Observation of Quantum Interference in Molecular Charge Transport
Constant M. Guedon, Hennie Valkenier, Troels Markussen, Kristian S. Thygesen, Jan C. Hummelen, Sense Jan van der Molen
OObservation of Quantum Interference in Molecular ChargeTransport
Constant M. Gu´edon*, Hennie Valkenier*, Troels Markussen, KristianS. Thygesen, Jan C. Hummelen, and Sense Jan van der Molen Kamerlingh Onnes Laboratorium, Leiden University,Niels Bohrweg 2, 2333 CA Leiden, The Netherlands Stratingh Institute for Chemistry and Zernike Institute for Advanced Materials,University of Groningen, Nijenborgh 4,9747 AG Groningen, The Netherlands Center for Atomic-scale Materials Design (CAMD), Department of Physics,Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark (Dated: May 22, 2018) a r X i v : . [ c ond - m a t . m e s - h a ll ] A ug s the dimensions of a conductor approach the nano-scale, quantum effectswill begin to dominate its behavior. This entails the exciting possibilityof controlling the conductance of a device by direct manipulation of theelectron wave function. Such control has been most clearly demonstratedin mesoscopic semiconductor structures at low temperatures. Indeed, theAharanov-Bohm effect[1], conductance quantization [2, 3] and universal con-ductance fluctuations[4] are direct manifestations of the electron wave nature.However, an extension of this concept to more practical temperatures has notbeen achieved so far. As molecules are nano-scale objects with typical energylevel spacings ( ∼ eV) much larger than the thermal energy at 300 K ( ≈ meV),they are natural candidates to enable such a break-through [5–11]. Fascinatingphenomena including giant magnetoresistance, Kondo effects and conductanceswitching, have previously been demonstrated at the molecular level[12–18].Here, we report direct evidence for destructive quantum interference in chargetransport through two-terminal molecular junctions at room temperature.Furthermore, we show that the degree of interference can be controlled bysimple chemical modifications of the molecule. Not only does this providethe experimental demonstration of a new phenomenon in quantum chargetransport, it also opens the road for a new type of molecular devices based onchemical or electrostatic control of quantum interference. The wave nature of electrons is fundamental to our understanding of almost all of chem-istry. In fact, the very existence of molecular orbitals is a direct result of spatial confinementof electron waves. This in turn leads to pronounced reactivity variation at different sitesof molecules. The electron wave character also plays a key role in mesoscopic physics,which studies quantum phenomena in charge transport. For example, the conductanceproperties of mesoscopic ring structures at low temperatures are dominated by quantuminterference. If the partial waves through both branches of the ring add up destructively(constructively) a suppression (enhancement) of the conductance is observed. For certainclasses of molecular junctions, a similar effect is expected [6–11]. However, in that casethe 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 of2rbitals, differing not only in space, but also in energy. Since the properties of molecularorbitals can be manipulated by chemical design, quantum interference promises controlover the conductance of molecular devices at the wave function level. In fact, conductancetuning over orders of magnitude at ambient temperatures comes within reach. Althoughvariations in charge transfer rates within donor-bridge-acceptor molecules can be explainedin terms of interference [19, 20], only indirect indications for interference have been foundin molecular conductance experiments [21, 22]. Here, we provide unambiguous evidence fordestructive quantum interference in two-terminal molecular junctions.To investigate the influence of quantum interference on molecular conductance properties,we synthesized five rigid π -conjugated molecular wires (see Supplementary Methods). Thefirst two molecules (AQ-MT and AQ-DT, left in Fig. 1a) contain an anthraquinone-unit.This makes them cross-conjugated [30] [23, 24]. The AQ-MT molecule is terminated by aprotected thiol group at one side only (monothiolated: MT), whereas AQ-DT is dithiolated(DT). The third molecular wire (AC-DT) contains a central anthracene-unit and is linearlyconjugated. Otherwise it is very similar to AQ-DT, e.g. both have a length of 24.5 ˚A. Fi-nally, two linearly conjugated reference compounds, oligo(phenylene-ethynylene)-monothioland -dithiol (OPE3-MT and OPE3-DT), are studied. We stress that apart from the thiols,all five molecules have the same phenylene-ethynylene endgroups.To measure transport, we first create self-assembled monolayers (SAMs) of each moleculeon 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 conductingatomic force microscopy (AFM) probe is brought in close contact to a SAM. In thisway, we can perform charge transport experiments through the molecular layer, using theAu-covered substrate and the AFM-tip as electrodes (Fig. 1b). We typically connect to afew hundred molecules, while measuring current, I , versus bias voltage V [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, wehave logarithmically binned the dI/dV -values (determined numerically) for each bias ap-plied (see Supplementary Methods). This effectively results in a sequence of 1D-histograms,plotted for each V . To illustrate this, Fig. 1d shows a cross-section of Fig. 1c at V = 0 V(blue histogram; see dashed line in Fig. 1c). This is the zero-bias 1D-histogram for AC-DT3 Au coated AFM tipAu coated substrate
SAc OO SAcAQ-DT SAc OO AQ-MT SAcSAcAC-DT SAcOPE3-MT SAcSAcOPE3-DTCross-conjugated Linear-conjugated a b c d
Bias voltage (V)
Log ( d I/ d V ) A’AAC-DT
AA’
AC-DTAQ-DT -10-5-9-8-6-7
Log ( d I/ d V ) FIG. 1:
Conductance measurements on molecular wires . a , chemical structure of themolecules used. AQ-DT and AQ-MT are both cross-conjugated, whereas AC-DT, OPE3-DT andOPE3-MT are linearly conjugated. AQ-DT, AC-DT and OPE3-DT are dithiolated and thus sym-metric; AQ-MT and OPE3-MT are monothiolated. The colour code is also used in the followingfigures. b , schematic view of the junction formed by the molecules self-assembled on a conductingsubstrate (Au) and the conducting AFM tip (Au), c , logarithmically binned 2D-histogram for the dI/dV -values vs. bias voltage V for AC-DT in Ω − , the colour scale indicates the number of counts(black: no counts; white: more than 40 counts) d , cross-section of the 2D-histogram shown in c along the line AA’ (zero-bias conductance) resulting in a 1D-histogram (blue). Shown in red is the1D-histogram for AQ-MT taken from Fig. 3a [27]. Representing our data in 2D-histograms has two major advantages. First, it allowsus to show a full data set in one plot, without a need for either determining an averagecurve or for data selection [27] [31]. Second, it enables us to distinguish general tendenciesin dI/dV -curves from statistical variations in the conductance values themselves. Thelatter are inherent to molecular transport studies [26, 27]. Figure 1c clearly illustrates thisadvantage: a symmetric valley-like shape is seen for the full data range. This shape isvirtually independent of the conductance values, which do scatter indeed (Fig. 1d).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 ofmagnitude lower than those of AC-DT. This is quite remarkable, since the energy differencebetween the HOMO and LUMO levels is very similar for these molecules (HOMO: highestoccupied molecular orbital; LUMO: lowest unoccupied molecular orbital) [32]. Furthermore,Fig. 1d cannot be trivially explained from a weaker coupling of AQ-DT to the AFM-tip, since4he endgroups of both molecules are exactly the same. As we shall elaborate on below, thelarge difference in conductance is instead indicative of destructive interference in the AQ-DTjunctions. In Fig. 2a we present calculations of the energy-dependent transmission function, T ( E ), for junctions containing AC-DT, AQ-DT, and AQ-MT. This function describes thequantum mechanical probability that an electron with energy E traverses the molecularjunction. Once T ( E ) is known, the I ( V )-curves can be calculated using Landauer’s formula(Supplementary Methods). In particular, the low bias conductance is given by dI/dV ( V =0) = 2 e /h · T ( E = E F ). For a molecular junction, T ( E ) typically exhibits peaks aroundthe orbital energies, where electrons can tunnel resonantly. In the energy gaps, T ( E ) isnormally rather featureless, as exemplified by AC-DT in Fig. 2a. However, for AQ-DTand AQ-MT, T ( E ) exhibits a strong dip or ’anti-resonance’. This feature is a result ofdestructive interference [6–11]. To reveal the origin of the anti-resonance, we transform thefrontier molecular orbitals into an equivalent set of maximally localized molecular orbitals(LMOs)[9]. The upper part of Fig. 2d shows the three relevant LMOs obtained for AQ-DT.Two are localized on the left and right parts of AQ-DT, respectively. These LMOs have thesame energy and correspond essentially to the sum and difference of the almost degenerateHOMO and HOMO-1 (Fig. 2a). The LMO localized in the center of AQ-DT is essentiallythe LUMO and has a higher energy. It is now clear that an electron with an energy, E ,lying inside the HOMO-LUMO gap can traverse the molecule via two distinct paths: eitherdirectly from the left to the right LMO or by going via the energetically higher LMO (arrowsin Fig. 2d). It can be shown that the upper and lower routes yield a phase difference of π within the HOMO-LUMO gap, i.e., the partial waves interfere destructively (SupplementaryMethods). Consequently, T ( E ) shows a strong minimum at the energy where the partialwaves have equal weight. Figure 2c illustrates this, by showing T ( E ) calculated for thelower and upper routes separately, as well as for the combined three-site model. Note thesimilarity to Fig. 2a. For AC-DT, the HOMO is well separated from the HOMO-1. Hence,a transformation to LMOs leads to only two, left and right localized, orbitals (Fig. 2b). Asthere is only a single path available, no interference effects occur for AC-DT.We now compare these calculations with the experiments in Fig. 1d. In Fig. 2a, the T ( E F )-values are around two orders of magnitude lower for AQ-DT than for AC-DT. Thisis in reasonable agreement with the strongly reduced conductance values for AQ-DT inFig. 1d. We thus have a first indication of interference in AQ-DT. To investigate this5 E-E F (eV) -10 -8 -6 -4 -2 T r a n s m i ss i o n E F E F -2 -1 0 1 2 E-E F (eV) -10 -8 -6 -4 -2 T r a n s m i ss i o n AC-DTAQ-DTAQ-MT E n e r g y bca AC−DTAQ−DT d E n e r g y FIG. 2:
Origin of interference in cross-conjugated molecules . a , Transmission functions T ( E ) for AC-DT (blue), AQ-DT (red) and AQ-MT (purple) calculated with DFT+Σ. The verticalbars mark the energies of the frontier orbitals HOMO-1, HOMO (left side) and LUMO (right side).The lower part of b and d pictures schematic transport models derived from the localized molecularorbitals presented in the upper parts. In the three-site model shown in d , there are evidently tworoutes through the molecule: a lower route directly from the left to the right site and an upper routevia the central orbital. Panel c shows T ( E ) for the lower (dotted line) and upper route (dashedline). A coherent addition of the transmission probability amplitudes from the two paths, with aphase difference of π , yields the three-site transmission function (solid line). This reproduces theessential features of a , for AQ-DT and AQ-MT. further, we inspect the full 2D-histogram of AQ-DT (Fig. 3a). For the full voltage range,its dI/dV -values are dramatically lower than those of AC-DT (Fig. 1c). However, the2D-histogram has a parabola-like appearance similar to AC-DT, i.e. we observe no anomaly6hat can be connected to the calculated transmission dip. Hence, although the surprisinglylow conductance of AQ-DT is most likely due to quantum interference, the evidence is onlyindirect. 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 dI/dV -curves for AQ-MT (SupplementaryFigures). Remarkably, these data do show a clear anomaly at zero bias voltage. Inparticular, the curvature of the dI/dV -traces in Fig. 3b is negative for all V (except around V = 0). What is equally striking in Fig. 3b is the large voltage range over which theanomaly extends. Even up to V = ± dI/dV -curves are dominated by the minimumat V = 0 V. This points to a characteristic energy scale of ≈ T ( E ) in Fig. 2a. Moreover, this largeenergy scale rules out Kondo effects and Coulomb blockade as possible explanations for theanomaly [33]. Hence, Fig. 3b makes a strong case for quantum interference.To further validate this interpretation, we calculate dI/dV -curves for AQ-MT from T ( E ) (see Supplementary Methods). A key role in these calculations is played by theposition of the anti-resonance in T ( E ) relative to E F . This position is difficult to predicttheoretically. This is related to the well-known problems of the applied methodology todescribe energy level alignments and to the uncertainty of the size of the surface dipolesin the experiments [34]. The position of the anti-resonance is particularly sensitive to sucheffects due to the low density of states in the HOMO-LUMO gap [35]. It is thus reasonableto treat the position of the transmission minimum as a free variable within a limitedenergy window. In Fig. 4a, we display dI/dV -curves for AQ-MT, calculated for threecases: no energy shift (compared to Fig. 2a) and shifts of ± . − . dI/dV -characteristic is in remarkable agreement with the measured curves in Fig. 3b. First,the V-like shape with negative curvature is reproduced. Second, the voltage scale and therange of dI/dV -values over which the minimum extends agree. Finally, the dI/dV -curvesare nearly symmetric in both calculation and experiment. The latter is indeed noteworthy,since AQ-MT is contacted asymmetrically. The symmetry in Fig. 3b must therefore bea consequence of T ( E ) being symmetric around E F or, equivalently, of E F laying nearthe interference minimum. To independently confirm that monothiols are asymmetrically7 Q-DT -10-8-6-4.5 0-1 1-10-8-6-4.5
OPE3-DT
Bias voltage (V)Bias voltage (V)
Log ( d I/ d V ) Log ( d I/ d V ) a bc d OPE3-MT
AQ-MT -10-8-6 0-1 1
FIG. 3:
Two-dimensional conductance histograms . a-d show logarithmically binned 2D-histograms of dI/dV (in Ω − ) vs. bias voltage V for AQ-DT ( a ), AQ-MT ( b ), OPE3-DT ( c ) andOPE3-MT ( d ). The colour scale indicates the number of counts and ranges from black (0 counts)to white (more than 40 counts). In d , a dashed line visualizes the asymmetry in the dI/dV -curvesof OPE3-MT, resulting from asymmetric coupling. The corresponding molecular structures can befound in Fig. 1a. coupled, we measured dI/dV -curves for OPE3-DT (Fig. 3c) and OPE3-MT (Fig. 3d).As expected, symmetric data are obtained for OPE3-DT, whereas asymmetric dI/dV -curves are found for OPE3-MT (see Fig. 4b for calculations). Hence, we conclude thatFig. 3b constitutes direct proof for quantum interference in AQ-MT molecular junctions [36].8 Bias voltage (V) -10 -8 -6 -4 d I/ d V ( S ) -1.0 0.0 1.0 Bias voltage (V) -10 -8 -6 -4 AQ-MT OPE-MT a b
FIG. 4:
Calculated dI / dV-curves for AQ-MT and OPE3-MT. a , dI/dV for AQ-MT ascomputed from the transmission function in Fig. 2a. T ( E ) was shifted by ∆ E = 0 . E = 0 . E = − . E F . We include asymmetry in the bias drop through a parameter η = 0 . E = − . dI/dV , spanning two orders of magnitude, are in excellent agreement withthe experiments (Fig. 3b). b , Similar calculation for OPE3-MT. Asymmetric curves and higherconductance values with smaller variation are found, consistent with Fig. 3d. In summary, our charge transport data provide direct evidence for destructive quantuminterference in two-terminal molecular junctions. The interference effects are intimatelylinked to the shapes and energies of the molecular orbitals and can thus be controlled bychemical design. The fact that interference in molecules is present at room temperatureopens the road to a new type of molecular devices. Specifically, these include interferencecontrolled molecular switches with very large on-off ratios[18, 23] and novel thermoelectricdevices, with thermopower values tunable in magnitude and sign[28].* These authors contributed equally to this work9 . METHOD SUMMARY
Samples were prepared by thermal deposition of 5 nm chromium and 200 nm goldonto silicon/silicon oxide substrates. These freshly prepared samples were immediatelytransferred into a nitrogen-filled glove-box. The molecular wires were dissolved in drychloroform (AC-DT, AQ-DT, AQ-MT) or in dry THF (OPE3-DT and OPE3-MT) at 0.5mM, in this glove-box. We added 10% (v/v) degassed triethylamine to these solutions todeprotect the thiol groups and immersed the gold samples for 2 days, to form densely-packedself-assembled monolayers [25] as confirmed by ellipsometry and XPS (see SupplementaryMethods). After immersion, the samples were rinsed three times with clean chloroform orTHF, and dried in the glove-box. The synthesis of AQ-DT and the characterization of allfive molecular wires is reported in the Supplementary Methods. Transport experimentswere performed on a Digital Instrument Multimode-AFM with a Nanoscope III controller.The conductance measurements themselves were controlled externally (see SupplementaryMethods). Calculations of junction geometries and transmission functions were performedwith the GPAW density functional theory code using an atomic orbital basis set correspond-ing to double-zeta plus polarization and the Perdew-Burke-Ernzerhof exchange-correlationfunctional. Before calculating the transmission functions, the occupied and unoccupiedmolecular orbitals were shifted in energy in order to account for self-interaction errors andmissing image charge effects in the DFT description. This approach (DFT + Σ) was recentlyfound to systematically improve the DFT-conductance values [29] (see SupplementaryMethods).
Acknowledgements
We are grateful to Tjerk Oosterkamp and Federica Galli formaking their equipment and expertise available to us. We thank Jan van Ruitenbeek,Marius Trouwborst for discussions and Daniel Myles for his initial synthetic efforts. Thisstudy was financed by a VIDI-grant (SJvdM) of the Netherlands Organization for ScientificResearch (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 thedata analysis; HV and JCH designed and synthesized the molecules, made and characterized10he SAM’s; TM and KST performed the calculations; CG, HV, JCH and SJvdM designedthe experiment. All the authors discussed the results and commented on the manuscript.
Author Information
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