbit coupling on the Au (111) surface. Although such a spin-splitting should, in principle, occur on all surfaces, the magnitude of the spin splitting depends very strongly on the nature of the surface. For instance, spin-orbit coupling has never been observed on either the Ag(111) or the Cu (111) surfaces. This is due to the fact that the magnitude of the spin-orbit coupling is determined largely by the atomic spin-orbit coupling and the gradient of the surface state wave function at the nucleus 7 ; theoretical calculations, which accurately predict the observed spin-orbit coupling on the Au(111) surface, predict the spin-orbit coupling on the Ag(111) to be a factor of 20 smaller than the spin-orbit coupling on the Au(111) surface 6,7 , well outside the range of current experimental observation. In addition to the Au(111) surface, photoemission experiments have discovered a variety of other metallic systems with spin-orbit coupling, such as on the Bi surfaces 8 , which exhibit an even larger spin-orbit coupling than that found on Au(111).Although most experimental observations of spin-orbit coupling in surface states are from photoemission spectroscopy, scanning tunneling microscopy (STM) has been used to observe spin-orbit interference in a magnetic sample 9 and in nonmagnetic systems with very strong spin-orbit coupling, such as on the Bi(110) surface 10 and in Bi/Ag(111) and Pb/Ag(111) surface alloys 11 . However, previous theoretical work 5 has argued that scanning tunneling microscopy (STM) could not be used to observe the spin-orbit coup...

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“…3,4 The resulting locking of spin to the crystal-momentum offers potential avenues for the realization of novel spintronic devices and quantum computation. Electronic states that are spin-split due to strong spin-orbit coupling also occur at the surfaces of some non-magnetic metals, including gold, [5][6][7][8][9] tungsten, [10][11][12][13][14][15][16][17][18][19][20][21][22][23] silver, 6,9 copper, 24,25 bismuth, [26][27][28][29][30][31] antimony, 32 and iridium. 33 Following the recent experimental observation at the tungsten (110) surface of Rashba-like spin-split and spin-polarized electronic states forming an anisotropic Dirac cone-like band structure, 13 there has been renewed interest in developing a better understanding of this system.…”

Section: Introductionmentioning

confidence: 99%

Rashba-Dirac cones at the tungsten surface: Insights from a tight-binding model and thin film subband structure

Kirczenow

2016

Phys. Rev. B

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A tight-binding model of bcc tungsten that includes spin-orbit coupling is developed and applied to the surface states of (110) tungsten thin films. The model describes accurately the anisotropic Dirac cone-like dispersion and Rashba-like spin polarization of the surface states, including the crucial effect of the relaxation of the surface atomic layer of the tungsten towards the bulk. It is shown that the surface relaxation affects the tungsten surface states because it results in increased overlaps between atomic orbitals of the surface atomic layer and nearby layers whereas electric fields that are due to charge transfer between the tungsten and the vacuum near the surface or between the bulk and surface layers do not significantly affect the Rashba-Dirac surface states. It is found that hybridization with bulk modes has differing strengths for thin film surface states belonging to the upper and lower Rashba-Dirac cones and results in reversal of the directions of travel of spin ↑ and ↓ electrons in most of the upper Rashba-Dirac cone relative to those expected from phenomenology. It is also shown that intrasite (not intersite) matrix elements of the spin-orbit Hamiltonian are primarily responsible for the formation of the Rashba-Dirac cones, and their spin polarization. This finding should be considered when modeling topological insulators, the spin Hall effect and related phenomena.

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Spin-orbit splitting of theL-gap surface state on Au(111) and Ag(111)

Cited by 259 publications

References 13 publications

Decay of electronic excitations at metal surfaces

Decay of electronic excitations at metal surfaces

Spin−Orbit Coupling Induced Interference in Quantum Corrals

Rashba-Dirac cones at the tungsten surface: Insights from a tight-binding model and thin film subband structure

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