Observation of Quantum Interference in Molecular Charge Transport
As the dimensions of a conductor approach the nano-scale, quantum effects will begin to dominate its behavior. This entails the exciting
possibility of controlling the conductance of a device by direct manipulation of the electron wave function. Such control has been most clearly
demonstrated in mesoscopic semiconductor structures at low temperatures. Indeed, the Aharanov-Bohm effect(1), conductance quantization
(2); (3) and universal conductance fluctuations(4) are direct manifestations of the electron wave nature. However, an
extension of this concept to more practical temperatures has not been achieved so far. As molecules are nano-scale objects with typical energy level
spacings ( eV) much larger than the thermal energy at 300 K ( meV), they are natural candidates to enable such a
break-through (5); (6); (7); (8); (9); (10); (11). Fascinating phenomena
including giant magnetoresistance, Kondo effects and conductance switching, have previously been demonstrated at the molecular level(12); (13); (14); (15); (16); (17); (18). Here, we report direct
evidence for destructive quantum interference in charge transport through two-terminal molecular junctions at room temperature. Furthermore, we
show that the degree of interference can be controlled by simple chemical modifications of the molecule. Not only does this provide the
experimental demonstration of a new phenomenon in quantum charge transport, it also opens
the road for a new type of molecular devices based on chemical or electrostatic control of quantum interference.
The wave nature of electrons is fundamental to our understanding of almost all of chemistry. In fact, the very existence of molecular orbitals is a direct result of spatial confinement of electron waves. This in turn leads to pronounced reactivity variation at different sites of molecules.
The electron wave character also plays a key role in
mesoscopic physics, which studies quantum phenomena in charge transport. For example, the conductance properties of mesoscopic ring structures at low
temperatures are dominated by quantum interference. If the partial waves through both branches of the ring add up destructively (constructively) a
suppression (enhancement) of the conductance is observed. For certain classes of molecular junctions, a similar effect is expected
(6); (7); (8); (9); (10); (11). However, in that case the picture of interference
resulting from distinct spatial paths is no longer valid. Instead, interference in a molecule must be described in terms of electron propagation via paths
of orbitals, differing not only in space, but also in energy. Since the properties of molecular orbitals can be manipulated by chemical design, quantum
interference promises control over the conductance of molecular devices at the wave function level. In fact, conductance tuning over orders of magnitude at
ambient temperatures comes within reach. Although variations in charge transfer rates within donor-bridge-acceptor molecules can be explained in terms of
interference (19); (20), only indirect indications for interference have been found in molecular conductance experiments
(21); (22). Here, we provide unambiguous evidence for destructive quantum interference in two-terminal molecular junctions.
To investigate the influence of quantum interference on molecular conductance properties, we synthesized five rigid -conjugated molecular wires (see
Supplementary Methods). The first two molecules (AQ-MT and AQ-DT, left in Fig. 1a) contain an anthraquinone-unit. This makes them cross-conjugated
To measure transport, we first create self-assembled monolayers (SAMs) of each molecule on thin Au layers (200 nm, Si-substrates). To obtain high-quality, densely packed SAMs, we use a procedure established recently (Supplementary Methods) (25). Next, a conducting atomic force microscopy (AFM) probe is brought in close contact to a SAM. In this way, we can perform charge transport experiments through the molecular layer, using the Au-covered substrate and the AFM-tip as electrodes (Fig. 1b). We typically connect to a few hundred molecules, while measuring current, , versus bias voltage (26). However, the exact number does vary. For this reason, we present our results in two-dimensional (2D) histograms. Figure 1c shows such a 2D-histogram for AC-DT. To construct this plot, we have logarithmically binned the -values (determined numerically) for each bias applied (see Supplementary Methods). This effectively results in a sequence of 1D-histograms, plotted for each . To illustrate this, Fig. 1d shows a cross-section of Fig. 1c at V (blue histogram; see dashed line in Fig. 1c). This is the zero-bias 1D-histogram for AC-DT (27). Representing our data in 2D-histograms has two major advantages. First, it allows us to show a full data set in one plot, without a need for either determining an average curve or for data selection (27)
Figure 1d compares the zero-bias conductance histograms for both AQ-DT (red) and AC-DT (blue). Interestingly, AQ-DT exhibits conductance values that are
almost two orders of magnitude lower than those of AC-DT. This is quite remarkable, since the energy difference between the HOMO and LUMO levels is very
similar for these molecules (HOMO: highest occupied molecular orbital; LUMO: lowest unoccupied molecular orbital)
We now compare these calculations with the experiments in Fig. 1d. In Fig. 2a, the -values are around two orders of magnitude lower for
AQ-DT than for AC-DT. This is in reasonable agreement with the strongly reduced conductance values for AQ-DT in Fig. 1d. We thus have a first indication of
interference in AQ-DT. To investigate this further, we inspect the full 2D-histogram of AQ-DT (Fig. 3a). For the full voltage range, its -values are
dramatically lower than those of AC-DT (Fig. 1c). However, the 2D-histogram has a parabola-like appearance similar to AC-DT, i.e. we observe no anomaly
that can be connected to the calculated transmission dip. Hence, although the surprisingly low conductance of AQ-DT is most likely due
to quantum interference, the evidence is only indirect. This situation is comparable to the one in Refs. (21); (22)
Let us next consider AQ-MT molecules, which should also exhibit an anti-resonance (Fig. 2a). Figure 3b shows the 2D-histogram of the -curves for AQ-MT (Supplementary Figures). Remarkably, these data do show a clear anomaly at zero bias voltage. In particular, the curvature of the -traces in Fig. 3b is negative for all (except around ). What is equally striking in Fig. 3b is the large voltage range over which the anomaly extends. Even up to V, the -curves are dominated by the minimum at V. This points to a characteristic energy scale of eV, which corresponds well with the width of the interference-induced dip in in Fig. 2a. Moreover, this large energy scale rules out Kondo effects and Coulomb blockade as possible explanations for the anomaly
To further validate this interpretation, we calculate -curves for AQ-MT from (see Supplementary Methods). A key role in these
calculations is played by the position of the anti-resonance in relative to . This position is difficult to predict theoretically. This is
related to the well-known problems of the applied methodology to describe energy level alignments and to the uncertainty of the size of the surface dipoles
in the experiments
In summary, our charge transport data provide direct evidence for destructive quantum interference in two-terminal molecular junctions. The
interference effects are intimately linked to the shapes and energies of the molecular orbitals and can thus be controlled by chemical design. The
fact that interference in molecules is present at room temperature opens the road to a new type of molecular devices. Specifically, these include
interference controlled molecular switches with very large on-off ratios(18); (23) and novel thermoelectric devices, with thermopower
values tunable in magnitude and sign(28).
* These authors contributed equally to this work
I Method Summary
Samples were prepared by thermal deposition of 5 nm chromium and 200 nm gold onto silicon/silicon oxide substrates. These freshly prepared samples were
immediately transferred into a nitrogen-filled glove-box. The molecular wires were dissolved in dry chloroform (AC-DT, AQ-DT, AQ-MT) or in dry THF (OPE3-DT
and OPE3-MT) at 0.5 mM, in this glove-box. We added 10% (v/v) degassed triethylamine to these solutions to deprotect the thiol groups and immersed the
gold samples for 2 days, to form densely-packed self-assembled monolayers (25) as confirmed by ellipsometry and XPS (see Supplementary Methods).
After immersion, the samples were rinsed three times with clean chloroform or THF, and dried in the glove-box. The synthesis of AQ-DT and the
characterization of all five molecular wires is reported in the Supplementary Methods. Transport experiments were performed on a Digital Instrument Multimode-AFM
with a Nanoscope III controller. The conductance measurements themselves were controlled externally (see Supplementary Methods). Calculations of junction
geometries and transmission functions were performed with the GPAW density functional theory code using an atomic orbital basis set corresponding to
double-zeta plus polarization and the Perdew-Burke-Ernzerhof exchange-correlation functional. Before calculating the transmission functions, the occupied
and unoccupied molecular orbitals were shifted in energy in order to account for self-interaction errors and missing image charge effects in the DFT
description. This approach (DFT + ) was recently found to systematically improve the DFT-conductance values
(29) (see Supplementary Methods).
Acknowledgements We are grateful to Tjerk Oosterkamp and Federica Galli for making their equipment and expertise available to us. We thank Jan van Ruitenbeek, Marius
Trouwborst for discussions and Daniel Myles for his initial synthetic efforts. This study was financed by a VIDI-grant (SJvdM) of the Netherlands
Organization for Scientific Research (NWO) as well as by the Dutch Ministry of Economic Affairs via NanoNed (HV, project GMM.6973).
Author Contributions CMG and SJvdM performed the AFM measurements and the data analysis; HV and JCH designed and synthesized the molecules, made and characterized the SAM’s; TM and KST performed the calculations; CG, HV, JCH and SJvdM designed the experiment. All the authors discussed the results and commented on the manuscript.
Author Information The authors declare no competing financial interests. Correspondence should be addressed to SJvdM (Molen@physics.leidenuniv.nl)
- Linear conjugation refers to a sequence of alternating single and double bonds between both ends of an organic molecule. Cross-conjugation implies that the sequence of alternating single and double bonds between both ends of the molecule is broken, although all C-atoms have formed double or triple bonds, i.e. all C-atoms are sp or sp hybridized.
- For completeness: I(V)-curves that were either flat (no contact) or that showed direct contact are excluded from Figs. 1 and 3. However, such curves represent a small minority of our data (), see Supplementary Methods.
- From UV-Vis measurements, we find an optical HOMO-LUMO gap of 2.88 eV for AQ-DT and 2.90 eV for AC-DT. Our calculations yield fundamental HOMO-LUMO gaps of 4.23 eV and 4.61 eV, respectively. Note that the optical gap and the fundamental gap differ by the electron-hole interaction.
- Coulomb blockade can also be ruled out via the experimental data. If Coulomb blockade were the dominant effect behind Fig. 3b, it should also be present in the other molecular junctions, which have the same length and hence lead to roughly the same capacitance. However, no anomaly is seen in Figs. 1c and 3a, 3c and 3d.
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- The computational limitation is illustrated best by comparing our calculations on AQ-DT (Fig. 2) with those in Ref. (22) (Fig. 5). In our Fig. 2, the anti-resonance lies to the right of , whereas in Ref. (22), it lies to the left.
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