Competing periodicities in fractionally filled one-dimensional bands 1 1 2 P.C. Snijders, S. Rogge, and H.H. Weitering 1Kavli Institute of NanoScience, Delft University of Technology, 2628 CJ Delft, The Netherlands 2Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN 37996, and Condensed Matter Sciences Division, 6 Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 0 (Dated: February 2, 2008) 0 We present a variable temperatureScanning Tunneling Microscopy and Spectroscopy (STM and 2 STS)studyoftheSi(553)-Auatomicchainreconstruction. Thisquasione-dimensional(1D)system n undergoes at least two charge density wave (CDW) transitions at low temperature, which can a be attributed to electronic instabilities in the fractionally-filled 1D bands of the high-symmetry J phase. Uponcooling,Si(553)-Aufirstundergoesasingle-bandPeierlsdistortion,resultinginperiod 3 doublingalong theimaged chains. This Peierls state is ultimately overcome bya competing triple- 2 period CDW, which in turn is accompanied by a ×2 periodicity in between the chains. These locked-inperiodicitiesindicatesmallchargetransferbetweenthenearlyhalf-filledandquarter-filled i] 1Dbands. Thepresenceandthemobilityofatomicscaledislocationsinthe×3CDWstateindicates c thepossibility of manipulating phase solitons carrying a (spin,charge) of (1/2,±e/3) or (0,±2e/3). s - l PACSnumbers: 73.20.At,73.20.Mf,71.10.Pm,68.37.Ef r t m AccordingtotheMermin-Wagnertheorem[1],thermo- despite theoretical efforts to understand the electronic . t a dynamic fluctuations preclude the formation of a long- structure [7, 8] the atomic structure and realspace loca- m rangeorderedbrokensymmetrystate in 1D,exceptatT tion of the surface state orbitals remains unknown. In- - = 0 K [2]. For all practical purposes, however, thermo- terestingly, the total band filling of this particular chain d dynamic phase transitions may still be possible in finite system is 4/3, i.e. corresponding to 8/3 electrons per n size1Dsystems. Furthermore,fluctuationsareinevitably surface unit cell. Two bands have a filling of 0.56 and o suppressed if the 1D chains are weakly coupled, or if the 0.51each,slightlymorethanhalf-filling. The thirdband c [ chains are coupled to a substrate [2, 3]. Prototypical hasafillingof0.27,inbetweenonequarterandone-third 1D metallic systems like the transition metal trichalco- filling. 3 v genides, organic charge transfer salts, blue bronzes, and In this Letter we present evidence for a defect medi- 4 probably all atomic Au-chain reconstructions on vicinal atedCDWtransition[9]inSi(553)-Auaccompaniedbya 7 Si substrates exhibit symmetry breaking phase transi- metalinsulatortransition. STMexperimentsrevealcom- 5 tions at finite temperatures [4, 5]. For a band filling of peting periodicities as a function of temperature which 0 1/n, the phase transition opens up a gap in the single 1 canbe mapped ontothe bandstructureofthe highsym- 5 particle excitation spectrum at wavevector kF = π/na, metry phase. STS data show a gradual gap opening at 0 andthecorrespondingbrokensymmetrystateadoptsthe low temperatures, which can be correlated with succes- t/ new periodicity of λ=π/kF =na, where a is the lattice sive gap openings in the three 1D bands. Interestingly, a parameter of the high symmetry phase [4]. phase slips are observed in the CDW condensate. These m phase slips should possess a fractional charge and a half - Fractional band fillings other than half filling pro- d integer or integer spin. The chain-length can be tuned vide an interesting subset of 1D systems which often n bymanipulatingthenumerousdefectswiththeSTMtip. o exhibit exotic physical phenomena. Depending on the This,inturn,suggeststhefeasibilityofstudyingandma- c relative magnitude of bandwidth and electron-electron nipulating fractional charges at the atomic scale. v: interaction, CDW states often compete with spin den- The Si(553)-Au structure was prepared by depositing i sity waves, Mott insulating states, or a Luttinger liquid X 0.24MLofAuatarateof0.005ML/swiththesubstrate state. Atomic-scale STM observations of surface phase r held at 920 K, followed by thermal annealing at 1120 K transitions provide important insights into the complex- a for1minuteandslowcoolingtoroomtemperatureorRT ity of symmetry breaking phenomena in reduced dimen- −1 sionality [6]. For instance, the recently reported 4×1- (1 Ks ). STM and STS experiments were performed to-8×2 phase transition in quasi-1D indium chains on in an Omicron variable temperature STM. All distances determinedinSTMimagesweremeasuredalongthefast Si(111) [6] involves a gap opening in a complex triple scan direction of the STM so as to minimize possible band Peierls system, resulting in a doubling of the pe- effects of thermal drift. riodicity along the atom chains. Another recently dis- coveredsystemwith three fractionally-filledbands is the Figure 1 shows an STM image of the surface taken at Si(553)-Au surface. Angle-resolved photoemission spec- room temperature (RT). Rather wide chains (∼0.8 nm) troscopy (ARPES) [7] revealed three metallic bands but with a spacing of 1.48 nm are observed. The chains are 2 cutby pointdefects appearingasvacanciesinbothfilled theI−V-curveisflatatzerobiasindicatingsemiconduct- state and empty state images. In the empty state im- ing behavior. We determine the size of the gap from the age,these vacanciesappearlargerthaninthe filledstate derivativeoftheI−V-curvesasdisplayedintheinsetof image, confirming the observations reported in Ref. 10. Fig.3; we infer that the excitationgapis symmetric and Note, however, that fewer defects are present as com- ∼ 150 meV wide. Thus, the condensation of this CDW pared to other work [7, 10], indicating that the defect is accompanied by a metal-insulator transition (MIT). concentration can possibly be varied by controlling the Although CDW instabilities in related surface systems annealinghistoryofthesurfacedespitepropositionsthat areoftenmanifestedbyanorder-disordertransition[12], thedefectsmightbeintrinsictothesurfaceasstabilizing the present observations are most straightforwardly in- chargedopants [7]. The insets show high resolution dual terpreted in terms of a displacive CDW transition. bias images. Clearly, the chains are composed of two rows of atoms, showing a zig-zag structure in the empty stateandaladder configurationinthefilledstate. Inthe empty state image all atom spacings are nearly equal to the bulk spacing of Si, a ∼ 3.8 ˚A resulting in bond an- glesnear60degrees. Inthefilledstateimagethespacing alongthe chainisequaltoawhereasthe spacingperpen- dicular to the chains is ∼ 4.7 ˚A. These data seem to be inconsistent with structure models that place Si honey- comb chains [11] near the step edges [7, 8] and with the single atom row structure suggested in Ref. 10. FIG. 2: (color online) (a) Empty state (1 V, 100 pA) STM imageat40Kandmagnification(b). In(b)a6×1unitcellis indicatedwithcombined×3and×2features. (c)Filledstate (-1V, 100 pA)STM image corresponding to (b). FIG. 1: (color online) (a) Empty state and (b) filled state (±0.5V,50pA) STM images taken simultaneously at RT. In- setsshowmagnifications. Thestructurein thechainsisindi- cated with dots. Upon cooling to ∼ 40 K, the zig-zag features are no longer observed. Instead, an up-down buckling with a FIG. 3: Area averaged STS curves measured at indicated ladderstructureinatripled unitcellisobserved(Fig.2), temperatures. Inset: numericalderivativesoftheSTScurves. resultingintwofeaturesofabout1.5alengthandwidths comparable to those observedat RT. The corrugationof Thecondensationscenarioinvolvingallthree1Dbands the filled state image is in anti-phase with that of the is elucidated by STM experiments at temperatures in- empty state image; at the location of the intensity max- termediate between RT and 40 K. Fig. 4 shows empty ima in the empty state image, a small dip exists in the state images measured at 70 K and at 110 K. At 70 K filledstateimage. Thisindicatesthatthesystemhascon- a vague tripled corrugation is visible in nearly all of the densed into a CDW with tripled periodicity, commensu- chains,withsignificantlyenhancedintensityneardefects. ratewiththesubstratelattice. Additionally,thefeatures In the middle of longer chains segments the bulk period in the valleys between the chains visible in the empty of3.8˚Ais stillvisiblethroughthe superimposed(vague) statearecompletelyorderedwithadoubled periodof2a, tripled periodicity. At 110 K, we observe a doubled peri- resulting in a unit cell of 6×1. odicityinthebulkofmostchains,but,againneardefects The I −V-curves and their numerical derivatives are atripledperiodicitydecayingintothechainsisobserved. shown in Fig. 3. The I −V-curve at RT exhibits a sig- Fromthesedataathighertemperatures,itisevidentthat nificantslope atzero bias,confirming the metallicity ob- theCDWpresentat40Knucleatesfromthe defectsand served in ARPES experiments [7]. In contrast, at 40 K spreads along the chains with decreasing temperature. 3 Even at RT, it is still possible to discern charge den- filling the latter to 1/3 [17]. The possible CDW precur- sity oscillations emanating from the defects. These os- sor near the chain ends at RT can also be explained by cillations have been attributed to zero-dimensional end this charge transfer: at RT a ×2 period exists locally in state effects [10]. Alternatively, the change in apparent between the chains near defects that are located on the height of the chain adjacent to a defect, i.e. a depres- chains [10]. This strongly suggests that already at RT sion over a distance of ∼ 1.5a next to the defect fol- the 0.56 filled band, located in the valleys between the lowed by a brighter segment (see Fig. 1(a):inset), and chains, is doping the chains near the defects to 1/3 fill- the non-metallic character of the chain ends established ing. With this charge transfer the total band filling of inRef. [10],arefullyconsistentwiththeinterpretationof the surface then remains constantat 4/3. Note that this aCDWprecursor,similartothatobservedinSn/Ge(111) evolutioninbandstructuremightalsoexplainthetrans- [9]. formationofthe featuresinthe emptystateSTMimage; from a zig-zag structure at RT to a ladder structure at 110 K and below. Surprisingly,the competitionbetweenperiodicitiesin- side the chains is eventually won by a ×3 CDW at the lowest temperature studied. Longer wavelength periods are progressively more difficult to fit into chains with randomly placed fixed defects. Furthermore, a 1/3 filled parabolic band has a higher DOS at the Fermi energy as compared to a 1/2 filled band, which according to a simpleBCStheoryargumentshouldresultinahigherTc for the 1/3 filled band. The magnitude of the interchain coupling for the different bands, though being fairly low as compared to other (bulk) 1D compounds [7], might provideinsightinto this seeming contradiction. It iswell FIG.4: (coloronline)Emptystate(1V,50pA)STMimages known that finite interchaincoupling reduces the transi- at 70 K and 110 K. ×3 and ×2 unit cells indicated in black tion temperature and indeed ARPES measurements in- and white, respectively. dicate a five times larger interchain coupling for the 1/3 filled band than for both of the 1/2 filled bands. This As mentioned above, the band structure of this sur- could explain why the ×3 CDW sets in at a lower tem- face measured by ARPES contains three metallic bands peraturethantheperioddoublingCDWobservedat110 [7]; two bands have a Fermi wavevectornear half-filling, K [18]. the third band contains 0.27×2=0.54 electrons adding Finite interchain coupling should be discernible in the up to a total filling of 4/3. None of the bands crosses STMimagesthroughdefinitephaserelationsbetweenpe- the Fermi energy exactly at a wave vector 2π/(n×a). riodicities in adjacent chains, provided that the temper- Nevertheless, we observe three commensurate periodici- ature is low enough. Careful analysis of the empty state ties evolving as a function of temperature: at 110 K a STM images at 40 K indeed reveals small domains of up clear ×2 period is detected in the chains, at 40 K a ×2 to three or four chains width, showing a constant phase period is observed between the chains accompanied by relation, but no long range order is detected. However, a ×3 period in the chains. Tentatively, we assign the ascanbe observedinFig.2(a, arrow)evenat40Kthere three observed periods to electronic instabilities in the are chains which do not exhibit a fully developed CDW; three metallic bands of the high symmetry phase, which the triple periodicity is not long range ordered, despite wouldlocatetheorbitalsofthe0.51and0.27filledbands the factthatafully developedtripleperiodwouldfitthe on top of the zig-zag chains and the orbitals of the 0.56 lengthofthischainsegment. Thisindicatesthatthesys- filled band in between the chains. At 110 K, the dou- temisaffectedbyasignificantamountofinterchaincou- bledperiodicity alongthe chainsoriginatesfroma CDW pling. This is further illustrated in Fig. 5(a). Two fairly transitioninthe0.51filledband;theothertwobandsre- long chains (>25 nm) are visible. Starting from the top mainmetallic. STS measurementssupportthis scenario, bothchains lacka clearcorrugation,butboth chainsde- still showing metallic behaviour at 110 K but with re- velopadefiniteup-downcorrugationtowardsthebottom. duced slope at zero bias, indicating a reduced DOS at Thewhitebarsillustrateaphaseslipof2π/3intheright the Fermi energy, see Fig. 3. ARPES at temperatures chain,immediately followedbytwosimilarphaseslipsin <100Kshowweakbackfoldingofthe0.27filledbandat the left chain. These phaseslipscannotbe explainedby the×2zoneboundary[7],alsoindicatingadoubledperi- a ×3 CDW mismatch in a finite chain segment because odicityinthisband. The×3CDWatlowertemperatures bothchainsshowaregionofsmallcorrugationatthetop canthenberationalizedbyasmallchargetransferof0.06 (andbeyond,notshown)withanill-definedphasesothe electronfromthe 0.56 filledband to the 0.27filledband, CDW is not phase locked by defects. Therefore the ori- 4 gin must be related to interchaincoupling; apparently, a consistent with ours. phaseslipinonechaincaninducephaseslipsinneighbor- ing chains via interchaincoupling. Interestingly, a phase slip (phase soliton) in a 1/3 filled band CDW carries a We thank Prof. Franz Himpsel for providing the (spin,charge) of (1/2,±e/3)or (0,±2e/3)[14]. Si(553)wafer. ThisworkissponsoredinpartbyNSFun- Fractionally charged phase slips have been studied der contractNo. DMR-0244570,the Stichting voor Fun- mostly theoretically. Only in polyacetylene, a phase slip damenteelOnderzoekderMaterieandtheRoyalNether- withafractionalchargeofe/2hasbeenobservedbycon- lands Academy of Arts and Sciences. We thank T.M. ductivity and NMR experiments [15]. To the best of Klapwijk for his stimulating support. Oak Ridge Na- our knowledge fractionally chargedphase slips in CDWs tional Laboratory is managed by UT-Battelle, LLC, for away from half filling have never been observed directly the US Department of Energy under contract No. DE- by imaging. Their presence opens up the possibility to AC-05-00OR22725. study and manipulate fractional charges at the atomic scale. They can possibly be manipulated by deliberately creating defects in the chains so as to generate a misfit for the ×3 CDW. In our STM experiments at 40 K de- [1] N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17, 1133 fects sometimes jump to different locations during imag- (1966), N.D.Mermin, Phys.Rev. 176, 250 (1968). ing. Forexample,Figs.5(b) and(c) showtwosequential [2] M.J. Rice, S. Str¨assler, Solid State Commun. 13, 1389 (∆t=180s) filled state images from the same area. The (1973), E. Pytte,Phys. Rev.B 10, 2039 (1974). white circle and the arrow show a group of three defects [3] M.Lee,E.A.Kim,J.S.Lim,M.Y.Choi,Phys.Rev.B69, which has moved two chains to the left. This behavior 115117(2004),N.Shannon,R.Joynt,J.Phys.: Condens. Matter 8, 10493 (1996). suggests that these defects consist of Si adatoms [7, 8], [4] G. Gru¨ner, A. Zettl, Physics Reports 119, 117 (1985). which have been relocated by tip induced migration. [5] H.W. Yeom et al.,Phys. Rev.B 72, 035323 (2005). [6] H.W. Yeom, K. Horikoshi, H.M. Zhang, K. Ono, R.I.G. Uhrberg, Phys.Rev.B 65, 241307(R) (2002), S.J. Park, H.W. Yeom, S.H.Min, D.H.Park, I.W. Lyo, Phys. Rev. Lett.93,106402(2004),G.Lee,J.Guo,E.W.Plummer, Phys.Rev.Lett.95,116103(2005),H.Morikawa,I.Mat- suda, S. Hasegawa, Phys. Rev. B 70, 085412 (2004), J. Guo,G.Lee,E.W.Plummer,PhysRev.Lett.95,046102 (2005). [7] J.N. Crain et al., Phys. Rev. Lett. 90, 176805 (2003), J.N. Crain et al., Phys.Rev.B. 69, 125401 (2004). [8] S. Riikonen, D. Sanchez-Portal, Nanotechnology 16, S218 (2005). FIG. 5: (color online) STM images at 40K. (a)Empty state [9] H.H. Weitering et al.,Science 285, 2107 (1999). (1V,100pA)imageshowingphaseslipsinthe×3CDW.(b) [10] J.N. Crain, D.T. Pierce, Science 307, 703 (2005). and (c): filled state (-1 V, 50 pA) images showing relocation [11] S.C. Erwin, H.H. Weitering, Phys. Rev. Lett. 81, 2296 ofdefects. Blackcircles: markers. Arrow: olddefectposition. (1998). White circle: new defect position. [12] J. Avila et al.,Phys. Rev.Lett. 82, 442 (1999). [13] J.R. Schrieffer, Nobel Symposium 24 (Academic, New In conclusion, we have presented an STM and STS York and London,1973), p.142. [14] W.P.Su,J.R.Schrieffer,Phys.Rev.Lett.46,738(1981), study of a chain structure with fractional band fillings. C. Kuhn,J. Phys.Condens. Matt. 7, 6221 (1995). Competing periodicities are observed as a function of [15] W.P. Su, J.R. Schrieffer, A.J Heeger, Phys. Rev. B 22, temperatureresultinginadefectmediatedCDWat40K. 2099 (1980). Theresultscanbemappedontothebandstructureofthe [16] J.R. Ahnet al., Phys.Rev.Lett. 95, 196402 (2005) high symmetry phase. The presence and mobility of the [17] According to Ref. [13], a commensurate CDW in a sys- chain dislocations in the CDW state indicates the possi- temwithincommensurateFermiwave-vectorscanbeob- bility of studying and possibly manipulating fractionally tainedbylockingthewavelengthoftheCDWtothelat- tice so as to be commensurate. However, then it would charged solitons with an STM tip. The availability of beexpectedthatthe0.27 filledbandwouldlock toa×4 other vicinal Si-Au chain structures with tunable inter- period corresponding to a filling of 0.25. chaincoupling[7]wouldprovidea promisingplayground [18] An alternative explanation is that the relatively large for 1D physics, accessible in realspace. Note added: Af- charge transfer into the 0.27 filled band induces signif- ter the submission of our manuscript, we became aware icantmorelatticestrain,therebyloweringitsTc ascom- of the paper by Ahn et al. [16]. Their observations are pared to the×2 CDW.