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Surface and Interface States of Periodically Rippled Graphene/Ru(0001)

g_image_potential_states.pngThe possibility to fabricate freestanding Graphene, a single atomic layer of graphite, has raised interesting questions with regard to its surface electronic structure. Due to the fact that this system exhibits a mirror plane with in fact two surfaces, the eigenstates of this system must be either a symmetric or antisymmetric superposition of the electronic states of each surface. This applies also to image-potential states, a class of intrinsic surface states that exist at all solid surfaces due to the interaction of an electron in the vacuum with the polarizable surface. This interaction can be described by the classical image-potential which gives rise to a hydrogen-like Rydberg series of electronic surface states with binding energies Consequently, it has been predicted that freestanding graphene should possess a double Rydberg-like series of image-potential states of even and odd symmetry:


Here, a± denotes the quatum defect of the even and the odd states, respectively. However, there are so far no experiments on freestanding graphene that provide clear evidence for these two series.

The Graphene/Ru(0001) Interface

gru_structure.pngThe focus of the experiment is the question how the surface states of graphene and those of a clean metal substrate evolve to a common interfacial electronic structure when both are brought into close contact. As shown for serveral organic/metal interfaces, the properties of interface states strongly depend on the adsorption height of the specific organic molecule. Thus, an exceptional interesting species of a thin single layer of graphene on a metal substrates is given by graphene/Ru(0001). Due to the strong bonding of the graphene to the substrate, the relative large latice missmatch results in a strong rippling of the graphene. This leads to a hexagonal 25x25 moiré superlatice of the graphene whose carbon atoms are bound covalently to the Ruthenium atom in the valleys (L-areas) with an adsorption heigth of 2.2 Å and rather physisorped in the hills (H-areas) with an adsorption heigth of 3.7 Å.
Since the unoccupied electronic structure of graphene/Ru(0001) is postioned energetically between the Fermi-level and the vacuum niveau, we employ the time-, energy- and angle-resolved two-photon photoemission experimental setup to gain information on the binding energies, ultrafast dynamics an lateral localization of the electronic states.

Binding Energies

gru_energy.pngThe two-photon photoemission spectrum of graphene/Ru(0001) holds a multiplicity of spectral features. The comparison of the spectrum only taken with the pump- or the probe laser beam with the combination of both as well as the choice of their photon energies enables us to identify these features unambigously.

We observe the first members n=1, 2 and n=1' of two independent series of image-potential states which at first glance may be attributed to the even and odd double series predicted for freestanding graphene. Actually these can be identified as two single series of lower and higher binding energies with respect to the different local work functions which are located in the L-areas and the H-areas, respectively. The reduction from a double to a single Rydberg-like series can be attribued to the symmetry braek due to the presence of the metal substrate.

Additionally we observe, that the confinement in the L-Areas shifts up the surface resonance S' of Ru(0001) in energy with respect to the Fermi level where it forms a new interfacial state S due to hybridizaton with the first image potential state while in the H-areas it is not modified.



The conducted angle-resolved two-photon photoemission spectroscopy is able to reveal the energy-dispersion of the initially unoccupied surface states with respect to the electron's momentum k|| parallel to the surface.

The image-potential states as well as the surface resonance and the interfacial state clearly show a parabolic dispersion within surface projected band structure. Since the electrons in these states are able to move freely along the surface the exhibit an effective mass meff near unity except the image-potential state n=1'. In comparison to the more connected L-areas the later state is more localized within the seperated H-areas which is indicated by its larger effective mass of meff = 2.

The strong corrugation of the graphene sheet also has a major impact on the surface band structure: All states show a remarkable backfolding at the surface Brilloiun zone boundaries of the moiré superlattice.


gru_ccf.pngThe ultrafst electron dynamics of the image-potential states as well as of the the surface resonance and the interfacial state can be accessed by a systematic variation of the time dealy between the pump- and the probe laser beam.

The decay dynamics reveal that in the L-areas the epitaxial graphene sheet decouples the image-potential states n=1 and n=2 from the metal substrate what expresses in sligthly longer ineleastic lifetimes compared to the pristine Ru(0001) surface. In contrast in the H-areas the inelastic lifetime of the (n=1')-state is similar to the pristine Ru(0001) surface what indicates a high elctronic coupling to the substrate and therefore a high probability density near the metal surface.

Due to the fact that the surface resonance S' as well as the the interfacial state S are intrisically more located at the metal surface than the image-potential states are, the lower inelastic lifetime of the interfacial state than the surface resonance is a result of the enhanced phase space at its energetic position with respect to the Fermi-level.



gru_probability_densities.pngThe theoretical modellation of graphene/Ru(0001) enables us to obtaine detailed information on the properties of the image-potential states at interface.  Due to the comparably large dimension of its lateral structurization graphene/Ru(0001) can be modelled as a simple one-dimensional potential perpendicular to the suface with bonding distances d that corresponds to the L- and H-areas. Thus, we are able to investigate the formation of the image-potential states of the graphene-Ru(0001) interface by systematically tuning d. The eigenvalues of the image potential states are obtained by numerically solving the Schrödinger-equation.

For large distances d (graphene and Ru(0001) are totally separated), the wave functions of the image-potential states of the graphene are like found for freestanding graphene, while Ru(0001) at the Ru(0001) there is now Rydberg-like seies due to the large differnce in work function. By reducing d the image-potential states are modified by the symmetry break due to the presence of the metal substrate in the order corresponding to their spacial extend from high to low quantum number n. This results in a reduction of their binding energy with respect to the vacuum level as well as a phase shift of their Wavefunction relativ to the graphene plane.

This mechnism eventually reduces the double Rydberg-like series of image-potential states of freestanding grafphene to a single d-depending series at the graphene/Ru(0001) interface. In the L-areas this series resembles this of the prisine Ru(0001) with an slight degree of decoupling as found experimentally. In the H-areas a  certain portion of the probability density slips unter the graphen sheet which enhances the observed elctronic coupling the substrate.

contact: Dr. Nico Armbrust, PD Dr. Jens Güdde, Prof. Dr. Ulrich Höfer


Zuletzt aktualisiert: 25.05.2016 · armbrusn

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