Physics of artificial nano-structures on surfaces

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<ul><li><p>Physics of artificial nano-structures on surfaces</p><p>M. Tsukadaa,*, N. Kobayashib, M. Brandbygec, S. Nakanishia</p><p>aDepartment of Physics, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku,</p><p>Tokyo, 113-0033, JapanbSurface and Interface Laboratory, RIKEN (The Institute of Physical and Chemical Research), 2-1</p><p>Hirosawa, Wako-shi, Saitama, 351-0198, JapancMikroelektronik Centret (MIC), Technical University of Denmark (DTU), Building 345 east, DK2800,</p><p>Lyngby, Denmark</p><p>Abstract</p><p>Quantum electron transport through nano-structures such as metal atomic wires ormolecular bridges is investigated with various theoretical approaches. The dierence of thequantization feature between Na and Al atom wires is explained based on the eigenchannel</p><p>analyses combined with the recursion-transfer matrix calculation. The eigenchannels arecalculated self-consistently for Au atom wires at finite bias voltage and the nonlinearconductance is explored in relation to the oset energies of d band channels. As for</p><p>molecular bridges, we find that a remarkable metalization is caused, if the coupling of themolecule with the metal electrode is enhanced. Internal current distribution within themolecular networks is discussed and exotic properties of the quantum transport is found. In</p><p>particular, a strong induced loop current is revealed circulating the ring part of themolecule. The direction of the loop current is switched sharply when the electron incidentenergy sweeps a degenerate molecular level. 7 2000 Published by Elsevier Science Ltd. Allrights reserved.</p><p>1. Introduction</p><p>Recent development of scanning probe microscopy (SPM) opened a new research</p><p>0079-6816/00/$ - see front matter 7 2000 Published by Elsevier Science Ltd. All rights reserved.PII: S0079 -6816 (00)00014 -9</p><p>Progress in Surface Science 64 (2000) 139155</p><p>www.elsevier.com/locate/progsurf</p><p>* Corresponding author. Tel.: +81-3-3812-2111 extn 4223; fax: +81-3-3814-9717.</p><p>E-mail address: tsukada@cms.phys.u-tokyo.ac.jp (M. Tsukada).</p></li><li><p>field of the science of artificial nano-structures, which will be an important basisof high technology in the 21st century. By means of SPM, one can observe theatomic details of the individual nano-structures, and fabricate them in a controlledway. Furthermore, various electronic, nano-mechanical, magnetic, and chemicalproperties of the nano-structures can be in principle investigated by the use ofSPM. For example the scanning tunneling microscopy (STM) is most advantageousto investigate the quantum transport through nano-structures.Among a variety of artificial nano-structures, the bridge systems sandwiched</p><p>between the tip of STM and sample surface are most attractive since the contactof the nano-structures with the electrode pad is established in a natural way. Infact, there have been many of the experimental studies for the metallic wire bridgesystems (atom bridge hereafter) and remarkable properties, such as the quantumstaircase of the conductance have been reported [1,33]. On the other hand, themolecular systems are promising to aord ideal nano-scale electronic circuitsystems, which might realize various new functions of the quantum devices.Though at the moment various technical problems such as the way of socketingthe molecule to conductive electrodes are to be developed, theoretical explorationof the novel properties as quantum devices would be important.Therefore, in the present article, we study the quantum transport features of</p><p>metallic atom bridges and molecular bridges sandwiched between the metallicelectrodes. As for the atom bridges, we clarify the details of eigenchannels [2,29]and their relation with the atomic/molecular orbitals of the bridge part. From thisview point, how the quantum transport properties depend on the atom kind andthe microscopic shape of the atom wires might be clarified. Moreover, the natureof the quantization of the conductance and detailed transmission spectra reflectingresonant scattering inside the bridge part will be discussed.As for the molecular bridge, the important issue is to achieve the metallic</p><p>conduction through the bridge part. This might be realized by the resonanttunneling, i.e., tuning the level of HOMO, or LUMO close to the Fermi level. Butthis may be possible only for a rather special case. The other method to achievethe high transmission is to use the metallization of the molecule due to the closecoupling to metal electrodes. We will discuss the possibility of this in the presentarticle. One of the remarkable findings we obtained in this article is a strong loopcurrent inside the molecular part induced by the source-drain current. Such a loopcurrent emerges when the electron energy approaches close to the degeneratelevels of the molecules and changes its direction and distribution by the relativelocation of the level and the electron energy. By the use of this remarkablefeature, one might control the phase of the induced quantum state of themolecular part, which might be promising for realizing various quantum functionsof the molecular bridges.</p><p>2. Al and Na atomic wires</p><p>First we present first-principles calculations of the transmission channels of</p><p>M. Tsukada et al. / Progress in Surface Science 64 (2000) 139155140</p></li><li><p>atom wires for two materials; one is an s valence metal, Na, and the other is an s-p valence metal, Al [3]. Detailed features of the transmission channels areelucidated for several atomic configurations, and a remarkable dierence of thebehaviors is found between Na and Al bridges. We will discuss how the behaviorsof the channels are influenced by geometrical changes for the atom wires, and whyquantized conductance is observed more clearly for a Na atom wire.The channels are investigated by the first-principles calculations combined with</p><p>eigenchannel decomposition [4]. The electronic states are calculated using the first-principles recursion-transfer matrix method [5,32,31], and the conductance [6] andthe local density of states (LDOS) [7] are decomposed into the eigenchannels[2,29]. The model consists of three Na or Al atoms between two semi-infinitejellium electrodes as shown in Fig. 1 (upper inset). The atomatom and the atomjellium bond lengths are taken to be 7.0 (5.4) and 3.0 (2.6) bohrs, and the middleatom is displaced in the x direction by d, keeping the same bond length.Fig. 1 shows the conductance and the channel transmissions of the wires as a</p><p>function of the displacement d. The conductance, the sum of individual channeltransmissions is expressed in the quantized unit, 2e 2/h. For the Na wire, theconduction is contributed by a single channel which is almost fully open. Thevalue of the conductance is close to 2e 2/h, and does not change with thedisplacement, d. On the other hand, for the Al wire, three channels contribute tothe conduction; one almost fully open and the other two half open. With increaseof d, each channel transmission decreases, and thus the conductance alsodecreases. The detailed mechanism of causing such behaviors is described in Ref.[3].Fig. 2 shows the channel resolved LDOS distributions on the plane normal to</p><p>Fig. 1. Conductance and channel transmission of NA (upper) and Al (lower) atom wires as a function</p><p>of displacement of d. Upper inset: schematic representation of the model used. Three Na or Al atoms</p><p>are sandwiched between jellium electrodes.</p><p>M. Tsukada et al. / Progress in Surface Science 64 (2000) 139155 141</p></li><li><p>the wire axis for the straight Na and Al wires. A single channel of the Na wirehas an s orbital character. On the other hand, the first channel of the Al wire hasa character of s and pz orbitals, while the second and the third channel, which aredegenerate, have a character of px or py orbitals. For the bent Al wire, threechannels contribute to the conduction as well as the straight case, by the s pzcharacter and the px character are mixed, and only the py character is similar tothe straight case.Fig. 3 shows the channel resolved DOS of the center atom and the channel</p><p>transmissions. The position of the onset energy of each channel relative to theFermi energy is important to understand the behavior of the channel. For the Nawire, the Fermi energy cuts just after the onset of the first channel. Therefore, theconductance is close to the quantized value, and does not change even for thebent wire. On the other hand, for the Al wire, the Fermi energy cuts the onset ofthe second and the third channels. This is the reason why the channeltransmission does not take the quantized value. We found that the conductance ofthe Al wire is sensitive to the geometrical change, and is reduced by the bending.Experimentally, quantization of the conductance of Na is clearly observed [8].</p><p>In actual observation of the conductance during the elongation process, theatomical configuration is changing. For the Na atom wire, the conductance isinsensitive to the geometrical changes, as has been seen above. This fact impliesthat the observation of the conductance quantization is easier for the Na wire.The present results indicate the decrease of the bending angle causes a</p><p>significant increase of the conductance for the Al wire. This is consistent with thepositive slope of the conductance experimentally observed [9].</p><p>Fig. 2. Channel resolved LDOS of Na (upper) and Al (lower) atom wire on the plane including the</p><p>center atom and normal to the wire-axis. The contour plots are in units of 2 102 hartree1 bohr3.The broken lines correspond to 1 103 hartree1 bohr3. The solid circles indicate the atomicpositions. An area with a side of 20 bohrs is displayed.</p><p>M. Tsukada et al. / Progress in Surface Science 64 (2000) 139155142</p></li><li><p>3. Au atomic wires</p><p>Fig. 4 shows the energy bands for Pb, Al, Nb and Au monoatomic wiresobtained using the tight binding model parametrized by fits to ab initio bandstructures [12,32]. In experiments using superconducting electrodes transmissionsof individual conductance channels have been extracted for contacts down to thesingle atom [10]. An agreement of the number of the bands with the number ofchannels at the Fermi energy is found. For Au, the top of the d band touches theFermi energy from the lower energy side. The transport through the d orbitals istherefore expected for a finite bias. In this section, we focus on the Au atombridges and discuss the details of the transmission properties.Eigenchannel properties of the Au atom wires are calculated at finite bias</p><p>voltage by a non-orthogonal tight-binding model with the non-equilibrium Greensfunction approach [13]. We assume local charge neutrality and include an on-sitepotential at each atom which is adjusted self-consistently in order to achieve theneutrality [11]. We apply the local neutrality also in the finite bias which enablesus to calculate the voltage drop through the contact.In Fig. 5, we consider a 3-atom long Au wire attached to layers of 4 and 9</p><p>atoms in both ends which again are connected to the (100) faces of two semi-infinite gold electrodes. All interatomic distances are assumed as the same as inthe bulk. We present the calculated self-consistent on-site potential (layeraveraged) and the change in this potential with applied voltage (voltage drop).In Fig. 6, we present the eigenchannel transmissions for the self-consistent</p><p>calculations of the 3-atom Au chain. For a finite bias an energy window (vertical</p><p>Fig. 3. Channel resolved DOS of the center atom and channel transmissions for the Na (upper) and Al</p><p>(lower) wires as a function of energy measured from the Fermi level. The left panels correspond to the</p><p>straight wires, and the right to the displacement of d=2.</p><p>M. Tsukada et al. / Progress in Surface Science 64 (2000) 139155 143</p></li><li><p>Fig. 4. Band structures of infinite Pb, Al, Nb and Au monatomic wires.</p><p>Fig. 5. The layer averaged atomic potential shifts (hfiiLayer) for dierent bias voltages. Layer 1correspond to the first (100) surface layer of the semi-infinite electrode. The voltage drop</p><p>(hfiiLayer(V)hfiiLayer(0)) is shown to the right. The largest voltage drop is seen in the entrance of thecontact between layer 2 and 3.</p><p>M. Tsukada et al. / Progress in Surface Science 64 (2000) 139155144</p></li><li><p>lines) of width eV contributes to the conductance. In the lower panels of Fig. 6,we show the projected density of states (PDOS) onto the atomic orbitals of themiddle atom. The PDOS is resolved into its eigenchannel components [13,14].The transmissions presented in Fig. 6 change with increased bias: the local</p><p>charge neutrality forces the (almost degenerate) dzx=dyz states down in energy anddelays the onset of the derived eigenchannels somewhat. We observe that thedzx=dyz-derived channels first begin to contribute inside the voltage window from avoltage bias of about 1.5 V.The transmission of the s=pz=dz 2 lz 0 channel within the voltage window in</p><p>lowered with increasing bias. The partially open dzx=dyz transmission channels aswell as the lowering of the s=pz=dz 2 transmission in the high bias regime lead to anincreased electron-ion momentum transfer (electron wind) where the currentcarrying electrons are backscattered. The backscattering takes place mainlybetween layers 2 and 3 according to the voltage drop in Fig. 5. An increasedelectron wind could be part of the reason for the apparent decrease in stability ofthe one-atom gold contacts found in Ref. [15].We have also considered shorter and longer chains [13]. In contrast to the result</p><p>for the 3-atom long chain, we find for a 2-atom long chain that the px=py orbitalsplay a more pronounced role in the 2nd and 3rd eigenchannels and the modelpredict a noticeable contribution from the 2nd and 3rd eigenchannels of about0.05 around EF: For a 6-atom long chain we find that the dzx=dyz contributions lie</p><p>Fig. 6. Upper panel: the eigenchannel transmissions of the 3-atom Au chain for 0 (left) and 2.0 (right)</p><p>volts bias. An almost fully transmitting single channel (solid line) is seen inside the voltage window and</p><p>two near degenerate channels are seen just below (dotted lines). For the higher bias voltages these</p><p>degenerate channels begin to enter the voltage window. Lower panel: the corresponding eigenchannel</p><p>density of states projected onto the atomic orbitals of the middle atom (denoted by 3 in Fig. 5).</p><p>M. Tsukada et al. / Progress in Surface Science 64 (2000) 139155 145</p></li><li><p>closer to EF: For long chains the dzx=dyz derived electronic states inside the chainwill approach the 1D band states (Fig. 4) with the sharp onset in thecorresponding transmission channels close to Fermi energy.The large non-linear conductance found in Ref. [16] is not seen in the results of</p><p>the present calculations. We find an almost linear behavior up to 2 Vcorresponding to a conductance close to G0 2e2=h: A less ecient screening(assumed to be complete in the present calculations of Au wires) and in the limitof long chains one could imagine a significant non-linearity due to the onset of dchannels. However, for the shorter chains other explanations of the experimentshave to be found.</p><p>4. Molecular bridges</p><p>Quantum...</p></li></ul>

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