Dirac-cone-like surface state in W(110): dispersion, spin texture and photoemission from first principles

Mirhosseini, Hossein; Flieger, Markus; Henk, Jürgen

doi:10.1088/1367-2630/15/3/033019

Cited by 35 publications

(46 citation statements)

References 42 publications

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“…1(d that we observe only at this photon energy. Given that along this crystal orientation an intrinsic out-of-plane spin component is not allowed, due to symmetry considerations, we attribute the observed component to a matrix element of the SARPES process [SR3]. We stress that, contrary to the anomalous behavior of P z , P x is wholly compatible between all the data sets, which strongly indicates that this latter component of the spin polarization is intrinsic.…”

Section: 855-858 (2008)mentioning

confidence: 80%

Giant spin splitting of the two-dimensional electron gas at the surface of SrTiO3

et al. 2014

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1 Two-dimensional electron gases (2DEGs) forming at the interfaces of transition metal oxides [1][2][3] display a range of properties including tunable insulatorsuperconductor-metal transitions [4][5][6], large magnetoresistance [7], coexisting ferromagnetism and superconductivity [8, 9], and a spin splitting of a few meV [10,11]. Strontium titanate (SrTiO 3 ), the cornerstone of such oxide-based electronics, is a transparent, nonmagnetic, wide-band-gap insulator in the bulk, and has recently been found to host a surface 2DEG [12][13][14][15]. The most strongly confined carriers within this 2DEG comprise two sub-bands, separated by an energy gap of 90 meV and forming concentric circular Fermi surfaces [12,13,15].Using spin-and angle-resolved photoemission spectroscopy (SARPES), we show that the electron spins in these sub-bands have opposite chiralities. Although the Rashba effect might be expected to give rise to such spin textures, the giant splitting of almost 100 meV at the Fermi level is far larger than anticipated [16,17].Moreover, in contrast to a simple Rashba system, the spin-polarized sub-bands are non-degenerate at the Brillouin zone centre. This degeneracy can be lifted by time-reversal symmetry breaking, implying the possible existence of magnetic order. These results show that confined electronic states at oxide surfaces can be endowed with novel, non-trivial properties that are both theoretically challenging to anticipate and promising for technological applications.The 2DEG at the surface of SrTiO 3 , formed by confined electrons of the t 2g conduction band with Ti-3d character, is universal in the sense that its constituent subbands, their fillings, and their Fermi surfaces are independent of the bulk sample doping and of whether the surfaces are prepared by cleaving [12,13] or by etching and in situ annealing [15]. This 2DEG consists on two light electron subbands dispersing down to about −180 meV and, respectively, −90 meV below the Fermi level (E F ), producing concentric Fermi surfaces around the Brillouin zone center, and heavy shallow subbands dispersing down to about −40 meV, forming ellipsoidal Fermi surfaces [12,13,15].In fact, the 2DEG in SrTiO 3 has been associated with a band-bending of ∼ 300 meV at the surface of the material [12,13,15]. In such a quantum well profile, the most bound light subbands are tightly confined near the surface, while the less bound heavy subbands are more delocalized towards the bulk [12,15]. The present work focuses on resolving the spin 2 structure of the strongly two-dimensional light subbands, which are the most technologically relevant in terms of their carrier concentration and mobility.The surface band-bending of ∼ 300 meV amounts to an electric field F ∼ 100 MV/m confining the conduction electrons near the surface. In a simple approximation, this field will induce a so-called "Rashba splitting" of the spin states in each subband, with the largest splitting occurring for the most bound subbands. In an ideal surface, the corresponding momentum separat...

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Section: 855-858 (2008)mentioning

confidence: 80%

Giant spin splitting of the two-dimensional electron gas at the surface of SrTiO3

et al. 2014

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“…Although the present model is parameterized by fitting to only the bulk electronic structure of tungsten, it also captures correctly the important effect 17 on the Rashba-Dirac cone surface states of the relaxation of the W(110) surface atomic layer towards the bulk that is observed experimentally. 44,45 It is shown below that this effect is due to the increased overlaps between atomic orbitals of the tungsten surface and bulk atomic layers induced by the relaxation.…”

Section: Introductionmentioning

confidence: 94%

“…The tungsten lattice parameter is a = 3.16Å. 17 that are the topic of the present work. H 0 ij , like standard extended Hückel theory, does not include spin-orbit coupling which is included in the present tight binding model using the formalism developed in Refs.…”

Section: Modelmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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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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One Step Model Description of HARPES: Inclusion of Disorder and Temperature Effects

Braun

Minář

Ebert

2015

Springer Series in Surface Sciences

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Dirac-cone-like surface state in W(110): dispersion, spin texture and photoemission from first principles

Cited by 35 publications

References 42 publications

Giant spin splitting of the two-dimensional electron gas at the surface of SrTiO3

Giant spin splitting of the two-dimensional electron gas at the surface of SrTiO3

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

One Step Model Description of HARPES: Inclusion of Disorder and Temperature Effects

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