Reply to “Comment on 'Spin–Orbit Coupling Induced Gap in Graphene

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Reply to “Comment on ‘Spin−Orbit Coupling Induced Gap in Graphene on Pt(111) with Intercalated Pb Monolayer’” Ilya I. Klimovskikh,*,† Mikhail M. Otrokov,†,§ Vladimir Yu. Voroshnin,† Daria Sostina,† Luca Petaccia,∥ Giovanni Di Santo,∥ Sangeeta Thakur,∥ Evgueni V. Chulkov,†,‡,⊥,§ and Alexander M. Shikin† †

Saint Petersburg State University, 198504 Saint Petersburg, Russia Tomsk State University, 634050 Tomsk, Russian Federation § Departamento de Fı ́sica de Materiales UPV/EHU, Centro de Fı ́sica de Materiales CFM-MPC and Centro Mixto CSIC-UPV/EHU, 20080 San Sebastián/Donostia, Basque Country, Spain ∥ Elettra Sincrotrone Trieste, Strada Statale 14 km 163.5, 34149 Trieste, Italy ⊥ Donostia International Physics Center (DIPC), 20018 San Sebastián/Donostia, Basque Country, Spain ‡

n a recent article,1 we studied the electronic and spin structure of graphene on Pt(111) with intercalated Pb monolayer. By means of ARPES, we have shown that the Dirac cone of graphene is characterized by the gap between the π and π* states in this system. The spin texture of the π and π* states and its correspondence with the Kane and Mele model for graphene with spin−orbit gap have been unveiled by spinresolved ARPES. In the Comment2 on our paper, Dedkov and Voloshina claim that (1) the notation of the superstructure used in our work is incorrect, and (2) spin-resolved data treatment is inappropriate. In this Reply, we show that the superstructure notation is indeed correct. Moreover, the statistical analysis of the reported spin-resolved ARPES data and new experimental data with better statistics support the main conclusion of our article.1 First, Dedkov and Voloshina claim that the notation of the √3 × √3R30° superstructure of graphene on Pt(111) is incorrect. However, previously in ref 3, we accurately studied this domain of graphene on Pt(111) by LEED and showed that the formed superstructure has √3 × √3R30° supercell relative to the Pt substrate. Dedkov and Voloshina believe that the notation should be (2/√3 × 2/√3)R30°−graphene/(1 × 1)− Pt(111) or the equivalent (2 × 2)−graphene/√3 × √3R30°− Pt(111). According to ref 4, the Wood’s notation of the superstructure has to be given relative to the substrate. As seen in Figure 1 of the Comment, the unit cell of graphene can indeed be presented by (2/√3 × 2/√3)R30° relative to the (1 × 1)−Pt(111). However, the unit cell of the formed superstructure, which reflects all the symmetries of the system, corresponds to √3 × √3R30° relative to the Pt substrate. The measured LEED pattern and schematic reciprocal lattices adapted from ref 3 are shown in Figure 1. In panel (b), the blue spots are related to the (1 × 1)−Pt(111) substrate, whereas the red spots are due to the graphene superstructure, which is definitely a √3 × √3R30° phase. If one considers the (2/√3 × 2/√3)R30° superstructure with respect to the 1 × 1− Pt(111) as proposed in the Comment, only the 1 × 1 blue spots and additional spots halfway between them on the blue hexagon will be present. Therefore, the (2/√3 × 2/√3)R30°−

I

© XXXX American Chemical Society

Figure 1. (a) LEED pattern of graphene on Pt(111) and (b) schematic reciprocal lattices.

Figure 2. Raw (gray symbols) and averaged (black symbols) spin polarization with corresponding error bars for graphene/Pb/ Pt(111) system measured at the emission angle corresponding to k∥ = 1.75 Å−1.

graphene/(1 × 1)−Pt(111) notation is not consistent with the measured LEED pattern, which calls for the √3 × √3R30° phase. The same notation √3 × √3R30° has been used for this domain of graphene on Pt(111) in ref 5. Second, Dedkov and Voloshina state that the analysis of the spin-resolved data in our article is incorrect and “conclude that Received: September 23, 2017

A

DOI: 10.1021/acsnano.7b06779 ACS Nano XXXX, XXX, XXX−XXX

Letter to the Editor

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ACS Nano

Letter to the Editor

Figure 3. Spin-resolved spectra obtained by the averaged spin polarization with corresponding error bars for graphene/Pb/ Pt(111) system measured at the emission angle corresponding to k∥ = 1.75 Å−1.

Figure 4. New spin-resolved spectra and spin polarization obtained at the same conditions as in Figure 3a (right) of ref 1, with corresponding error bars for graphene/Pb/Pt(111) system measured at the emission angle corresponding to k∥ = 1.75 Å−1. No averaging procedure was applied to this data set. The spectrum had been taken at BESSY II synchrotron at the UE-56 beamline.

the spin-splitting of 100 meV presented in Figure 3a of ref 1 does not exist”. The main controversy Dedkov and Voloshina find in the averaging of the spin polarization is the belief that it is “an absolutely inappropriate step for the treatment of spinresolved photoemission data”. They also believe that the averaging procedure leads to increase of the polarization error from ΔP to √NΔP or even to NΔP, where N is the number of averaging points. However, this error estimation is valid for the sum of the values and not for the average and obviously is irrelevant to our data treatment. The averaging procedure is described by the simple formula: Pav =

1 N

Therefore, the averaging procedure decreases the error of measurements. The statistical error in spin polarization measurements is given by6,7 1 1 ΔP = ΔA ≃ (5) S S I where A is the asymmetry

(1)

i=1

where Pi is the raw spin polarization taken from the experiment. The resulting error is calculated as N i=1

=

≃

1 N

⎛

∑ ⎜ΔPi

ΔPav =

⎝

2 ∂Pav ⎞ ⎟ = ∂Pi ⎠

(2)

N

∑ (ΔPi)2 ≃ i=1

1 N ΔP = ΔP / N N

and I = IL + IR.

The relevant raw and averaged spin polarizations presented in the right panel of Figure 3a of our article1 are reshown in Figure 2 with the associated error bars, calculated by using eqs 4 and 5. The number of points used for the averaging is N = 5; that is, each point was averaged with its two nearest neighbors. This leads to a decrease in the error of the averaged spin polarization values (eq 4) at the expense of the error on the associated binding energy (BE) positions, which of course increase. The choice of N is mainly dictated by the needed energy resolution. Owing to the averaging procedure with N = 5, the energy error increases to ±40 meV (the energy step during the experiment was 20 meV), which is also shown in Figure 2. The value of the averaged spin polarization Pav reaches 3.5% with the error ΔPav of 1.3% in the region of interest around 0.3 eV of BE and confirms a nonzero spin polarization. Notably, the spin polarization in this region is nonzero also for the statistical significance level of 5%, that is, the standard of statistical significance.

N

∑ Pi

IL − IR IL + IR

(3)

(4) B

DOI: 10.1021/acsnano.7b06779 ACS Nano XXXX, XXX, XXX−XXX

ACS Nano

Letter to the Editor

Spin-Orbit Coupling Induced Gap in Graphene on Pt(111) with Intercalated Pb Monolayer. ACS Nano 2017, 11, 368−374. (2) Dedkov, Y.; Voloshina, E. Comment on “Spin−Orbit Coupling Induced Gap in Graphene on Pt(111) with Intercalated Pb Monolayer. ACS Nano 2017, DOI: 10.1021/acsnano.7b00737. (3) Klimovskikh, I. I.; Tsirkin, S. S.; Rybkin, A. G.; Rybkina, A. A.; Filianina, M. V.; Zhizhin, E. V.; Chulkov, E. V.; Shikin, A. M. Nontrivial Spin Structure of Graphene on Pt(111) at the Fermi Level due to Spin-Dependent Hybridization. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90, 235431. (4) Wood, E. Vocabulary of Surface Crystallography. J. Appl. Phys. 1964, 35, 1306−1312. (5) Otero, G.; González, C.; Pinardi, A. L.; Merino, P.; Gardonio, S.; Lizzit, S.; Blanco-Rey, M.; Van de Ruit, K.; Flipse, C. F. J.; Méndez, J.; et al. Ordered Vacancy Network Induced by the Growth of Epitaxial Graphene on Pt(111). Phys. Rev. Lett. 2010, 105, 216102. (6) Jozwiak, C. A New Spin on Photoemission Spectroscopy. Ph.D. Thesis, University of California, Berkeley, 2010. (7) Hoesch, M.; Greber, T.; Petrov, V. N.; Muntwiler, M.; Hengsberger, M.; Auwärter, W.; Osterwalder, J. Spin-Polarized Fermi Surface Mapping. J. Electron Spectrosc. Relat. Phenom. 2002, 124, 263−279.

The spin-resolved spectra Iup,down can be calculated using the well-known formula: Iup,down = (1 ± P)I /2

(6)

Correspondingly, the error for the spin-up spectrum (the same as for the spin-down one) can be obtained as ΔIup =

=

1 (1 + P)2 ΔI 2 + I 2ΔP 2 = 2

1 1 I 1 + 2P + P 2 + 2 ≃ 2 SN

≃1.9 ×

I

(7)

(8) (9)

The resulting spin-resolved spectra with the error bars are shown in Figure 3. The spin-split π* state is clearly visible in the region around 0.3 eV of BE. Moreover, we had opportunity to remeasure the spinresolved ARPES spectra of graphene/Pb/Pt(111) with better statistics (total intensity is more than 4 times larger). The raw spin polarization and the corresponding spin-polarized spectra with error bars are shown in Figure 4. These new results, obtained without any averaging procedure, show again a nonzero spin polarization with a maximum value of 2.9 ± 1.5% in the region around 0.3 eV of BE. The spin-splitting of the graphene state in the spin-up and spin-down spectra shown in the top panel of Figure 4 is also consistent with the previous result.1 Unfortunately, in ref 1, we made an accidental misprint in the caption of Figure 3 (where “multiplied by the Sherman function” is reported instead of “divided by the Sherman function”), but in the Methods section, the correct formula is presented.

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. ORCID

Ilya I. Klimovskikh: 0000-0003-0243-0322 Luca Petaccia: 0000-0001-8698-1468 ACKNOWLEDGMENTS The work was partially supported by grant of Saint Petersburg State University for scientific investigations (No. 15.61.202.2015). We acknowledge support by the University of the Basque Country (Grant Nos. GIC07IT36607 and IT756-13), the Spanish Ministry of Science and Innovation (Grant Nos. FIS2013-48286-C02-02-P, FIS2013-48286-C0201-P, and FIS2016-75862-P), and Tomsk State University competitiveness improvement programme (Project No. 8.1.01.2017). The part of photoemission measurements was supported by Russian Science Foundation (Project No. 17-1201047). The authors acknowledge support from the Russian− German laboratory at BESSY II and the “German−Russian Interdisciplinary Science Center”(G-RISC) program. A.G. Rybkin, D. Estyunin, and O. Vilkov are thanked for help with the measurements. Authors also thank Dr. D. Usachov for intense discussions. REFERENCES (1) Klimovskikh, I. I.; Otrokov, M. M.; Voroshnin, V. Y.; Sostina, D.; Petaccia, L.; Di Santo, G.; Thakur, S.; Chulkov, E. V.; Shikin, A. M. C

DOI: 10.1021/acsnano.7b06779 ACS Nano XXXX, XXX, XXX−XXX