Electronic transport at finite voltages in free-standing gold atomic chains
of up to 7 atoms in length is studied at low temperatures using a scanning
tunneling microscope (STM). The conductance vs voltage curves show that
transport in these single-mode ballistic atomic wires is non-dissipative up to
a finite voltage threshold of the order of several mV. The onset of dissipation
and resistance within the wire corresponds to the excitation of the atomic
vibrations by the electrons traversing the wire and is very sensitive to
strain.Comment: Revtex4, 4 pages, 3 fig

A. I. Yanson

A. M. Duif

B. Ludolph

C. Untiedt

Carlos Untiedt

D. Sánchez-Portal

E. G. Emberly

G. Rubio-Bollinger

Gabino Rubio-Bollinger

H. Onishi

I. K. Yanson

J. M. Ziman

M. Brandbyge

M. Büttiker

M. Okamoto

Nicolás Agraït

R. de Picciotto

R. Landauer

Sebastián Vieira

Z. Yao

English

arXiv

Crossref

Physical Review Letters

Onset of Energy Dissipation in Ballistic Atomic Wires

Electronic transport at finite voltages in free-standing gold atomic chains of up to seven atoms in length is studied at low temperatures using a scanning tunneling microscope. The conductance vs voltage curves show that transport in these single-mode ballistic atomic wires is nondissipative up to a finite voltage threshold of the order of several mV. The onset of dissipation and resistance within the wire corresponds to the excitation of the atomic vibrations by the electrons traversing the wire and is very sensitive to strain.This work has been supported by CICyT Grant No. PB97-0068

Agraït de la Puente, Nicolás

Untiedt, Carlos

Rubio Bollinger, Gabino

Vieira Díaz, Sebastián

Repositorio Institucional de la Universidad de Alicante

VOLUME 88, NUMBER 21 P H Y S I C A L R E V I E W L E T T E R S 27 MAY 2002216803-1Onset of Energy Dissipation in Ballistic Atomic WiresNicolás Agraït,* Carlos Untiedt,† Gabino Rubio-Bollinger, and Sebastián VieiraLaboratorio de Bajas Temperaturas, Departamento de Física de la Materia Condensada C-III,and Instituto Universitario de Ciencia de Materiales “Nicolás Cabrera,”Universidad Autónoma de Madrid, E-28049 Madrid, Spain(Received 29 October 2001; published 13 May 2002)Electronic transport at finite voltages in free-standing gold atomic chains of up to seven atoms inlength is studied at low temperatures using a scanning tunneling microscope. The conductance vs voltagecurves show that transport in these single-mode ballistic atomic wires is nondissipative up to a finitevoltage threshold of the order of several mV. The onset of dissipation and resistance within the wirecorresponds to the excitation of the atomic vibrations by the electrons traversing the wire and is verysensitive to strain.DOI: 10.1103/PhysRevLett.88.216803 PACS numbers: 73.63.Nm, 68.37.Ef, 73.40.JnThe trend toward miniaturization in electronics will soonlead to devices of nanometer scale in which quantum ef-fects become relevant. The ultimate quantum conductor isa perfect one-dimensional wire, such as an atomic chain[1,2] or semiconducting heterostructure [3]. In these wiresthe electrons are ballistic since there are no defects to in-hibit resistance-free currents [3]. The limiting factor in thecurrent-carrying capacity of a wire is dissipation, whichresults in heating. Two mechanisms contribute to the re-sistance of a metallic wire: elastic scattering with defectsand impurities and inelastic scattering with the lattice vi-brations [4]. In the absence of scattering, electrons canpropagate freely and transport is said to be ballistic. Thissituation is possible in the nanoscale where the mean-freepath of electrons can be much longer than the length of thedevice.The two-terminal zero-bias resistance of a single-modeballistic wire is the resistance quantum h2e2. This re-sistance is entirely associated with the connections of thewire to the electrodes [5], being the intrinsic resistance ofthe wire zero, as recently demonstrated in quantum wiresfabricated from GaAsAlGaAs heterostructures [3], andin agreement with Landauer framework [6,7]. Within thisframework, the applied voltage serves to unbalance thechemical potentials for propagating electrons in each di-rection and drops entirely at the contacts and not within thewire. The Joule dissipation associated with this resistanceis assumed to take place far away from the contact (at aninelastic relaxation length), where electrons and holes relaxto the Fermi level of the electrodes. This picture is correctfor bias voltages close to zero, which implies vanishinglysmall currents (note that the resistance-free currents in theexperiment of Ref. [3] were smaller than 1 nA).In this Letter we study transport at finite voltages andthe mechanism of dissipation in ballistic wires. Our ex-periments are performed in freely suspended gold atomicwires of up to seven atoms in length, fabricated using alow-temperature scanning tunneling microscope (STM)[1,2]. Very recently the forces and conductance have beenmeasured simultaneously [8] during the process of chain0031-90070288(21)216803(4)$20.00formation giving insight into the formation mechanisms.The mechanical and electronic properties of these metallicnanostructures are of great interest not only from the pointof view of the applications but also from a fundamentalpoint of view, since the system has few atoms and shouldbe amenable to detailed modeling.Atomic wires of gold are fabricated at low temperatures(4.2 K), using an STM. Fabrication of an atomic wire is asfollows [1]: a metallic contact is formed between a tip anda substrate of an STM, both made out of Au, with 99.99%purity. Elongation of the contact results in a decrease in itssize. In the final stage a one-atom contact is formed, andas we continue elongating there is a certain probability thatan atomic chain forms [1]. The length of the wire can beestimated from the length of the last plateau before rupture,whose conductance is approximately one in units of 2e2h.The atomic wires are very stable at low temperature andthe measured curves are completely reproducible as longas the tip position is not changed. Typically an experimenton a given atomic wire takes about one-half hour, and endswhen the wire breaks as a result of further elongation. Thedifferential conductance G of the wires as a function ofvoltage is measured using a lock-in technique, with a smallmodulation of 1 mV. The derivative of the differentialconductance dGdV is calculated numerically.Experimentally, it is observed [1] that the zero-bias con-ductance of Au wires of up to seven atoms in length is closeto G0  2e2h, the quantum conductance unit, indepen-dently of their length, reflecting the fact that gold wireshave a single almost completely open quantum channel, asconfirmed by theoretical calculations [9–11]. This agreeswith Picciotto et al. [3], showing that the resistance is atthe contacts, not within the chain. These atomic wires donot show Ohmic behavior: the conductance is voltage de-pendent. We measure the differential conductance G dIdV of atomic wires of different lengths (from one toseven atoms). Typical differential conductance curves forshort and long atomic wires are shown in Figs. 1(b)–1(d).The differential conductance G shows a hump at zerobias, dropping about 1% in the range (20 mV). Often the© 2002 The American Physical Society 216803-1VOLUME 88, NUMBER 21 P H Y S I C A L R E V I E W L E T T E R S 27 MAY 20020.890.900.910.92 cbshort wire (S)aG(2e2 /h)0.970.980.991.001.01short wire (M)-30 -20 -10 0 10 20 30-0.8-0.40.00.40.8G0-1dG/dV(V-1 )bias voltage (mV)-30 -20 -10 0 10 20 30-0.8-0.40.00.40.8S3S3S2S2S1S1bias voltage (mV)0 50121 2 3ruptureruptureshort wirelong wire LMSconductance(2e2 /h)displacement (Å)0.970.980.991.001.01L2L1L4L3L2L1G(2e2 /h)-30 -20 -10 0 10 20 30-3-2-10123L4L3long wire (L)dG0-1dG/dV(V-1 )bias voltage (mV)0 5 10 15 20 25M3M3M2M2M1M11 2 31234FIG. 1. (a) Short and long atomic wire, 4 Å long and 22 Å long, respectively. At the point of rupture, the atomic wire collapsesand the conductance, which is negligible in the scale of this figure, corresponds to the tunneling regime. To reestablish contact, theelectrodes must reapproach by a distance of the order of the chain length. Panels (b), (c), and (d) show the differential conductanceand its derivative at points S, M , and L, respectively, marked by the arrows. The various curves in (b), (c), and (d) were acquiredat intervals of 0.3, 0.3, and 0.5 Å, respectively. Note that the vertical scales are identical in these panels.differential conductance curves show asymmetries and os-cillations due to elastic scattering which results in interfer-ence effects [12,13].These symmetric drops in the conductance are charac-teristic of inelastic scattering of electrons, and the range ofvoltages is typical of phonons. At cryogenic temperatures,the differential conductance of larger ballistic metallic con-tacts (100–1000 atoms in cross section) is also voltagedependent, and has been used to obtain energy-resolvedinformation on the interaction of electrons with phononsand other elementary excitations. This well-establishedtechnique is known as point-contact (PC) spectroscopy[14–16]. When a voltage drop V is applied to a metalliccontact, whose radius is smaller than the electron mean-free path, electrons are injected into the higher voltageelectrode with excess energies of up to eV . These electronshave a finite probability of exciting a vibrational mode ofthe lattice, i.e., emitting a phonon. At these low tempera-tures the probability of phonon absorption is very low be-cause the equilibrium phonon population is almost zero.The resulting dGdV vs voltage curves, or PC spectra, areproportional to the phonon density of states (DOS) timesthe electron-phonon coupling strength. The spectra scalewith the zero-bias conductance as ~ G320 , reflecting thefact that only electrons that are scattered close to the con-tact, i.e., within a distance to the contact of the order of thecontact radius, have a finite probability of being backscat-tered and, consequently, of being detected as a reductionin conductance. The standard spectra for Au have peaks at10 and 18 mV, corresponding to the maxima in the trans-216803-2verse and longitudinal phonon DOS at 10 and 18 meV,respectively. The transverse peak being stronger than thelongitudinal peak.In contrast to the PC spectra of larger ballistic contacts,the spectra of atomic wires are very sensitive to the atomicconfiguration at the contact. Figures 1(b) and 1(c) showthe differential conductance and spectra at two differentsituations during the elongation of a short atomic wire,positions labeled S and M in Fig. 1(a), respectively. At Sthe atomic wire is likely to be just one atom long, while atM the contact has been further stretched about 3 Å that is,the wire is about two atoms long. The evident broadeningof the conductance hump is typically observed for atomicwires longer than one atom. The signal is about three timeslarger than that given by the semiclassical theory of PCspectroscopy [15,17]. Figure 1(d) corresponds to the longwire (about seven atoms long) in Fig. 1(a). For this longwire the conductance drop takes place quite sharply, whichresults in a sharp peak in the spectra. This dependence ofthe spectra on the length of the wire indicates that mostof the measured signal comes from processes occurringwithin the wire itself.The observed spectra for the longer atomic wires are asignature of their one dimensionality. In an infinite one-dimensional conductor, momentum is conserved, and, con-sequently, electrons can only excite longitudinal vibrationsof the atomic chain whose wave number is twice theFermi wave number kF , hence only one phonon mode willshow in the spectra. For a linear atomic chain with inter-atomic distance a and one conduction electron per atom,216803-2VOLUME 88, NUMBER 21 P H Y S I C A L R E V I E W L E T T E R S 27 MAY 2002kF equals p2a, and, consequently, electrons will onlyexcite phonons of wavelength 2a, that is, zone-boundaryphonons. In this process an electron dissipates its energy,losing one quantum of vibrational energy h¯v2kF and beingbackscattered. Here, v2kF is the frequency of the excitedvibrational mode. In a ballistic conductor, this phononemission process will be possible only for voltages Vlarger than Vph  h¯v2kFe, since the chemical potentialsfor right-going electrons and for left-going electrons areunbalanced by eV . Consequently, the onset of dissipationis marked by a sudden decrease in the conductance, sincethe backscattered electrons do not contribute to the cur-rent. The position of the peak in the spectra Vph gives thefrequency of the 2kF phonon, and its height Aph, whichis related to the conductance drop, is proportional to theprobability of the phonon emission process. The magni-tude of the conductance drop (about 1% for a chain of20 Å in length) is consistent with an inelastic mean-freepath of about 2000 Å in an infinite wire, which is rea-sonable for a metal at low temperatures. Experimentally,the sharpness of the conductance drop [see Fig. 1(d)] islimited by thermal smearing (2 meV) and by the finite-ness of the atomic wires. A linear monoatomic chain ofN atoms will have N longitudinal vibrational modes. Foran atomic chain of length L coupled to rigid electrodes,the wavelengths of the different modes n are simply givenby ln  2Ln. However, since the atomic chain is me-chanically coupled to the bulk (the electrodes), the discretemodes of the chain will broaden into resonances, whosewidth will depend on the mechanical coupling betweenchain and electrodes. In addition, momentum conservationin the electron-phonon interaction will not hold strictly ina finite system, and, as a consequence, in a short atomicchain the electrons will be able to interact with phonons ofwavelengths different from 2a. This will lead not only toa smearing in the spectra but also to the possibility of ob-serving other vibrational modes, especially in the shortestchains.Experimentally, it is observed that the position and am-plitude of the peak in the spectra of a given atomic wire arevery sensitive to its state of strain. As shown in Fig. 1(d),stretching the wire results in a decrease of the frequencyof the phonon and an increase in the emission probability.This phonon softening indicates that the elastic constant ofan atomic chain decreases as it is stretched. The increasein the emission probability indicates an enhancement ofthe electron-phonon interaction. In Fig. 2, we have plottedthe position of the peak in the spectra and its amplitude formany different atomic wires. The emission probability in-creases with the length of the wire [18], and the variationsdue to stretching are much larger than for short wires.An atomic wire can be stretched elastically only a lim-ited distance (1 Å) before breaking or changing to anew configuration. These configurational changes result instress relaxations correlated to abrupt conductance jumps[8], whose magnitude is much smaller than a conductance216803-30.00.71.42.12.8aCBAAph(V-1)0 2 4 6 8 10 12 14 16 18 20 220510152025 bA CBVph(meV)length (Å)FIG. 2. (a) Magnitude Aph and (b) position Vph of the phononpeak in the PC spectrum as a function of length chain. For clar-ity, we present only 22 representative chains out of more than100 studied. Each chain is represented by a different symbol.The chains labeled A and B are the short and long wires, re-spectively, of Fig. 1; C is the wire in Fig. 3. The length of thechain is estimated from the length of the last plateau.quantum 2e2h. Some of the stress relaxations correspondto the incorporation of an extra atom into the atomic wire,while other relaxations come from atomic rearrangementsoccurring in the electrode region close to the wire [8]. InFigs. 3(b)–3(d), we show the evolution of the conduc-tance, and the amplitude and position (in energy) of thephonon peak as the wire is elongated along 3 Å before18 19 20121416 daV ph (meV)length (Å)1.21.62.0 cA ph ( V  -1  )0.961.00 brelaxationsconductance (2e2 /h)-5 0 5 10 15 200.00.20.40.60.81.01.21.41.61.82.0chain lengthretraction lengthconductance(2e2 /h)length (Å)FIG. 3. (a) Evolution of the conductance for a 20-Å-longatomic wire. (b) Zoom of the last part of this evolution show-ing abrupt jumps in the conductance corresponding to forcerelaxations due to atomic rearrangements between the elasticstages. (c) and (d) show the magnitude Aph and position Vph,respectively, of the phonon peak in the PC spectra.216803-3VOLUME 88, NUMBER 21 P H Y S I C A L R E V I E W L E T T E R S 27 MAY 2002chain rupture. The final length of the wire was 21 Å [seeFig. 3(a)]. Note that jumps in the amplitude and positionof the phonon peak in the spectra are correlated to con-ductance jumps and, consequently, to stress relaxations.The observed phonon softening with elastic deformationis consistent with the results of the ab initio calculationsof Sánchez-Portal et al. [19] for linear and zigzag atomicwires. Our results are compatible with both types of wires.Detailed theoretical calculations would be necessary fora quantitative understanding of the electron-phonon inter-action and its enhancement with elastic strain in metallicatomic wires.As we have seen, dissipation in one-dimensional atomicwires occurs through the process of phonon emission byhot electrons. In contrast to what happens in a three-dimensional geometry, the hot electrons can excite a singlevibrational mode of the atoms of the wire, and this re-quires electrons with sufficient energy. As a consequence,for voltages below Vph, no dissipation occurs within theatomic wire. The maximum dissipationless current that anatomic wire can carry is then G0Vph  1 mA, which isan enormous current density 107 Amm2. For voltagesabove Vph, the wire progressively heats up. For a givenvoltage a balance is established among the energy re-leased by the electrons, the energy absorbed by the elec-trons (phonon absorption), and the energy lost by thermalconduction to the electrodes. In our experiments, atomicchains could sustain voltages of up to 500 mV (note thatin the same conditions an atomic contact could stand2000 mV). Phonon emission by hot electrons in a one-dimensional conductor was investigated previously in thecontext of carbon nanotubes [20]. In this case, the muchlonger length of the wires leads to qualitatively differentresults.In summary, we have studied the voltage dependence ofthe conductance of metallic atomic wires at low tempera-tures, showing that inelastic scattering of electrons sets inat a finite voltage due to the excitation of the vibrations ofthe ions of the atomic chain. This well-defined thresholdfor dissipation is characteristic of the electron-phonon in-teraction in one-dimensional systems. We observe that themechanical tensioning of the atomic chain results in bondsoftening, which is reflected in a decrease of the phonon216803-4frequency and a dramatic enhancement of the electron-phonon interaction.This work has been supported by CICyT GrantNo. PB97-0068.*Electronic address: nicolas.agrait@uam.es†Present address: Kamerlingh Onnes Laboratorium, Postbus9504, NL-2300 RA Leiden, The Netherlands.[1] A. I. Yanson et al., Nature (London) 395, 783 (1998).[2] H. Onishi, Y. Kondo, and K. Takayanagi, Nature (London)395, 780 (1998).[3] R. de Picciotto et al., Nature (London) 51, 411 (2001).[4] J. M. Ziman, Electrons and Phonons (Oxford University,Oxford, 1960).[5] M. Büttiker, Phys. Rev. Lett. 57, 1761 (1986).[6] R. Landauer, IBM J. Res. Dev. 1, 223 (1957).[7] R. Landauer, Philos. Mag. 21, 863 (1970).[8] G. Rubio-Bollinger, S. R. Bahn, N. Agraït, K. W. Jacobsen,and S. Vieira, Phys. Rev. Lett. 87, 026101 (2001).[9] E. G. Emberly and G. Kirczenow, Phys. Rev. B 60, 6028(1999).[10] M. Okamoto and K. Takayanagi, Phys. Rev. B 60, 7808(1999).[11] M. Brandbyge et al., Phys. Rev. B 60, 17 064 (1999).[12] C. Untiedt, G. Rubio-Bollinger, S. Vieira, and N. Agraït,Phys. Rev. B 62, 9962 (2000).[13] B. Ludolph et al., Phys. Rev. Lett. 82, 1530 (1999).[14] I. K. Yanson, Zh. Eksp. Teor. Fiz. 66, 1035 (1974) [Sov.Phys. JETP 39, 506 (1974)].[15] A. M. Duif et al., J. Phys. Condens. Matter 1, 3157 (1989).[16] I. K. Yanson and O. I. Shklyarevskii, Sov. J. Low Temp.Phys. 12, 509 (1986).[17] This value is given only as a reference, since the semiclas-sical theory of PC cannot be applied to a one-atom contact.Note that, according to the theory of PC spectroscopy [16],for a one-atom contact of Au, the (Sharvin) conductancewould be 50% smaller than a conductance unit, and the ef-fective volume in which the phonons are generated wouldbe smaller than the atomic volume.[18] The theory of PC spectroscopy gives a linear dependenceon length of the effective volume in which the electronsare scattered in the case of a clean channel [16].[19] D. Sánchez-Portal et al., Phys. Rev. Lett. 83, 3884 (1999).[20] Z. Yao et al., Phys. Rev. Lett. 84, 2941 (2000).216803-4

Onset of energy dissipation in ballistic atomic wires

Onset of dissipation in ballistic atomic wires

Onset of dissipation in ballistic atomic wires

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