Experimentally exploring quantum physics requires most sensitive instrumentation.  A scanning tunneling microscope (STM) operated at cryogenic temperature and in ultrahigh vacuum appears to be particularly well suited.  The Experimental Physics 1 / Surface Physics group at TU Ilmenau in close cooperation with the Theoretical Physics Department of TU Denmark has recently succeeded in experimentally realizing and thoroughly understanding a molecular magnifier for quantum vibrations of a two-dimensional material.  The results of this joint and fruitful study have recently been accepted for publication in Physical Review Letters, the prime journal for physical research.

Figure 1 presents the key experimental findings.  Passing the tunneling current injected from the STM tip across graphene (green) to the metal substrate (blue) (I in Fig. 1(a)) leads to a featureless spectrum of the differential conductance (dI/dV, I: current, V: sample voltage, Fig. 1(b)).  The situation changes markedly when the tunneling current is flowing across a molecule residing atop graphene (II in Fig. 1(a)).  The dI/dV spectrum now exhibits steplike changes at voltages symmetrically positioned around zero bias (Fig. 1(c)), which are typical signatures of vibration excitations.  To identify the origin of the vibrations and to understand the underlying mechanism, additional experiments were carried out.


Figure 1: (a) Side view of the unit cell used in the simulations. In I the junction comprises the STM tip (yellow), graphene (green) and the metal substrate (blue); in II a single phthalocyanine molecule is added to the junction. (b) Spectrum of dI/dV acquired atop graphene (I in (a)). (c) Spectrum of dI/dV acquired atop the phthalocyanine molecule (II in (a)).

Figure 2 demonstrates that for the effect to occur an orbital resonance must chemically be engineered. A phthalocyanine (2H-Pc) molecule adsorbed on graphene-covered Ir(111) gives rise to a cloverlike pattern with uniform contrast in STM images (Fig. 2(a)).  After abstraction of pyrrolic H from the molecular center by injecting high-energy tunneling electrons from the STM tip, i.e., after performing the on-surface single-molecule reaction 2H-Pc → Pc + 2H (Fig. 2(b)), the product molecule Pc appears with bright and rich submolecular contrast (Fig. 2(a)).  While intact 2H-Pc exhibits a rather flat evolution of dI/dV (Fig. 2(c)), pyrrolic-H-abstracted Pc shows a strong resonance around zero bias (Fig. 2(d)).  Intriguingly, 2H-Pc does not give rise to inelastic signals (Fig. 1(b)), while Pc does (Fig. 1(c)).  Therefore, the inelastic excitation of vibrational modes is likely related to the molecular orbital resonance covering the spectral range of vibrations.

To further shed light onto the role of the molecular resonance and the origin of vibrational excitations density functional and non-equilibrium Green function calculations were performed in Denmark.  In agreement with the experiments, only Pc exhibits a transmission resonance close to the Fermi energy (E = 0 in Fig. 3(a)), which is associated with the degenerate highest occupied molecular orbital of Pc.  Moreover, the inelastic signals are only enhanced for Pc (Fig. 3(b)), in very good agreement with the experimental observation.  In addition, the bias polarity dependence of the inelastic signal strength is well reproduced and and shown to be due to the asymmetric line shape of the calculated transmission resonance.


Figure 2: (a) STM image of molecule-covered graphene on Ir(111) (sample voltage: 0.78 V, tunneling current: 25 pA, size: 8 nm × 5 nm). A 2H-Pc and Pc molecule are marked by dashed circles. (b) Ball-and-stick models illustrating the abstraction of pyrrolic H from 2H-Pc to give Pc. (c) Spectrum of dI/dV acquired atop 2H-Pc adsorbed on graphene-covered Ir(111). (d) As (c), acquired atop Pc
Figure 3: (a) Elastic electron transmission function for Pc (solid line) and 2H-Pc (dashed line) as a function of energy (the Fermi energy is set to zero). (b) Inelastic electron transmission for Pc and 2H-Pc. G0 denotes the quantum of conductance. (c) Phonon inelastic transmission (dIXi/dV) for Pc decomposed according to phonon mode weights on atoms (symbols are explained in the text). Inset: Close-up view of an energy range where a graphene out-of-plane phonon (reversed triangles) is particularly strong. (d) Mixing of graphene phonon and Pc vibrational modes with out-of-plane polarization.

The calculations are furthermore capable of assigning the vibrational character to the inelastic signals and, thus, of resolving the remaining ambiguity in the origin of the vibrations.  To this end, the inelastic conductance is decomposed into components using the vibrational modes and their weights projected onto the molecule and graphene.  From the vibrational mode vector, vλ, projections onto in-plane (xy) and out-of-plane (z) atom motions of the molecule (m) and graphene (g) are defined and referred to as wλX = ΣX|vλ(X)|2 with XÎ {mxy, mz, gxy, gz} and ΣXwλX = 1.  Individual contributions to the inelastic dIi/dV signal are then defined as

(ħ=h/(2π), h: Planck constant, e: elementary charge, σ = ±1, γλσ: inelastic scattering rate for vibrational mode λ with energy ħωλ, ∂ℑ/∂V: broadened step function) and are plotted in Fig. 3(c).  Importantly, Fig. 3(c) shows that the inelastic signal at 50 meV is exceptional in that the strongest contribution originates from a graphene out-of-plane phonon mode.  At the same time, an out-of-plane vibration of Pc contributes significantly to this signal.  These observations lend evidence to the physical mechanism underlying the magnification of a graphene phonon signal via a single molecule, which requires the efficient coupling of lattice and molecule vibrations with matching symmetry. The mixing of vibrational quanta can be quantified by using the weights wλX.  Figure 3(d) shows the variation of wλgzwλmz with the vibrational energy.  The product of weights is maximal if for a particular mode both graphene and Pc contribute equally.  The latter applies to a vibrational mode at 50 meV, which for graphene represents an out-of-plane acoustic mode at the high-symmetry M-point of the Brillouin zone while it is a twisting vibration of all isoindole moieties of the molecule.  For several other vibrational modes large products are attained, too; however, their inelastic scattering rate γλσ is orders of magnitude lower (Fig. 3(c)).

In conclusion, identifying new concepts and novel mechanisms in quantum physics is facilitated by model systems, which can artificially be assembled and analyzed with a modern scanning tunneling microscope and which serve as a suitable input for state-of-the-art simulations.  In the joint experimental and theoretical work reported here, an adsorbed single molecule was demonstrated to magnify inelastic signals of the substrate it resides on.  An orbital resonance overlapping the spectral range of substrate phonons as well as the sufficiently high coupling between symmetry-equivalent vibrational modes of adsorbate and substrate are required to this end.  The findings contribute to the understanding of inelastic electron transport through quantum objects in general and graphene phonon excitation by tunneling electrons in particular.

Parts of the discussed experiments were performed with the scanning probe apparatus funded by the  Federal Ministry of Education and Research within the ForLab project.  The continuous supply with liquefied helium from the helium recovery used in the ForLab project was of key importance to the success of the experiments.



Prof. Dr. Jörg Kröger
Technische Universität Ilmenau
Departmet of
Mathematics and Natural Sciences
Group Experimental Physics 1/Surface Physics