Tunable Fermi level and hedgehog spin texture in gapped graphene

Spin and pseudospin in graphene are known to interact under enhanced spin–orbit interaction giving rise to an in-plane Rashba spin texture. Here we show that Au-intercalated graphene on Fe(110) displays a large (∼230 meV) bandgap with out-of-plane hedgehog-type spin reorientation around the gapped Dirac point. We identify two causes responsible. First, a giant Rashba effect (∼70 meV splitting) away from the Dirac point and, second, the breaking of the six-fold graphene symmetry at the interface. This is demonstrated by a strong one-dimensional anisotropy of the graphene dispersion imposed by the two-fold-symmetric (110) substrate. Surprisingly, the graphene Fermi level is systematically tuned by the Au concentration and can be moved into the bandgap. We conclude that the out-of-plane spin texture is not only of fundamental interest but can be tuned at the Fermi level as a model for electrical gating of spin in a spintronic device.

(a) ARPES dispersion of Dirac cone sampled along Γ − K of graphene SBZ. Anisotropic intensity of π and π * bands due to Brillouin zone effects is seen. Yellow frame denotes acceptance frame of spin analyser positioned precisely at K-point. Red frame denotes angular localization of spin hedgehogs around K. (b) Spin-resolved EDC spectrum simulated by integration of ARPES intensity over yellow frame reveals equal intensity of π and π * peaks.
(c,d) Same as (a,b) but yellow frame of spectrometer is misaligned by 0.12 • toward 1 st SBZ.
Intensity disbalance between π and π * is identical to that seen in spin-resolved spectrum in Figure 3(f) (in the article), but red frame of spin hedgehog remains perfectly inside of yellow frame of analyser and therefore is fully acquired. Photoemission measurements were performed with photon energy of 62 eV. Figure 7. Relevance of spin hedgehogs in graphene to spintronics. (a)

Supplementary
Valley Hall effect (VHE) emerging in graphene with inequivalent orbital magnetic moments of K and K ′ valleys. When the electric field E in−plane is applied in the graphene plane and collinear to the current direction, deflection of the charge carriers toward the edge of the stripe occurs due to valley-polarized scattering induced by a Berry phase effect. This causes different population of Dirac cones at K and K ′ valleys at opposite edges of the graphene stripe. This idea was firstly formulated in Ref. [20] but for valley associated pseudo spin and not for real spin. (b) Scheme of Y-shaped spin separator utilizing the effect of spinvalley scattering for spin filtering of electric currents. The spin separator is attached to three conducting gates/leads. Gates 2 and 3 (collectors) have equal potentials V G2 and V G3 . Voltage at gate 1 (emitter) V G1 is different. The difference between V G1 and V G2,G3 drives electric current through Y-shaped graphene flake, but, at the same time, creates an in-plane electric field which activates spin-valley scattering. As a result, charge carriers with one spin are deflected toward gate 2 (red arrow) and charge carriers with the opposite spin toward gate 3 (blue arrow). Principle of valleytronic device utilizing spin-valley scattering was proposed in Ref.
[21] but for using Zeeman effect for spin-polarization of K and K ′ valleys and not spin hedgehogs (which in present study are already available in ground state without application of external field). [e.g. graphene/Ir(111)] it is known that energy gaps occur as minigaps at the crossings of replicas with the main Dirac cone [8][9][10][11]. The width of the minigaps is determined by the amplitude of the modulating lateral superpotential [9,12]. The case of 2ML of intercalated Au is more complicated. Supplementary Figure 3 shows that the lower Dirac cone demonstrates a curvature just below E F (lower edge of the gap) but the upper cone of π * band has moved above the Fermi level and neither width of the gap between π and π * nor middle of the gap can be read directly from the ARPES dispersion.
In this case we apply an extrapolation scheme assuming that upper and lower Dirac cones are mirror symmetric. Such scheme provides an estimate for the minimal value of E g . As shown in Supplementary Figure 3(b) the linear dispersion of the π-band is extrapolated by straight lines and the crossing point between them is taken as Dirac energy E D . The width of the gap E g is determined as twice the difference between E D and the lower edge of the gap. In this way we obtain E D =E F (±10 meV) meaning that graphene is charge neutral and  Figures   5(b,e)], but the measured out-of-plane spin polarization S OP is zero [ Supplementary Figures   5(c,f)]. Such behaviour fully complies with the scenario of the Rashba effect in graphene [15,16]. We should emphasize that the measurements of in-plane and out-of-plane spin components are feasible despite certain polar rotation of the sample (θ) toward K. There is only minor projection of in-plane spins onto the S OP axis while measuring an out-of-plane signal because the rotation of θ toward K is small (θ ∼24 • at photon energy hν ∼60 eV) and additionally reduced by non-zero tilt τ . The resulting magnitude of out-of-plane projection is less than 1 3 of the in-plane component and nearly undetectable. Particular care was taken to ensure the correct observation of the hedgehog-type out-ofplane spin texture at K. Although projection of Rashba-type (in-plane) spin polarization onto S OP axis is negligible, one may naively argue that the spin polarization of exchangesplit 3d bands in the underlying Fe film may contribute. In order to exclude such possibility Finally, we want to emphasize that the measured hedgehog-type spin textures originate from the outer band of spin-orbit spilt Dirac cone, which is sketched in Figure 3

Supplementary Note 5 Precision of sample alignment
We would like to comment on the momentum resolution of the spectrometer and on the accuracy of sample orientation, and show that small experimental errors are negligible for the correct interpretation of our spin-and angle-resolved photoemission measurements. Spinresolved spectra revealing out-of-plane spin polarization (spin hedgehog) in the gap of the Dirac cone [ Figure 3(f) in main article] display slightly different intensities of lower (π) and upper (π * ) bands at the gap edges. However, precisely at K, intensities of upper and lower cones have to be equal, as ARPES data in Figure 3(a) in the article shows. This suggests that the sample had slight angular misalignment in the spin-resolved measurement. This small misalignment originates from the transfer lens setup (aperture positioning) of our state-of the-art spectrometer which allows for simultaneous acquisition of ARPES dispersions and spin-resolved EDCs without changing the sample position. This is an important feature of the spectrometer and the small misalignment is, hence, principally unavoidable. Our analysis below shows that the resulting experimental mistake is negligible and has no effect on the results obtained.
The error introduced by the transfer lens is easily estimated by the angular dependence of the ARPES signal. Relatively large differences of the intensities of upper and lower Dirac cone in the gap result already from a minor angular misalignment of the the sample. The reason for this is the distribution of photoelectron intensity in the Dirac cones, which is extremely anisotropic due to a Brillouin zone effect [6]. Due to this effect, the intensity of the lower cone (π) in the 2 nd surface Brillouin zone (SBZ) is suppressed by factor of ∼50 as compared to its intensity in the 1 st SBZ. For the upper cone (π * ) the situation is opposite.
Its intensity in the 2 nd SBZ is enhanced while in the 1 st SBZ it is dramatically suppressed.
This scenario is clearly seen in Supplementary Figures 6(a,c) which show zoomed dispersion of Dirac bands along the Γ − K direction of the SBZ (k passes from 1 st to 2 nd SBZ through K-point). The anisotropy of intensities is so strong that even small angular inaccuracies should cause significant imbalance between intensities of π and π * peaks.
Since spin resolved data shown in Figure 3 in the article (and in Supplementary Figure   5) was measured in the direction perpendicular to Γ − K (optimal geometry for elimination of Brillouin zone effects and observation of both sides of Dirac cones), the misalignment causing unequal intensities of π and π * in Figure 3(f) corresponds to misalignment along Γ − K. This allows us to estimate the angular misalignment from ARPES data shown in Supplementary Figures 6(a,c).
In Supplementary Figure 6(a) the angular acceptance frame of the spin-ARPES spectrometer used for Figure 3(f) (0.7 • ) is denoted by a yellow rectangle and positioned precisely at K. The EDC profile, representing the corresponding spin-resolved spectrum, is acquired by integration of ARPES intensity within yellow frame and is shown in Supplementary Figure   6(b). In this spectrum peaks of π and π * bands have equal intensity. In our analysis we have scanned the position of the spectrometer frame along Γ − K and looked for the intensity variations of π and π * peaks. The intensity imbalance seen in Figure 3 [18]), the localization region of out-of-plane spins around the K-point is given by where ν F is the Fermi velocity of Dirac fermions, and λ R the Rashba parameter for the spin-orbit interaction in the graphene. The Rashba splitting seen in Figures 3(c) and 3(d) in the article (∼70-80 meV) means λ R ∼25-30 meV, which gives for the localization of the hedgehog ∆k S ∼0.015Å −1 (or 0.25 • at 62 eV photon energy). The angular localization of the spin hedgehog around K is marked in Supplementary Figures 6(a,c) by a red frame.
Apparently, the red frame remains perfectly inside of the yellow frame of the spectrometer in the case of 0.12 • sample misalignment (and would remain there for even larger errors).
This in turn means that the entire spin hedgehog around K is acquired by the spectrometer which confirms the out-of-plane spin obtained in the measurement.
We can also roughly estimate the sensitivity of the spin-resolved measurement and the expected magnitude of out-of-plane spin polarization. Indeed, the angular localization A similar effect was later elaborated theoretically by Tsai et al. [20] but for real spin based on the high-spin-orbit material with broken sublattice symmetry silicene. It was suggested to use an electric field applied perpendicular to graphene in order to create a Zeeman-type splitting of the Dirac cone. Such induced spin-polarization has opposite sign at K and K ′ valleys. Scattering of electrons to the valleys with spin polarization opposite to the electron spin is suppressed. This spin-valley scattering is expected to be much more effective than the simple valley-only scattering described in Ref. [19] and may allow for nearly 100% filtering of electron spin [20].
The scheme of a possible device utilizing the effect of spin-valley scattering (originally proposed in Ref. [20]) is shown in Supplementary Figure 7(b). This is a spin separator consisting of a Y-shaped flake of graphene attached to three conducting gates/leads. It is assumed that gates 2 and 3 (collectors) have equal potential V G2 and V G3 , while the voltage at gate 1 (emitter) V G1 is different. The potential difference between V G1 and V G2,G3 drives electric current through the graphene flake, but, at the same time, creates an in-plane electric field which activates spin-valley scattering. As a result charge carriers with one spin are deflected toward gate 2 (red arrow) and charge carriers with the opposite spin toward gate 3 (blue arrow).
The present case of graphene/Au/Fe(110) is very interesting in the context of such device since it has high spin-orbit splitting and broken sublattice symmetry and out-of-plane spin polarization in the gap of Dirac cones, which according to Ref. [18], changes its sign at K and K ′ valleys. It is also remarkable that no external electric field is needed to achieve spin polarization of valleys in graphene/Au/Fe(110), since it is induced not by a Zeeman field but through extrinsic spin-orbit interactions.
Although graphene/Au/Fe(110) cannot be directly used for the construction of an effective spin separator since it has conducting substrate and cannot bear 2D currents, it is a useful system allowing to study and understand physics relevant to valleytronic devices and graphene-gate junction therein.

Supplementary Note 7
Preparation of graphene on Fe(110) All sample preparations were done in situ. The Fe(110) substrate was prepared as several tens of monolayers (ML) of Fe grown on W(110). The W(110) crystal was initially cleaned by repeated cycles of annealing in oxygen (partial pressure of oxygen 1×10 −7 mbar, temperature 1500K) followed by short flashing of the sample up to 2300K in ultra-high vacuum (UHV) environment [1,2]. The sample preparation is reported in Supplementary Figure 8.  (110) is additionally evidenced by the presence of a faint dispersion due to a surface resonance at ∼3 eV (at Γ-point) denoted as SR [17].
Graphene was synthesized by chemical vapour deposition of ethylene or alternatively propylene. The Fe(110) sample was heated to 950-1050K in UHV. Then the hydrocarbon was let into the chamber at a partial pressure of 5×10 −6 mbar for 10 minutes. The successful synthesis of graphene depends strongly on the partial hydrocarbon pressure and sample temperature. In the case of insufficient control over these parameters an Fe surface carbide is formed. Its valence band structure is shown in Supplementary Figure 8 and graphene (orange dashed lines) extracted from experimental LEED measurements. One sees that the principle diffraction spots at the corners of LEED patterns (see the area inside of dashed circle) are not in registry with each other due to surface lattice mismatch between Fe and graphene. This structural difference determines the 2D repetition of diffraction spots (black points) with periodicity (7×17) in terms of graphene hexagons [4]. This moiré constellation around a principle graphene spot as it occurs in LEED is zoomed in Supplementary Figure 9 Intercalation with Au was achieved by deposition of one up to several monolayers of Au on graphene/Fe(110) and subsequent annealing at 750-800K. We have studied two concentrations of Au for which band structures and charge doping of graphene were found clearly defined and homogeneous over the surface. The first phase, showing n-type doping and a 1D electronic structure, is achieved at nominally 1.4ML of intercalated Au. This phase is referred in the manuscript as 1ML-phase. The second phase (charge neutral) is achieved after increasing the total amount of intercalated Au up to 2.3ML. This phase with higher Au concentration is referred in the paper as 2ML-phase. For higher concentrations of intercalated Au we found no differences in the band structure as compared to 2ML.