In a recent letter [Phys. Rev. Lett. 105 (2010) 036804] the unoccupied
electronic states of single layers of graphene on ruthenium are investigated.
Here we comment on the interpretation, which deviates in four points from [J.
Phys.: Condens. Matter 22 (2010) 302001] and outline the corresponding
consequences

Greber, T.

Zhang, H. G.

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arXiv

H. G. Zhang

T. Greber

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Physical Review Letters

Comment on “Potential Energy Landscape for Hot Electrons in Periodically Nanostructured Graphene”

Zhang, H G

Greber, T

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arXiv:1008.1777v1  [cond-mat.mtrl-sci]  10 Aug 20101Comment on ”Potential Energy Landscape forHot Electrons in Periodically NanostructuredGraphene”In a recent letter [1] the unoccupied electronic statesof single layers of graphene (g) on ruthenium are inves-tigated. It is shown that elevated graphene areas witha diameter of about 2 nm (H-areas or ”hills”) look likequantum dots [1, 2]. Regions where graphene binds tothe substrate are the L-areas or ”valleys”, and separatethe dots.Here we comment on the two interpretations [1] and[2], which deviate in four points (see Figure 1) and out-line the corresponding consequences. First we want todiscuss the assignment of the first field emission reso-nance (FER1) that originates from the first image po-tential state 0.85 eV below the vacuum level [3, 4]. The3 eV peak in the L-area is assigned in Ref.[2] to the firstfield emission resonance, with a corresponding state ata significantly higher energy (0.08±0.03 eV) in the H-area. Note that the different energies of FER1 on thehills and in the valley and the discrimination of higherFER’s on H and L exclude this peak to be related tocross talk. Figure 2 shows however that both assign-ments of FERn are compatible with an empirical trendE(n) = E0 − Bn−2 + Cn of the FER energies. Bothshow smaller E0’s on the L-areas and thus indicate alarger local work function on the H-areas [5]. The ob-tained B values give a hint on which peak identificationholds: While [1] results in B=0.6 eV, interpretation [2]results in B=2.7 eV. A B which is larger than the 0.85eV of the image state, indicates that the −1/4z imagepotential with a hard wall mirror on the metal side, doesnot apply, but that there is an anomalous FER energylowering in the g/Ru(0001) system. Ref.[2] identifies thislowering to be due to the graphene quantum well, whichdelocalizes the FER wave functions. From this the as-signment of the other peaks in interpretation [2] follows:The strong resonance on the H-areas is a quantum wellresonance (QWR) with a counterpart in the L-areas at500 meV higher energy, which is due to the thinner wellin the L-areas. Furthermore, interpretation [2] gives ar-guments for the peak intensities and has, in the sense ofL-area valley3 eVH-area hill +0.08 eVRef. [2]Ref. [1] Ref. [2]Ref. [1]FER2QWRFER1FER2FER1NISFER2 FER2FER1 QWRFER14.4 eVFIG. 1: Peak assignments in the L- and H-areas ofg/Ru(0001). The first two Field Emission Resonances (FER1and FER2), the New Interfacial State (NIS) of Ref.[1] and theQuantum Well Resonance (QWR) from Ref.[2] are marked.9876543Energy above EF (eV)87654321Field Emission Resonance Quantum Number n  Ref. [1] Ref. [2] image potential states E(n) = E0 - B n-2 + C nFIG. 2: Field Emission Resonance energies (FER1 to FER8)on the L-areas in g/Ru(0001) (Energy values from [1]). Bothassignments Ref.[1] and Ref.[2] may be fitted to an empiricaltrend E(n) = E0 − Bn−2 + Cn. For comparison an imagepotential state series for E0=3.9 eV, B=0.85 eV and C=0 isshown.Occams razor, the advantage that all FER’s follow thetrend of the local work functions.On the other hand, the non-observation of the ”newinterfacial state” (NIS) on the H-areas in Ref.[1] leavesa problem. Besides this, the localisation of the electronsin the 4.4 eV peak is ”outside” the graphene [1] or”inside” [2], which is an essential difference if the stateshall be used in the context of a quantum dot array orthe dynamics of hot electrons. Although the conceptof the double Rydberg series of free standing graphene[6] also imposes new states, it is not clear whether it isof use for the present situation, because the substratebreaks the symmetry. The first principles calculationsin [1] base on calculations within a (1x1) Ru(0001) cellwith strained graphene on top. They do not include theimage potential tail nor the lateral localisation (Ref.[2]estimates the effect for the hills to be in the order of 0.2eV). This, and the straining of the graphene could givea substantial change of the energies, with respect to thevacuum and/or Fermi level, and we expect that first prin-ciple calculations which include these considerations areconsistent with the model and the assignments in Ref.[2].H.G. Zhang1, and T. Greber2, 1Institute of Physics,Chinese Academy of Sciences, Beijing 100190, China,2Physik-Institut, University of Zu¨rich, 8057 Zu¨rich,Switzerland. August 11, 2010.[1] B. Borca et al., Phys. Rev. Lett. 105, 036804 (2010).arXiv:1004.0593.[2] H.G. Zhang et al., J. Phys.: Condens. Matter 22, 302002(2010). arXiv:0911.4024.[3] G. Binnig et al., Phys. Rev. Lett. 55, 991 (1985).2[4] D. Straub and F. J. Himpsel, Phys. Rev. B 33, 2256(1986).[5] T. Brugger et al., Phys. Rev. B 79, 045407 (2009).[6] V.M. Silkin, et al.,. Phys. Rev. B 80, 121408(R) (2009).

Comment on "Potential energy landscape for hot electrons in periodically nanostructured graphene"

Comment on "Potential Energy Landscape for Hot Electrons in Periodically
  Nanostructured Graphene"

Comment on "Potential Energy Landscape for Hot Electrons in Periodically Nanostructured Graphene"

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