Revealing the hidden atom in graphite by low-temperature atomic force microscopy

Hembacher, Stefan; Giessibl, Franz J.; Mannhart, J.; Quate, C. F.

doi:10.1073/pnas.2134173100

Cited by 160 publications

(143 citation statements)

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“…4 were ≈ 0.3 nm/s, therefore time delays in the acquisition channels are negligible and the I, γ and ∆E ts images match precisely in forward and backward scans. In our previous simultaneous STM/AFM measurement on graphite [17], we found a lateral shift of 68 pm of the current maxima with respect to the corresponding γ maxima. While the tip is not perfectly symmetric with respect to the z-axis (see caption Fig.…”

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confidence: 60%

“…While the tip is not perfectly symmetric with respect to the z-axis (see caption Fig. 4), it is evidently more symmetric than in [17]. Arai and Tomitori [25] have recently shown that force interactions are also a function of bias.…”

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confidence: 96%

“…Because this value is more than two orders of magnitude greater than the estimate above, it is expected that long-range forces have caused a large contribution in that experiment. Here, we use FMAFM with sub-nm amplitudes which greatly reduces the influence of long-range forces [13] and enables simultaneous STM operation [17]. We use a low-temperature STM/AFM operating at 4.9 K in ultrahigh vacuum [18].…”

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Local Spectroscopy and Atomic Imaging of Tunneling Current, Forces, and Dissipation on Graphite

et al. 2005

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Theory predicts that the currents in scanning tunneling microscopy (STM) and the attractive forces measured in atomic force microscopy (AFM) are directly related. Atomic images obtained in an attractive AFM mode should therefore be redundant because they should be similar to STM. Here, we show that while the distance dependence of current and force is similar for graphite, constant-height AFM-and STM images differ substantially depending on distance and bias voltage. We perform spectroscopy of the tunneling current, the frequency shift and the damping signal at high-symmetry lattice sites of the graphite (0001) surface. The dissipation signal is about twice as sensitive to distance as the frequency shift, explained by the Prandtl-Tomlinson model of atomic friction.The capability of scanning tunneling microscopy (STM) [1] and atomic force microscopy (AFM) [2] to resolve single atoms in real space makes them powerful tools for surface science and nanoscience. When operating AFM in the repulsive mode, protrusions in the images simply relate to the atoms because of Pauli's exclusion law. In contrast, the interpretation of STM images is more complicated. The Tersoff-Hamann approximation [3], valid for tips in an s-state, interprets STM images as a map of the charge density of the sample at the Fermi energy. Depending on the state of the tip, atoms can either be recorded as protrusions or holes, and tip changes can reverse the atomic contrast [4,5]. Theoretical predictions regarding the relation of forces and tunneling currents I state that tunneling currents and attractive forces are directly related, thus AFM would not provide any new physical insights over STM. Chen [5] has found that the square of the attractive energy between tip and sample should be proportional to I with experimental evidence in [6]. Hofer and Fisher [7] suggested that the interaction energy and I should be directly proportional, experimentally found in [8,9]. In this Letter, we investigate the experimental relationships between tunneling currents and conservative as well as dissipative forces for graphite probed with a W tip by performing local spectroscopy on specific lattice sites. While force spectroscopy on specific lattice sites [10] and combined force and tunneling spectroscopy on unspecific sample positions [8,9] have been performed before, the measurements reported here encompass site-specific spectra of currents and forces, supplemented by simultaneous constant-height measurements of currents and forces that allow a precise assessment of the validity of the theories regarding currents and forces in scanning probe experiments.In graphite (see Fig. 1), the electrons at E F are concentrated at the β sites, and only these atoms are 'seen' by STM at low-bias voltages. The state-of-theart method for atomic resolution force microscopy is frequency modulation AFM (FMAFM) [11], where the frequency shift ∆f of an oscillating cantilever with stiffness k, eigenfrequency f 0 and oscillation amplitude A is used as the imaging signal [12,13]. The b...

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Local Spectroscopy and Atomic Imaging of Tunneling Current, Forces, and Dissipation on Graphite

et al. 2005

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“…1) stands out, as it is the configuration of layers in natural graphite. 24,28 Alternative configurations like AA stacking were found in ab initio calculations to be energetically unfavorable; 29 they can, however, be thought of as either mechanically shifted samples or sections of curved bilayers (e.g., sections of two shells in a large multiwall carbon nanotube) where the alignment unavoidably varies over distance. Compared to the Hofstadter butterfly of a single sheet of graphene, 22 two asymmetries are visible in all three plots: The electron-hole symmetry (E ↔ −E) is broken down by the interlayer coupling already at zero magnetic field: while the lowest-energy states of a single graphene layer have constant phase over all atoms and can couple efficiently into symmetric and antisymmetric hybrid states of the bilayer system, the states at high energies have alternating phases for neighboring atoms, so interlayer hybridization is prohibited by the second-nearest-neighbor interlayer coupling.…”

Section: Norbert Nemec and Gianaurelio Cunibertimentioning

confidence: 99%

Hofstadter butterflies of bilayer graphene

Nemec

Cuniberti

2007

Phys. Rev. B

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We calculate the electronic spectrum of bilayer graphene in perpendicular magnetic fields nonperturbatively. To accomodate arbitrary displacements between the two layers, we apply a periodic gauge based on singular flux vortices of phase 2π. The resulting Hofstadter-like butterfly plots show a reduced symmetry, depending on the relative position of the two layers against each other. The split of the zero-energy relativistic Landau level differs by one order of magnitude between Bernal and non-Bernal stacking. After the theoretical prediction of the peculiar electronic properties of graphene in 1947 by Wallace 1 and the subsequent studies of its magnetic spectrum, 2,3 it took half a century until single layers of graphene could be isolated in experiment 4 and the novel mesoscopic properties of these two-dimensional (2D) Dirac-like electronic systems, e.g., their anomalous quantum Hall effect, could be measured. 5,6,7 Inspired by this experimental success, graphene has become the focus of numerous theoretical works. 8,9,10,11,12 For bilayers of graphene, an additional degeneracy of the Landau levels and a Berry phase of 2π were predicted to lead to an anomalous quantum Hall effect, different from either the regular massive electrons or the special Dirac-type electrons of single-layer graphene, 13 which was confirmed in experiment shortly afterwards 14 and used for the characterization of bilayer samples. 15The low-energy electronic structure of a single layer of graphene is well described by a linearization near the corner points of the hexagonal Brillouin zone (K points), resulting in an effective Hamiltonian formally equivalent to that of massless Dirac particles in two dimensions. 16

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“…Dynamic AFM [1] in the frequency modulation (FM) mode [2] has resolved the true geometric structure of a broad range of materials [3][4][5]. FM AFM experiments on carbon-based materials [6][7][8][9][10][11][12][13] show atomic contrast in Δf images and, depending on the setup, in the dissipation channel. While the origin of the dissipation is not well understood, the Δf contrast has been linked with the nature of the tip-sample interaction [14].…”

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Atomic-Scale Variations of the Mechanical Response of 2D Materials Detected by Noncontact Atomic Force Microscopy

et al. 2016

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We show that noncontact atomic force microscopy (AFM) is sensitive to the local stiffness in the atomicscale limit on weakly coupled 2D materials, as graphene on metals. Our large amplitude AFM topography and dissipation images under ultrahigh vacuum and low temperature resolve the atomic and moiré patterns in graphene on Pt(111), despite its extremely low geometric corrugation. The imaging mechanisms are identified with a multiscale model based on density-functional theory calculations, where the energy cost of global and local deformations of graphene competes with short-range chemical and long-range van der Waals interactions. Atomic contrast is related with short-range tip-sample interactions, while the dissipation can be understood in terms of global deformations in the weakly coupled graphene layer. Remarkably, the observed moiré modulation is linked with the subtle variations of the local interplanar graphene-substrate interaction, opening a new route to explore the local mechanical properties of 2D materials at the atomic scale. DOI: 10.1103/PhysRevLett.116.245502 Atomic force microscopy (AFM) and scanning tunneling microscopy (STM) are tools of choice for characterizing the unique mechanical and electronic properties of graphene (G) and other 2D materials. Dynamic AFM [1] in the frequency modulation (FM) mode [2] has resolved the true geometric structure of a broad range of materials [3][4][5]. FM AFM experiments on carbon-based materials [6][7][8][9][10][11][12][13] show atomic contrast in Δf images and, depending on the setup, in the dissipation channel. While the origin of the dissipation is not well understood, the Δf contrast has been linked with the nature of the tip-sample interaction [14].G properties can be efficiently tuned by the interaction with metals [15,16]. The interaction strength varies widely from the strong coupling with Rh [17,18] and Ru [19] to the weak limit (Ir [20], Pt [21]), where G retains its unique electronic properties [22]. The different lattice parameters of G and the metal underneath are accommodated through the formation of commensurate structures known as moiré patterns, where C atoms become inequivalent due to their different bonding configuration with the metal. The resulting "true" topographic corrugation of G-the difference in height among the topmost and the bottom C atom-varies widely, even in the weakly interacting cases, where it ranges from ≈50 pm on Ir [23,24] to practically flat (≤ 3 pm) on Pt [21].While STM can easily resolve these moiré patterns, even in the G=Pt case [21,25], AFM experiments have only been reported in highly corrugated cases as Ru [26], Rh [27], and Ir [12,28]. Focusing on the most challenging case, G=Ir, experiments with a Kolibri sensor using a W tip clearly resolved the moiré in constant height (CH) AFM images [28]. Measurements with a tuning fork using both inert (CO-terminated) and reactive (Ir-terminated) tips [12] were able to identify the atoms with both tips at any tip-sample distance. This atomic-scale resolution allowed the ...

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Revealing the hidden atom in graphite by low-temperature atomic force microscopy

Cited by 160 publications

References 31 publications

Local Spectroscopy and Atomic Imaging of Tunneling Current, Forces, and Dissipation on Graphite

Local Spectroscopy and Atomic Imaging of Tunneling Current, Forces, and Dissipation on Graphite

Hofstadter butterflies of bilayer graphene

Atomic-Scale Variations of the Mechanical Response of 2D Materials Detected by Noncontact Atomic Force Microscopy

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