Dynamic Jahn-Teller effect in electron transport through single C60 molecules

Scanning tunneling spectra on single C60 molecules that are sufficiently decoupled from the substrate exhibit a characteristic fine structure, which is explained as due to the dynamic Jahn-Teller effect. Using electron-phonon couplings extracted from density functional theory we calculate the tunneling spectrum through the C60- anionic state and find excellent agreement with measured data.

Scanning tunneling spectra on single C60 molecules that are sufficiently decoupled from the substrate exhibit a characteristic fine structure, which is explained as due to the dynamic Jahn-Teller effect. Using electron-phonon couplings extracted from density functional theory we calculate the tunneling spectrum through the C − 60 anionic state and find excellent agreement with measured data. Orbital electronic degeneracy and stability of the nuclear configuration are incompatible unless the atoms of a molecule lie on a straight line. This statement is due to Jahn and Teller [1], who proved its general validity in 1937 using group theory [2]. The theorem has important implications for non-linear molecules with a degenerate electronic ground state, particularly when the degenerate electrons participate in the binding of the molecule. In such cases the molecule undergoes a structural distortion which lifts the electronic degeneracy by reducing the symmetry of the nuclear configuration, known as the static Jahn-Teller (JT) effect. In certain situations several distortions can lower the symmetry of the molecule, and hence lift the electronic degeneracy. When such distorted states are also degenerate, the system will fluctuate between these equivalent configurations by quantum tunneling, resulting in pseudorotations [3] and restoration of the parent symmetry, denoted the dynamic JT effect [4,5].
The buckminsterfullerene C 60 is an exceptionally symmetric molecule, and its symmetry governs many of its physical and chemical properties. In group theory it is classified by the icosahedral point group I h , the group with the highest number of symmetry operations in three dimensions [4]. The geometrical symmetry is also reflected in the electronic and vibrational properties, which are both highly degenerate. For instance, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are orbitally fivefold and threefold degenerate, respectively. By adding electrons or holes to C 60 these degeneracies are explored and, hence, JT physics is expected to play an important rôle [6].
Indeed, the JT effect has been reported in photoemission (PE) spectra of C 60 in the gas phase for different charge states of the molecule [7,8,9,10,11]. Here, a fine structure in the intensity spectrum has been explained as originating in the underlying electron-phonon (e-ph) coupled problem. Signatures of JT have also been found in luminescence spectra of C 60 nanocrystals [12]. A more direct consequence of the JT effect has been observed in low-temperature scanning tunneling microscopy (STM) images of potassium-doped fullerenes (K 3 C 60 ) on Au(111), revealing a significant static deformation of the molecular structure [13]. While vibronic effects have also been studied in the transport properties of C 60 molecules [14,15,16], the dynamic JT effect in single-molecule conductance has not been reported so far, presumably due to the difficulty of decoupling a molecule sufficiently from its environment.
From the theoretical side there has been a substantial interest in describing the e-ph coupled problem in C 60 , primarily motivated by the discovery of the superconducting phase of alkali doped fullerides A 3 C 60 and its relation to the "conventional" e-ph mechanism [17,18,19]. An accurate calculation of the e-ph coupling constants is fundamental to such descriptions. In comparison with couplings fitted to photoemission data on C − 60 , it has been argued that couplings derived from density functional theory (DFT) are too weak [7]. Contrary, DFT couplings were later shown to accurately account for photoemission data on C + 60 [10]. This apparent controversy calls for complementary studies of the e-ph interaction that put DFT-derived couplings to test.
In this Letter, we report on the JT fingerprint in the conductance spectra of single C 60 molecules in a tunneling junction. Fullerenes were decoupled from a Au(111) surface by a template of organic molecules. Scanning tunneling spectroscopy reveals a broad sideband above a sharp LUMO-derived resonance. To understand this we calculate the tunneling spectrum by solving the JT problem from first principles. The vibrational modes, frequencies, and e-ph couplings are derived from DFT, and the excitation spectrum of the vibronic ground state is computed numerically by nonequilibrium Green's function (NEGF) techniques as well as by exact diagonaliza- tion. The theoretical results explain the origin of the experimentally observed fine structure as due to the dynamic JT effect.
The electronic decoupling of the molecule from its metallic substrate is crucial for studying any JT-induced fine structure of the molecular resonances. To reduce this interaction experimentally we use a novel strategy based on codeposition of C 60 and 1,3,5,7tetraphenyladamantane (TPA) on Au(111), which results in spontaneous formation of nanostructures where the C 60 cages are lifted away from the surface by support from TPA molecules [22,23]. One of the observed structural motifs are double rows of alternating TPA and C 60 , cf. Fig. 1(a). This dielectric template yields troughs for single C 60 molecules to be trapped between neighboring double rows as sketched in Fig. 1(b). Differential conductance (dI/dV − V ) spectra taken over the center of these molecules reveal strong non-linearities around −2.2 V, 1.3 V and 2.5 V, associated with the HOMO, LUMO and LUMO+1 derived resonances, respectively ( Fig. 1(b)). The corresponding large gap of ∼ 3.5 eV is a clear sign of a weakly interacting molecule with its surrounding [23]. Even more striking is the observation of a very sharp LUMO-derived resonance (FWHM ∼ 60 meV), reflecting a long lifetime in the order of 10 fs of the (8) I: Partial electron-phonon coupling constants λν/N (0) = 2/9 P i,j |M ν i,j | 2 / ων of the Ag and Hg intramolecular modes for C60, c.f. Eq. (10) of Ref. [18], with N (0) being the density of states. The sum of all modes gives a coupling strength of λ GGA /N (0) = 76.1 meV [26] in good agreement with previous calculations [18,19,20,21].
tunneling electron. Hence, this system is ideal to study e-ph couplings. However, instead of single vibronic peaks [16], we observe a broad sideband at ∼ 230 meV above the LUMO energy, which lies well outside of the 200-meV-wide vibrational spectrum of C 60 .
Tunneling electrons through an isolated C 60 molecule will probe the excitation spectrum as resulting from a dynamic JT interaction with the vibrations. Near the LUMO-derived resonances in focus here, we exclude the HOMO and LUMO+1 states from our treatment since these are well separated in energy. Further, group theory gives that only the A g and H g intramolecular phonons couple to the t 1u LUMO states [6]. Thus, the JT problem for C − 60 is described by the following Hamiltonian where c † i (c i ) is the one-electron creation (annihilation) operator corresponding to one of the three degenerate single-particle LUMO states |i and b † ν (b ν ) is the bosonic creation (annihilation) operator of each of the 42 (8 fivefold degenerate H g and 2 non-degenerate A g ) vibrational modes ν. The parameters ε 0 , ω ν , and M ν i,j represent the bare LUMO energy, the vibrational frequency of mode ν, and the coupling constant for the scattering of an electron from state |i to state |j under creation or annihilation of a phonon in mode ν, respectively. These parameters (see Tab. I) are obtained from DFT calculations [24,25,26] applying the scheme described in Ref. [27] to the neutral [21], isolated C 60 molecule.
In our STM configuration the molecule under investigation is much less coupled to the tip than to the substrate, i.e., Γ t ≪ Γ s in terms of the tip Γ t and substrate Γ s tunneling rates. Under this condition the electron occupancy of the molecular states is effectively in equilibrium with the substrate and the differential conductance H g (4) H g (5) H g (6) H g (7) A g (2) H g (8) ( at a bias voltage V s is to a first approximation proportional to ρ(µ s + eV s )Γ t , where ρ is the local density of states (LDOS). This takes into account both couplings to the leads as well as to the vibrations. We have considered two different methods for calculating ρ, namely exact diagonalization with the Lanczos scheme (LS) as well as NEGF within the self-consistent Born approximation (SCBA) [28]. Figure 2(a) shows the computed JT spectrum from SCBA for two different values of the total electronic broadening Γ = Γ t + Γ s ≈ Γ s (FWHM). The spectrum is composed of a main peak followed by a series of sidebands at higher excitation energies. Depending on the broadening, the LUMO spectrum might appear as one main peak with a single sideband separated by 230 meV. A similar structure has also been reported in photoemission [7,8,9,10]. It is important to realize that the fine structure in the LDOS does not relate in a simple way to the fundamental frequencies of the A g and H g modes (in the range 32-195 meV as indicated with vertical dotted lines in Fig. 2). Hence, for JT systems it is not possible to directly relate vibronic structure in spectroscopy with molecular frequencies. Another important fact is that the vibronic spectrum is threefold degenerate, i.e., the parent symmetry of the LUMO is restored by the A g and H g modes as expected from the dynamic JT effect [29]. Hence, the molecule is not statically distorted.
To gain an understanding of the contributions from the different vibrational modes to the total spectrum, we show in Fig. 2(b) the LDOS as resulting from a calculation with the coupling to only one type of mode at a time. Although the sideband structure is much simpler, one observes that the peak separation for all H g modes is larger than the phonon energy. This nontrivial behavior is generic to the T 1u ⊗h g JT problem [6]. Figure 2(b) also shows that, except for the more strongly coupled A g (2) mode, SCBA and LS yield essentially the same results for the LDOS due to the weak e-ph couplings.
We next turn to a comparison with the experiment.
The measured tunneling spectra on different molecules exhibit certain variations in peak position and structure around the LUMO resonance. This variation is likely due to slightly different environments, and possibly also molecular orientation, of the selected C 60 species. In Fig. 3 we compare the dI/dV -spectra of three different molecules with theoretical spectra by applying an appropriate substrate coupling Γ. The relative peak height as well as the position of the sideband with respect to the main peak are in very good agreement. This fact supports the interpretation that these spectra indeed exhibit the free-molecule JT effect.
Alternative mechanisms, such as the weak spin-orbit coupling in carbon [4] or the Stark effect from the applied voltage, cannot account for the 230 meV splitting seen in Fig. 3. Although details in the weak electronic coupling of the C 60 molecule to its environment may have an influence in the experimentally recorded spectra, we believe that this effect solely cannot produce such an agreement as the JT theory presented above for a decoupled molecule. Furthermore, from the different timescales of electron tunneling events and residence times in the molecule, we can also exclude heating effects. Based on the NEGF-SCBA calculations we find that heating would be important if the current through the LUMO states is raised by two orders of magnitude.
In Fig. 3(a) we also show how the calculated spectrum changes by a scaling of the DFT-derived e-ph couplings corresponding to λ ν → 1/2 λ GGA ν and λ ν → 2 λ GGA ν . As seen, these scalings decimate the agreement with experiment in terms of peak ratio and separation, thus pointing towards reasonable values of the e-ph coupling strength within DFT.
In summary, we have explained the dynamic JT effect as it is revealed in electron tunneling spectroscopy through the C − 60 anionic state of sufficiently isolated molecules. The experimental realization of this situation was based on a novel experimental preparation procedure of codeposition of C 60 and TPA molecules on Au(111), where C 60 molecules on top of the double row template are exceptionally decoupled, geometrically and electronically, from the metallic substrate. Low-temperature STM dI/dV spectra recorded under such conditions display a delicate fine structure around the LUMO-derived resonance, that closely resembles the theoretically computed JT spectrum. This quantitative agreement further supports that the calculated e-ph couplings from DFT provide an accurate description for the vibrational interactions in the molecule.