This journal is the Owner Societies 2014 Phys. Chem. Chem. Phys.

Cite this:DOI: 10.1039/c4cp00016a

Electronic transport, transition-voltagespectroscopy, and the Fano eect in singlemolecule junctions composed of a biphenylmolecule attached to metallic andsemiconducting carbon nanotube electrodes

Carlos Alberto Brito da Silva Junior,a Jose Fernando Pereira Leal,bc

Vicente Ferrer Pureza Aleixo,d Felipe A. Pinheiroe and Jordan Del Nero*f

We have investigated electronic transport in a single-molecule junction composed of a biphenyl

molecule attached to a p-doped semiconductor and metallic carbon nanotube leads. We find that the

currentvoltage characteristics are asymmetric as a result of the different electronic natures of the right

and left leads, which are metallic and semiconducting, respectively. We provide an analysis of transition

voltage spectroscopy in such a system by means of both FowlerNordheim and LauritsenMillikan plots;

this analysis allows one to identify the positions of resonances and the regions where the negative differ-

ential conductance occurs. We show that transmittance curves are well described by the Fano lineshape,

for both direct and reverse bias, demonstrating that the frontier molecular orbitals are effectively

involved in the transport process. This result gives support to the interpretation of transition voltage

spectroscopy based on the coherent transport model.

Introduction

Since the pioneering idea of a molecular rectification diodeproposed by Aviram and Ratner,1 electronic transport in singlemolecules of the donorbridgeacceptor type has been extensivelyinvestigated.2 In single molecule junctions the nature of theelectrodes and their connection to the molecular bridge governelectronic transport in a crucial way. Significant progress has beenmade in theoretical modeling electronic transport when the donoror/and acceptor are replaced by metallic or semiconductingelectrodes to investigate the dependence on the bridge structureand the electronic properties of the leads.3 The metalmoleculecoupling depends onmany parameters, such as the type of chemical

linkage between both, the molecular conformation, and thetunneling barrier height.4,5 For instance, the interactionbetween bridge and electrode is generally a weak electrostaticinteraction, similar to the physisorption that occurs at manysolid/gas and solid/liquid interfaces.2,6,7 As another example,electronic conduction in metalbridgemetal and metalbridgesemiconductor junctions has been investigated to identifythe role of molecular size and structure, as well as temperature andthe magnitude of the barrier for tunneling between donor andacceptor.8 All these factors strongly influence the currentvoltagecharacteristics of molecular junctions, as it has been demonstratedboth experimentally and theoretically.4,5

In single-molecule junctions the so-called alligator-clips,such as nitrogen and sulfur, are used to establish electroniccontact between an inorganic electrode (e.g. Ag, Au, Al, Pb, Hg)and organic bridges (usually carbon atomic wires, saturatedand unsaturated carbon chains). Ideally, infinite carbon atomicwires are semiconducting due to Peierls distortion. However,short carbon atomic wires are usually modeled as metallic.9

This model is justified since the energy barrier between theinorganic lead and organic bridges is typically very high, whichalso induces a disruption of the electronic bridgeelectrodeinteraction.10 The tunneling process in molecular devices isdominated by the height and width of the barrier resulting fromthe presence of molecules between the electrodes. The barrier

a Faculdade de Ciencias Naturais, Universidade Federal do Para, 68800-000,

Breves, PA, Brazil. E-mail: cabsjr@ufpa.brb Pos-Graduaao em Fsica, Universidade Federal do Para, 66075-110, Belem,

PA, Brazilc Departamento de Ciencias Naturais, Universidade do Estado do Para, 68745-000,

Castanhal, PA, Brazild Faculdade de Engenharia Eletrica, Universidade Federal do Para, 68455-700,

Tucuru, PA, Brazile Instituto de Fsica, Universidade Federal do Rio de Janeiro, 21941-972,

Rio de Janeiro, RJ, Brazilf Departamento de Fsica, Universidade Federal do Para, 66075-110, Belem,

PA, Brazil. E-mail: jordan@ufpa.br

Received 2nd January 2014,Accepted 17th July 2014

DOI: 10.1039/c4cp00016a

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height when the leads are both metallic (metallic and semi-conductor) is given by the energy difference between the Fermilevel of the electrodes (the edge of the conduction or valenceband) and the closest molecular energy levels (HOMO and/orLUMO).11,12 Experimentally, the connection bridgeelectrode isimplemented using scanning probe microscopy (SPM), scanningtunneling microscopy (STM), or conducting probe atomic forcemicroscopy (CP-AFM) with a gold tip without the presence ofalligator clips.2,1315

Alternatively, theoretical and experimental studies on single-molecule electronic transport have revealed that junctionsmade of metallic carbon nanotubes (CNTs) leads oer manyadvantages compared to inorganic metallic electrodes.16,17

Recently electronic transport and Transition Voltage spectro-scopy (TVS) analysis have been investigated in single-moleculejunctions composed of both inorganic metallic14,15 and organicmetallic leads.17 TVS is based on the analysis of the FowlerNordheim plot, which exhibits a sell point Vmin. In junctionswith organic metallic leads Vmin corresponds to voltages wherenegative differential resistance occurs, corroborating the coher-ent transport model interpretation of TVS. The fact that themetallic electrodes are made up of carbon nanotubes leads toimportant differences in the behavior of Vmin compared to thecase of molecular junctions with nonorganic contacts.17 Ascarbon nanotubes can be either metallic or semiconducting,considering these materials as electrodes in single-moleculejunctions could lead to novel electronic transport phenomenaand applications. However, to the best of our knowledge thiscase has never been treated so far.

The aim of the present work is hence to fill this gap byinvestigating electronic transport and TVS analysis in single-molecule junctions composed by metallic and semiconductingcarbon nanotubes (Fig. 1). We provide an analysis of TVS in sucha system by means of both FowlerNordheim and LauritsenMillikan plots. This analysis allows one to identify the positionsof resonances and the regions where the negative differentialconductance occurs. We also demonstrate that transmittancecurves are well described by the Fano lineshape, for both directand reverse bias. These results suggest that the frontier mole-cular orbitals are effectively involved in the transport process,corroborating the coherent transport model in single-moleculeelectronics and the current interpretation of TVS.

Methodology

Preceding the electronic transportation calculations, the molecularsystem was optimized using the B3LYP18 level and the 6-311G**basis set. The B3LYP functional has been employed to successfullydescribe electronic transport in singlemolecules attached to carbonnanotube electrodes.16,17,19 The relative positions of the lead carbonatoms were frozen in a typical nanotube formation as presentedin Fig. 1 as well as the distance between the nanotube and phenylrings. A full relaxation was performed during the subsequentgeometric optimization.

Electronic transport calculations are grounded on the Non-Equilibrium Greens function (NEGF) formalism coupled toab initio DFT.17,20,21 This theoretical procedure has been demon-strated to be highly reliable in predicting electronic transportproperties such as current and transmission coecients.17,19,22

In addition, this methodology has been shown to be ecient indetermining the transport properties of molecular devicesattached to very large electrodes.17,22

A systematic study, with a methodology very similar to theone employed here, of electronic transport using metallic andsemiconducting CNTs leads was done by Lee et al. in ref. 23,where the presence of these electrodes gives rise to a Schottky-likebehavior, depending on the direction and strength of their dipolemoments. Also, they investigated the possibility of controlling theIV characteristics of these systems by manipulating the doping ofthe CNT units.23

A similar DFT/NEGF23 calculation was carried out to disclosethe electrical transport properties of organic junctions connected tolarge reservoirs (electrodes). To compute the IV characteristics ofmetallic CNTbiphenylp-doped semiconductor CNT, we takeinto account the first principles methodology implemented in aFORTRAN code as previously presented,17 as well as the SIESTApackage.22

The current calculations consist of two steps: (a) molecularrelaxation of the organic system is performed by means ofquantum mechanical methodologies with a specific functionaland basis set (B3LYP/6-311G**). To simulate the molecularjunction, each optimized molecule composed by carbon atomsof the lead was translated into a semi-infinite junction withseveral carbons in the surface. The supercell consists of twocarbon nanotubes as the left (single wall (9,0)) and right (singlewall p-doped (8,0)) layers with 184 atoms for both layers in thescattering region plus the phenyl rings as the connectorbetween them. The moleculeorganic electrode contact distancewas initially set from 1.30 up to 1.50 and then optimizedshowing no difference in the final result. A double-z pluspolarization basis set was used for all atoms in the organicmolecule with a local density approximation in the transportcalculation and norm-conserving pseudo potentials. All atomswere relaxed including in the optimization process resulting in aforce field less than 0.11 eV 1. To achieve the self-consistencyin the calculation, it is necessary to compute the charge densityby integrating the contributions from scattering states betweenthe left and right lead chemical potentials, given by the FermiDirac distribution. The energy spacing around the Fermi level for

Fig. 1 Model geometry: biphenyl derivative bridging the gap between thesingle-wall (9,0) carbon nanotube and the p-doped (8,0) carbon nanotube.

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in/out states from bulk used in this paper are a typical 11 meVin accordance with well-known work in the field (ref. 24 andreferences therein). The self-consistency is achieved afteroptimization of different charge densities. Before calculating theelectronic current through the entire system (molecule coupled toCNTs electrodes), one should characterize the electronic propertiesof individual capped CNTs separately. Fig. 2 reveals that themetallic and p-doped semiconductor CNTs exhibit ohmic andnon-ohmic behavior, respectively. This result confirms that theCNTs can be considered to be bulk-like and hence are adequate forbeing employed as electrodes in Landauer transport calculations.As the semiconductor lead is p-doped, a narrow energy band existsin the energy region of the undoped semiconductor. The electronictransport between the leads is followed after the molecular relaxa-tion including an applied bias between the leads and the electricsignature is calculated utilizing the NEGF method.

The electronic current through the system is given by theLandauerButtiker formula with an integration of the transmissioncoefficient square between the chemical potentials.2527

I 2eh

uR Vb uL Vb

T E;Vb dE: (1)

The transport coefficient T(E,Vb) is a function of the energy levelE at a specific bias Vb. The uR(Vb) and uL(Vb) are the energy biasregions.

Electronic transport and transitionvoltage spectroscopy

Before the simulation of CNT p-doped (8,0) semiconductorbiphenylCNT (9,0) metallic junctions, we characterize theelectronic transport properties of individual CNTs used asleads. In Fig. 2 the IV (currentvoltage) signature of cappedCNTs, characterized by (8,0) and (9,0) as Hamada indices.These calculations were done using the DFT/NEGF method asa function of the external bias voltage Vb revealing a typical

ohmic and quasi-ohmic (non-resonant) behavior demonstratingthat the (9,0) CNT is metallic and the (8,0) CNT is a p-dopedsemiconductor.

Also, the investigation of the electrical signature for otherCNT sizes were performed and no qualitative dierences com-paring with Fig. 2 were found.

Finally, the CNTs presented in this figure can be utilized asbulk-like and they are adequate for being used as left/rightleads following the Landauer methodology.

Fig. 3 presents the FowlerNordheim (FN) plot, ln(I/V2)versus V1, and LauritsenMillikan (LM) plot, ln(I) versus V1

for (9,0) CNTbiphenylp-doped (8,0) CNT.28 For historicalreasons, it has become customary to use FN for analyzing fieldemission currentvoltage data in bulk metals. However, LMplots are in fact easier to understand and are utilized in a widerange of materials. Also, LM plots are more flexible to makecorrections for all physical sources of voltage dependence in thedata, or to estimate uncertainties in derived parameter valueswhen the precise forms of voltage dependences are not known.29

The analysis of the FN and ML plots, shown in Fig. 3, revealsthat there are two resonances at0.026 V and0.236 V (reversebias), where the first corresponds to the minimum voltage(Vmin). For the forward bias two resonances occur at 0.053 Vand 0.184 V, while one negative dierential resistance (NDR)occurs at 0.367 V, corresponding to the local minimum voltage(Vmin). The LM plot shows one NDR at0.183 V that correspondsto the minimum voltage (Vmin) for the reverse bias; for theforward bias there is one resonance at 0.053 V (that coincideswith the FN plot) and two NDRs at 0.131 V and 0.367 V (thatcoincide with the FN plot), corresponding to the minimumvoltage (Vmin).

Fig. 3 shows that FN and ML graphs exhibit dierent valuesof resonance and NDR. The currentvoltage characteristics (IV)and the normalized conductancevoltage (G/G0 V) curve areshown in Fig. 4. The resonance and NDR can be betteridentified in Fig. 4(a), presenting strong coupling in thisjunction for the same applied bias. However, when the NDR

Fig. 2 Currentvoltage characteristics of individual capped carbon nano-tubes used as leads, calculated by means of the DFT/NEGF methodology.CNTs with Hamada indexes (8,0) (black diamonds) as quasi-semiconducting p-doped and (9,0) (open red circles) as metallic wereconsidered.

Fig. 3 Forward (full symbols) and reverse (open symbols) bias for (bluecircles) FowlerNordheim (FN) and (red triangle) LauritsenMillikan (LM)graph for (9,0) CNTbiphenylp-doped (8,0) CNT. The points labeled bycircles correspond to voltages where negative differential conductanceand resonances occur.

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shows up, the coupling changes from strong to weak.22 Whenthe HOMO level crosses the Fermi level EF a resonance occurs;when the LUMO level crosses the Fermi level a NDR occurs.These situations correspond to transmission peaks at EE EF inFig. 5.17

Fig. 4 shows the asymmetric (a) currentvoltage (IV) and (b)differential conductance characteristics for the system investi-gated. Fig. 5 exhibits the transmittance curves for differentvoltages for (a) reverse and (b) forward bias, respectively. In thefollowing we pinpoint the major findings that can be inferredfrom these figures, together with Fig. 3: negative applied bias:(i) at 0.026 V there is a resonance captured by the FN plot

(Fig. 2), an increase in conductance [Fig. 4(b)], and transmit-tance centered at E EF = 0 [Fig. 5(a)]; (ii) for 0.184 V negativedifferential resonance occurs, as the LM plot reveals (Fig. 3), adecrease in conductance [Fig. 4(b)], and transmittance centeredat E EF = 0 [Fig. 5(a)]; (iii) for 0.236 V a resonance shows up,as it is clear from the FN plot (Fig. 3), a small increase inconductance [Fig. 4(b)] and transmittance centered at E EF = 0[Fig. 5(a)]. Positive applied bias: (iv) a resonance, present atboth LM and FN plots, occurs at 0.053 V (Fig. 3), a smallincrease in conductance [Fig. 4(b)] and transmittance centeredat E = EF [Fig. 5(b)]; (v) negative differential resonance emergesat 0.131 V, as shown in the LM plot (Fig. 3), a decrease inconductance [Fig. 4(b)], and transmittance centered at E EF =0 [Fig. 5(b)]; (vi) negative differential resonance occurs for0.184 V, as demonstrated by the FN plot (Fig. 3), a smallincrease in conductance [Fig. 4(b)] and transmittance notcentered at E = EF [Fig. 5(b)]; (vii) at 0.367 V there is a regionof negative differential resonance captured by both LM and FN(Fig. 3) plots, a decrease in conductance [Fig. 4(b)] and trans-mittance centered at E = EF [Fig. 5(b)].

The regions where NDR occurs are related to suppression inthe current, suggesting that there is a crossover from strong toweak coupling19 between the electrodes (CNT (9,0) and p-doped(8,0) CNT) and the molecular bridge (biphenyl). In a modelwhere electronic transport can be described by a tunnelingbarrier, this crossover can be attributed to the fact that theSchottky barrier is very small in the p-doped CNT (8,0)biphenyljunction. This behavior is asymmetric in the IV curve because theleft and right electrodes are metallic and semiconducting, respec-tively, so that the barrier height is different for the reverse andforward bias. A similar result has been reported in the literature.11

Fig. 5 reveals that, for certain values of the applied voltagebias, the transmittance curves are asymmetric and cannot bedescribed by the typical Lorentzian lineshape. Instead suchcurves are very well described by the Fano lineshape:

Te s0e q2

1 e2 ; (2)

with e = 2(E ER)/G where ER and G are position and width ofthe resonance, s0 is normalized, and q is the asymmetryparameter (see inset of Fig. 5). In general, the Fano eect inelectronic transport results from the interference between theexcited leaky modes in the central transport region (e.g. quan-tum dot, molecular bridge) and the incoming wavefunctionfrom the electrodes.30 In the present case, the fact that thetransmittance curves are well described by the Fano lineshapesuggests that the molecular frontier orbitals are being occupiedduring the transport process; since these states have a finitelifetime, they eventually leak and interfere with the incidentwavefunction, resulting in the Fano asymmetric transmittancecurves. This result supports the scenario in which the coherenttransport model provides an adequate description of electronictransport in the molecular junctions under investigation,corroborating the current interpretation of transition voltagespectroscopy.31

Fig. 4 (a) Currentvoltage (IV) and (b) normalized conductancevol-tage (G/G0 V) curves for CNT (9,0)biphenylp-doped CNT (8,0).

Fig. 5 Transmittance-energy barrier graph for dierent voltages in (a)reverse and (b) forward bias.

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Fig. 6 shows the density of states (DDOS) for biphenylderivative bridging the gap between the single-wall (9,0) carbonnanotube and the p-doped (8,0) carbon nanotube and it comesfrom the imaginary contribution of the retarded Green functionin all molecular sites. The dashed line indicates the Fermi levelposition. The results indicate a conductor behavior with noenergy gap for the considered configuration and the Fermi levelis in the middle of band.

An inspection of Fig. 7 indicates that the HOMO surface isalmost localized on the semiconductor NTC lead with a smalloverlap in the first biphenyl atom. The LUMO state is delocalizedon the left lead (metallic NTC) phenyl showing strong coupling(the pi orbitals overlap between the electrode and the molecule)when compared with the right electrode.

Conclusions

We investigate electronic transport in semiconductormoleculemetal junctions consisting of a biphenyl molecule attached top-doped semiconducting and metallic carbon nanotubes. The factthat the right and left leads have different electronic properties(metallic and semiconductor) is at the origin of interesting

electronic transport phenomena. Indeed, we find that the currentvoltage characteristics are asymmetric. Also, we provide an analysisof transition voltage spectroscopy in such systems bymeans of bothFowlerNordheim and LauritsenMillikan plots; this analysisallows one to identify the positions of resonances and the regionswhere the negative differential conductance occurs. We demon-strate that transmittance curves are well described by the Fanolineshape, for both direct and reverse bias. This result suggeststhat the frontier molecular orbitals are effectively involved in thetransport process, corroborating the coherent transport model insingle-molecule electronics. By unveiling the connection betweenFano resonances and transition voltage spectroscopy, we provide anovel way to understand and interpret FowlerNordheim plots,largely used in single-molecule electronics.

Acknowledgements

This work was partially supported by the Brazilian agenciesCNPq, CAPES, FAPERJ, VALE/FAPESPA, Rede Nanotubos deCarbono/CNPq, INCT Nanomateriais de Carbono/CNPq, andELETROBRAS/ELETRONORTE. CABSJR and VFPA are gratefulfor the UFPA/PROPESP/PARD project and to CENAPAD-SP forcomputational support. CABSJR acknowledges Mr J. A. Rodrigues-Neto and Mr M. E. S. Sousa for fruitful discussions.

References

1 A. Aviram and M. Ratner, Chem. Phys. Lett., 1974, 29,277283.

2 R. L. McCreery, Chem. Mater., 2004, 16, 44774496.3 M. M. Saitner, F. Eberle, J. Baccus, M. DOlieslaeger,P. Wagner, D. M. Kolb and H. G. Boyen, J. Phys. Chem. C,2012, 116, 2181021815.

4 J. J. Kushmerick, S. K. Pollack, J. C. Yang, J. Naciri,D. B. Holt, M. A. Ratner and R. Shashidhar, Ann. N. Y. Acad.Sci., 2003, 1006, 277290.

5 H. Nakayama and S. Kimura, Chem. Phys. Lett., 2011, 508,281284.

6 R. M. Metzger, B. Chen, U. Hopfner, M. V. Lakshmikantham,D. Vuillaume, T. Kawai, X. Wu, H. Tachibana, T. V. Hughes,H. Sakurai, J. W. Baldwin, C. Hosch, M. P. Cava, L. Brehmerand G. J. Ashwell, J. Am. Chem. Soc., 1997, 119, 1045510466.

7 S. Hong, R. Reifenberger, W. Tian, S. Datta, J. I. Hendersonand C. P. Kubiak, Superlattices Microstruct., 2000, 28,289303.

8 A. Nitzan and M. A. Ratner, Science, 2003, 300, 13841389.9 F. Borrnert, C. Borrnert, S. Gorantla, X. Liu, A. Bachmatiuk,J.-O. Joswig, F. R. Wagner, F. Schael, J. H. Warner,R. Schonfelder, B. Rellinghaus, T. Gemming, J. Thomas,M. Knupfer, B. Buchner and M. H. Rummeli, Phys. Rev. B:Condens. Matter Mater. Phys., 2010, 81, 0854391.

10 T. Albrecht, Nat. Commun., 2012, 3, 829839.11 A. Salomon, T. Boecking, O. Seitz, T. Markus, F. Amy,

C. Chan, W. Zhao, D. Cahen and A. Kahn, Adv. Mater.,2007, 19, 445450.

Fig. 6 The electronic density of states spectra (DDOS) for the corres-ponding device presented in Fig. 1. The dashed line indicates the Fermilevel position.

Fig. 7 LUMO and HOMO, respectively, for the investigated system withno applied bias.

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12 L. H. Yu, N. Gergel-Hackett, C. D. Zangmeister, C. A. Hacker,C. A. Richter and J. G. Kushmerick, J. Phys.: Condens. Matter,2008, 20, 37411413741145.

13 R. M. Metzger, J. Mater. Chem., 2008, 18, 43644396.14 J. M. Beebe, B. Kim, J. W. Gadzuk, C. D. Frisbie and

J. G. Kushmerick, Phys. Rev. Lett., 2006, 97, 0268011.15 J. M. Beebe, B. Kim, C. D. Frisbie and J. G. Kushmerick, ACS

Nano, 2008, 2, 827832.16 N. A. Bruque, M. K. Ashraf, G. J. O. Beran, T. R. Helander

and R. K. Lake, Phys. Rev. B: Condens. Matter Mater. Phys.,2009, 80, 155455115545513.

17 C. A. B. Silva Jr., S. J. S. da Silva, E. R. Granhen, J. F. P. Leal,J. Del Nero and F. A. Pinheiro, Phys. Rev. B: Condens. MatterMater. Phys., 2010, 82, 0854021.

18 A. D. J. Becke, Chem. Phys., 1993, 98, 13721377;J. P. Perdew, M. Ernzerhof and K. Burke, J. Chem. Phys.,1996, 105, 99829985; A. D. Becke, Phys. Rev. A: At., Mol.,Opt. Phys., 1988, 38, 30983100; S. H. Vosko, L. Wilk andM. Nusair, J. Phys., 1980, 58, 12001211.

19 W. Y. Kim, S. K. Kwon and K. S. Kim, Phys. Rev. B: Condens.Matter Mater. Phys., 2007, 76, 0334151.

20 A. Saraiva-Souza, R. M. Gester, M. A. Reis, F. M. Souza andJ. Del Nero, J. Comput. Theor. Nanosci., 2008, 5, 22432246;A. Saraiva-Souza, F. M. Souza, V. F. P. Aleixo, E. C. Girao,J. Mendes Filho, V. Meunier, B. G. Sumpter, A. G. Souza Filhoand J. Del Nero, J. Chem. Phys., 2008, 129, 204701204704.

21 M. Brandbyge, J.-L. Mozos, P. Ordejon, J. Taylor andK. Stokbro, Phys. Rev. B: Condens. Matter Mater. Phys.,2002, 65, 165401165417.

22 K. Stokbro, J. Taylor and M. Brandbyge, J. Am. Chem. Soc., 2003,125, 36743675; J. Taylor, M. Brandbyge and K. Stokbro, Phys.Rev. Lett., 2002, 89, 13830111383014; Z. K. Qian, S. M. Hou,R. Li, Z. Y. Shen, X. Y. Zhao and Z. Q. Xue, J. Comput. Theor.Nanosci., 2008, 5, 671676.

23 S. U. Lee, M. Khazaei, F. Pichierri and Y. Kawazoea, Phys.Chem. Chem. Phys., 2008, 10, 52255231.

24 X. D. Cui, A. Primak, X. Zarate, J. Tomfohr, O. F. Sankey,A. L. Moore, T. A. Moore, D. Gust, L. A. Nagahara andS. M. Lindsay, J. Phys. Chem. B, 2002, 106, 86098614.

25 R. Landauer, IBM J. Res. Dev., 1957, 1, 1223; M. Buttiker,Phys. Rev. Lett., 1986, 57, 17611764.

26 A. Hernandez, V. M. Apel, F. A. Pinheiro andC. H. Lewenkopf, Physica A, 2007, 385, 148160.

27 S. Datta, Quantum transport: Atom to transistor, CambridgeUniversity Press, 2005.

28 M. Tsukada and M. Airaidai, Phys. Rev. B: Condens. MatterMater. Phys., 2010, 81, 23511412351147.

29 R. G. Forbes, J. Appl. Phys., 2009, 150, 11431311143138.30 A. E. Miroshnichenko, S. Flach and Y. Kivshar, Rev. Mod.

Phys., 2010, 82, 22572298.31 E. H. Huisman, C. M. Guedon, B. J. van Wees and S. J.

van der Molen, Nano Lett., 2009, 9, 39093913.

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