Spin polarization of surface states on W(1 1 0): Combined influence of spin–orbit interaction and hybridization

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

“…3, the spin quantization axis is in the (110) plane and perpendicular to the wave vector of the subband Bloch state. As expected for Rashba spin-split states 1,2 and consistent with experiments and previous theories for (110) surfaces of macroscopic tungsten crystals, [13][14][15][16][17][18][19][20][21]23 …”

“…The degree of quantitative agreement between the above results for the Rashba-Dirac surface states and both experiments and ab initio calculations for macroscopic tungsten crystals [13][14][15][16][17][18][19][20][21][22][23] is quite remarkable since all of the parameters of the tight binding model (described in Section II) have been fitted only to the electronic band structure [41][42][43] of bulk bcc tungsten. The only information about the tungsten surface that has been used as input in the present work is structural, namely, the experimentally measured relaxation distance 44,45 of surface atomic layer towards the bulk.…”

“…The energy splittings between the upper and lower cones are much larger in theΓ−H direction than in theΓ−N direction, as expected from previous work on the surfaces of macroscopic crystals. [13][14][15][16][17][18][19][20][21]23 The strongly spin polarized surface states are shown in Fig. 3 for a cut through the 2D Brillouin zone along the linē H−Γ−H in the Brillouin zone.…”

“…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. [13][14][15][16][17][18][19][20][21][22][23] It has been demonstrated 14 that the experimentally observed anisotropic Dirac cone-like band structure can be fitted accurately by a phenomenological third order Rashba model for surfaces with C 2v symmetry. 34 Ab initio calculations 15,17,19,20,22,23 have also accounted for the experimental data, including the Dirac conelike dispersion and the spin polarizations of the observed surface states.…”

“…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.…”