Orbital-symmetry-selective spin characterization of Dirac-cone-like state on W(110)

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

“…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.…”

“…[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. However, it is also of interest to investigate the underlying physics with the help of a tight-binding model that, unlike the anisotropic Rashba phenomenology, 14 is atomistic and also can provide insights that are complimentary to those obtained from ab initio calculations.…”

“…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.…”

“…However, it is also of interest to investigate the underlying physics with the help of a tight-binding model that, unlike the anisotropic Rashba phenomenology, 14 is atomistic and also can provide insights that are complimentary to those obtained from ab initio calculations. 15,17,19,20,22,23 Such a tightbinding model is introduced here and applied to tungsten thin films with (110) surfaces and their electronic subband structure.…”