Nonlinear lattice dynamics as a basis for enhanced superconductivity in YBa 2 Cu 3 O 6.5

Transcription

1 Nonlinear lattice dynamics as a basis for enhanced superconductivity in YBa 2 Cu 3 O 6.5 R.Mankowsky 1*,A.Subedi 2*,M.Först 1,S.O.Mariager 3,M.Chollet 4,H.T.Lemke 4,J.S. Robinson 4,J.M.Glownia 4,M.P.Minitti 4,A.Frano 5,M.Fechner 6,N.A.Spaldin 6,T.Loew 5,B. Keimer 5,A.Georges 2,7,8 anda.cavalleri 1,9,1 *"These"authors"contributed"equally"to"this"work." 1"Max"Planck"Institute"for"the"Structure"and"Dynamics"of"Matter,"22761"Hamburg,"Germany" 2"Centre"de"Physique"Théorique,"École"Polytechnique,"CNRS,"91128"Palaiseau"Cedex,"France" 3"Swiss"Light"Source,"Paul"Scherrer"Institut,"5232"Villigen,"Switzerland" 4"Linac"Coherent"Light"Source,"SLAC"National"Accelerator"Laboratory,"Menlo"Park"9425,"California,"USA" 5 Max"Planck"Institute"for"Solid"State"Research,"7569"Stuttgart,"Germany "" 6"Eidgenössische+Technische+Hochschule+Zürich,+Materials+Theory,+893"Zürich,"Switzerland"" 7"Collège"de"France,"11"place"Marcelin"Berthelot,"755"Paris,"France" 8"Département"de"Physique"de"la"Matière"Condensée"MaNEP,"Université"de"Genève,"1211"Genève,"Switzerland" 9"Department"of"Physics,"Oxford"University,"Clarendon"Laboratory,"Oxford"OX1"3PU,"UK" 1"Center"for"FreebElectron"Laser"Science"CFEL"and"University"of"Hamburg,"22761"Hamburg,"Germany" " THz$frequency optical pulses can resonantly drive selected vibrational modes insolidsanddeformtheircrystalstructure 1,2,3.Incomplexoxides,thismethodhasbeenused to melt electronic orders 4,5,6, drive insulator to metal transitions 7,8 or inducesuperconductivity 9.Strikingly,coherentinterlayertransportstronglyreminiscentofsuperconductivity can be transiently induced up to room temperature in YBa2Cu3O6+x 1,11. By combining femtosecond X$ray diffraction and ab# initio densityfunctionaltheorycalculations,wedetermineherethecrystalstructureofthisexoticnon$equilibrium state. We find that nonlinear lattice excitation in normal$state YBa2Cu3O6+xat1Kcausesastaggereddilation/contractionoftheCu$O2intra/inter$ bilayer distances, accompanied by anisotropic changes in the in$plane O$Cu$O bondbuckling. Density functional theory calculations indicate that these motions cause 1

2 dramaticchangesintheelectronicstructure.amongstthese,theenhancementinthe dx2$y2characterofthein$planeelectronicstructureislikelytofavorsuperconductivity. Theresponseofacrystallatticetostrong,resonantexcitationofaninfraredWactivephonon mode can be described by separating the crystal Hamiltonian into its linear and nonlinear termsh=hlin+hnl.thelinearterm "# = " " describesharmonicoscillationsaboutthe equilibriumatomicpositions,withωirdenotingthefrequencyandqirthenormalcoordinate oftheinfraredwactivemode.inthelimitoflowestorder(cubic)couplingtoothermodeswith generic coordinate QR, the nonlinear term can be written as " = " " " ". In this expression, a12and a21 are anharmonic coupling constants. (See online MethodssectionandExtendedDataFigures1and2fordetailsonnextordercoupling).Fora centrosymmetriccrystallikeyba2cu3o6.5, " iszeroasqirisoddinsymmetrywhile is even.furthermore,as " isofevensymmetry " isnonzeroonlyifqrisevenandhence Ramanactive. Thus,thetotalHamiltonianreducesto = " " + " ",whichpredictsa shiftinthepotentialenergyminimumalongqrforanyfinitedistortion " (seefigure1a). Correspondingly, for a periodically driven QIR mode, the dynamics are described by the coupledequationsofmotion " + 2 " " + " " = + 2 " " and = " ". Figure 1b pictorially represents these dynamics. Upon resonant midwinfrared excitation of QIR,aunidirectionalforceisexertedalongthenormalcoordinateQR,whichisdisplacedbya magnitude proportional to ". This effect remains sizeable only as long as QIR oscillates coherently,typicallyforseveralpicoseconds. 2

3 We next discuss the specific case of YBa2Cu3O6.5,whichcrystallizes in a centrosymmetric orthorhombic unit cell with D2h symmetry, comprising bilayersof conducting CuO2 planes separatedbyaninsulatinglayercontainingyttriumatomsandcuwochainsthatcontrolthe doping of the planes (Fig. 2a). The YBa2Cu3O6.5 sample contained both oxygen rich and oxygen deficient chains, and exhibited shortwrange OrthoWII ordering of the vacancies(fig. 2b).NotealsothattheinWplaneOWCuWObondsarebuckled(Fig.2c). In our experiments, midwinfrared pump pulses of ~3 femtoseconds (fs) durationwere focusedtoamaximumfluenceof~4mj/cm 2 andapeakelectricfieldof~3mv/cm.these pulseswerepolarizedalongthecaxisofyba2cu3o6.5andtunedtoresonancewiththesame 67cm W1 frequency(~15µm,83mev)b1uinfraredwactivemode 12 (seefigure2a)thatwas previously shown by means of timewresolved THz spectroscopy to enhance interlayer superconductingcoupling 1,11. In analyzing the nonlinear lattice dynamics caused by this excitation, we note that the nonlinearterm isnonzeroonlyifqrisofagsymmetry,becausethesquareofthe irreduciblerepresentationofb1uisag.thus,onlyagmodescancoupletotheopticallydriven B1umotionofFigure2a.YBa2Cu3O6.5has72opticalphononmodes,ofwhich33areRaman active.thesecanbefurtherdividedinto22bgmodes,whichbreakinwplanesymmetry,and 11Agmodes,whichpreservethesymmetryoftheunitcell(seeExtendedDataFigure3).The geometries of these 11 Ag modes and their coupling strength to the driven B1u mode were computed using first principles density functional theory calculations within the local densityapproximation.at3mv/cmfieldstrengthofthemidwinfraredpumppulse,weexpect a peakamplitude for theb1u motion corresponding to 2.2pm increase in apical oxygenwcu distance,whichwasusedasabasisto calculate energy potentials of the Ag modes for a frozendistortionofthismagnitude(seefigure3a).onlyfourphononmodesag(15,21,29, 3

4 74) were found to strongly couple to the driven B1u mode, all involving a concerted distortion of the apical oxygen atoms towards the CuO2 plane and an increase in CuWO buckling (Figure 3b). The calculations also predict weak coupling to three further modes Ag(52,53,61),consistingofbreathingmotionoftheoxygenatomsintheplane(Fig.3c).The remainingfourmodesag(14,39,53,65)donotcoupletotheb1umode(seeextendeddata Table1fordetails). To experimentally determine the absolute amplitude of these distortions in the conditions relevant for enhanced superconductivity 1,11, we measured time resolved xwray diffraction using5fs,6.7kevpulsesfromthelclsfreeelectronlaser,whichwassynchronizedtothe optical laser that generated the midwinfrared pump pulses. Changes in diffraction intensity wererecordedforfourbraggpeaksatabasetemperatureof1k,abovetheequilibrium transitiontemperaturetc=52k.thesepeakswereobservedtoeitherincreaseordecrease promptly after excitation (see Figure 4) and to relax within the same timescale as the changesinthethzopticalproperties 1,11.ForeachBraggreflectionwecalculatedchangesin diffraction as function of B1u amplitude considering a displacement of only the four dominantramanmodesag(15,21,29,74)orall11modesoffigure3,takingintoaccount the relative coupling strengths. We simultaneously fitted the four experimental diffraction curvesusingonlytwofreeparameters:theamplitudeofthedirectlydrivenb1umotionand the relative contributions of two exponential relaxation components (τ1 = 1 ps, τ2 = 7 ps) extracted from the THz measurements 1,11. Very similar results were found when consideringonlythefourdominantmodesorallmodes(seegreenandredfittingcurvesin Figure4). The transient lattice structure determined from these fits involves the following elements. Firstly, we observe a decrease in the distance between the apical oxygen and the copper 4

5 atomsofthesuperconductingplanes(figure5).thismotionisfarsmallerandoppositein sign than the difference in the static apical oxygen positions between LaW and HgWbased cuprates,forwhichtcincreasesatequilibrium 13.Therefore,thetransientenhancementof superconducting transport cannot be explained by this analogy. More suggestively, the copperatomsaredrivenawayfromoneanotherwithinthebilayersandtowardoneanother betweendifferentbilayers.thisstaggeredmotionisofapproximately.63%(seefigure5a) and qualitatively follows the decrease in intrawbilayer tunneling and the enhancement of interwbilayer tunneling 1,11. Finally, an anisotropic.32 increase in the inwplane OWCuWO buckling(differentalongaandbaxes)isobserved(seeextendeddatatable2). AlthoughtheJosephsoncouplinginlayeredcupratesinvolvesmanymicroscopicparameters thatarenotkeptintoaccounthere 14,15,16,DFTcalculationsinthedistortedcrystalstructure wereusedtoassessthesalienteffectsontheelectronicproperties (see Extended Data Figures 4 to 6). Our calculations predict an energy lowering of the oxygen deficient chain bandsbyfewtensofmev.becauseatequilibriumthesebandsareveryclosetothefermi level, this small shift strongly reduces the hybridization of the chains with the plane CuW orbital,leadingtoadftfermisurfacewithastrongercu characterandhigherhole doping. This effect is likely to favor superconductivity. We also speculate that as the DFT Fermisurfacechangesshapeandsize,itisquitepossiblethatthatchargedensitywaveorder may also be destabilized 17,18,19, which would also aid superconductivity. The present calculations will serve as a starting point for a full manywbody treatment, to be complemented by more exhaustive experimental characterizations of the transient electronicstructure. Moregenerally,weseenonlinearphononicsasanewtoolfordynamicalmaterialsdiscovery, withopticallatticecontrolprovidingaperturbationwwanalogoustostrain,fieldsorpressure 5

6 WW thatcaninduceexoticcollectiveelectronicbehaviors. KnowledgeofthenonWequilibrium atomic structure byultrafastxwray crystallography, which we provide for the first time in this work, is the essential next step towards engineering these induced behaviors at equilibrium. ReferencesMainText 1 Först,M.etal.Nonlinearphononicsasanultrafastroutetolatticecontrol,Nature"Physics7, 854W856(211). 2 Först, M. et al. Displacive lattice excitation through nonlinear phononics viewed by femtosecondxwraydiffraction,solid"state"communications169,24 27(213) 3 Subedi, A., Cavalleri, A. & Georges, A. Theory of nonlinear phononics for coherent light controlofsolids,physical"review"b89,2231(214) 4 Tobey, R.I. et al. Ultrafast Electronic Phase Transition in La1/2Sr3/2MnO4 by Coherent Vibrational Excitation: Evidence for Nonthermal Melting of Orbital Order, Physical" Review" Letters11,19744(28) 5 Först,M.etal.Drivingmagneticorderinamanganitebyultrafastlatticeexcitation,Physical" Review"B84,24114(211) 6 Först,M.etal.MeltingofChargeStripesinVibrationallyDrivenLa1.875Ba.125CuO4: AssessingtheRespectiveRolesofElectronicandLatticeOrderinFrustrated Superconductors,Physical"Review"Letters112,1572(214) 6

7 7 Caviglia,A.D.etal.UltrafastStrainEngineeringinComplexOxideHeterostructures,Physical" Review"Letters18,13681(212) 8 Rini,M.etal.ControloftheelectronicphaseofamanganitebymodeWselectivevibrational excitation,nature449,72w74(27) 9 Fausti,D.etal.LightWInducedSuperconductivityinaStripeWOrderedCuprate,Science331, 189W191(211) 1 Kaiser, S. et al. Optically induced coherent transport far above Tc in underdoped YBa2Cu3O6+δ,Physical"Review"B89,184516(214) 11 Hu, W. et al. Optically enhanced coherent transport in YBa2Cu3O6.5 by ultrafast redistributionofinterlayercoupling,nature"materials13,75w711(214) 12 Homes,C.C.etal.OpticalpropertiesalongthecWaxisofYBa2Cu3O6+x,forx=.5W>.95 Evolutionofthepseudogap,Physica"C254,265W28(1995).(1995). 13 Pavarini,E.etal.BandWStructureTrendinHoleWDopedCupratesandCorrelationwithTcmax Physical"Review"Letters87,473(211) 14 Shah,N.&Millis,A.J.Superconductivity,phasefluctuationsandthecWaxisconductivityin biwlayerhightemperaturesuperconductors."physical"review"b65,2456(21) 15 Chaloupka,J.,Bernhard,C.&Munzar,D.MicroscopicgaugeinvarianttheoryofthecWaxis infraredresponseofbiwlayercupratesuperconductorsandtheoriginofthe superconductivitywinducedabsorptionbandsphysical"review"b79,184513(29) 7

8 16 Yu,L.etal.EvidenceforTwoSeparateEnergyGapsinUnderdopedHighWTemperature CuprateSuperconductorsfromBroadbandInfraredEllipsometryPhysical"Review"Letters 1,1774(28) 17 Ghiringhelli,G.etal.LongWRangeIncommensurateChargeFluctuationsin (Y,Nd)Ba2Cu3O6+x,Science337,821W825(212). 18 BlancoWCanosa, S. et al. Resonant XWray Scattering Study of Charge Density Wave CorrelationsinYBa2Cu3O6+x.Physical"Review"B9,54513(214) 19 Chang,J.etal.Directobservationofcompetitionbetweensuperconductivityandcharge densitywaveorderinyba2cu3o6.67,nature"physics8,871w876(212) 8

9 A.C. conceived this project. R.M. and M.F. lead the diffraction experiment, supported by S.O.M., M.C., H.T.L., J.S.R., J.M.G., M.P.M., and A.F.. R.M. and A.S. analyzed the data. A.S. performed the DFT calculations, with support from A.G., M.F. and N.A.S.. The sample was grown by T.L and B.K.. R.M. and A.C. wrote the manuscript, with feedback from all coauthors. Acknowledgements The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/27W213) / ERCGrantAgreementn (QMAC).FundingfromthepriorityprogramSFB925ofthe GermanScienceFoundation(DFG)isgratefullyacknowledged. PortionsofthisresearchwerecarriedoutattheLinacCoherentLightSource(LCLS)atthe SLACNationalAcceleratorLaboratory.LCLSisanOfficeofScienceUserFacilityoperatedfor the U.S. Department of Energy Office of Science by Stanford University. This work was supported by the Swiss National Supercomputing Centre (CSCS) un der project ID s44. This work was supported by the Swiss National Science Foundation through its National CenterofCompetencesinResearchMUST. AuthorContributions AuthorInformation CorrespondenceandrequestsformaterialsshouldbeaddressedtoAndreaCavalleri (andrea.cavalleri@mpsd.mpg.de)orromanmankowsky(roman.mankowsky@mpsd.mpg.de) 9

10 Figures a 15 b Q IR V R (a.u.) 1 5 Q R Q R amplitude (a.u.) 3 t Figure1 Coherentnonlinearlatticedynamicsinthelimitofcubiccoupling.a)Astatic distortion " shiftstheequilibriumpotential(dashedline)ofallmodesqr thatarecoupled through " coupling,displacingtheequilibriumpositiontowardsanewminimum(solid line). b) The dynamical response of the two modes involves an oscillatory motion of the infraredmode(redline)andadirectional"displacementofqr (blueline).thedisplacementis proportionalto " andsurvivesaslongasqiriscoherent. 1

11 a Intra Bilayer b c Inter Bilayer c c a Intra Bilayer c a O Cu Y Ba a Figure2 StructureofYBa2Cu3O6.5(a)StructureoforthorhombicYBa2Cu3O6.5andmotions oftheopticallyexcitedb1umode.theschematicontheleftshowsthetwotunnelingregions withinandbetweenthebilayers.(b)cuwochains,whichareeitherfilled(rightcu)orempty (leftcu)intheorthowiistructure.(c)superconductingcuo2planes(blue). 11

12 Figure 3 First principle calculations of cubic coupling between 11 Ag modes anddriven B1u mode. (a) Energy potentials of all Ag modes for a frozen B1u displacement of.14a,correspondingtoachangeinapicaloxygen copperdistanceof2.2pm.thexwaxisis the amplitude of the Ag Eigenvector (u is the atomic mass unit). Arrows indicate the potentialminima.(b)strongcouplingoccurstotheag(15,21,29,74)modes,thatcomprise a decrease in apical oxygenwcopper distance and an increase in inwplane buckling. (c) The Ag(52, 61, 63) modes are weakly coupled and govern a breathing motion of the oxygen atomsinthecuo2plane. 12

13 (211) 1K.4 (14) 1K di/i in %.2. di/i in % time in ps time in ps (211) 1K.4 (24) 1K di/i in %.2. di/i in % time in ps time in ps 2 4 Figure 4 Time dependent diffracted peak intensity for four Bragg reflections. A displacive lattice distortion is observed. The experimental data is fitted (solid curves) by adjustingtheb1uamplitudeandtherelativestrengthofthetworelaxationchannels(τ1=1ps and τ2=7 ps) extracted from the optical experiments of Refs. 1 and 11. The relative amplitudesandsignsofthecurvesaredeterminedfromthecalculatedstructureusingonly thefourstrongestcoupledmodes(green)orallagmodes(red).theerrorbarsareextracted fromthemeasurementsas1wσ(67%)confidenceinterval. 13

14 a b c a c c a b d 2.6 e 6 d (pm) 1 1 intrabilayer interbilayer d/d (%) Buckling (Deg) along a along b 4 2 α/α (%) Time Delay (ps) Time Delay (ps) 8 1 Figure5 Transientlatticestructure.(a)Wefindaconcerteddisplacivelatticedistortion (b,c)withadecreaseintheapicaloxygen Cudistancesby2.4pmatoxygendeficientsites andanincreaseinowcuwobuckling.(d)theintrawbilayerdistanceincreases,whiletheinterw bilayerdistancedecreases.here,thecopperatomsoftheplanesatoxygendeficientchain sites(lefthandsidein(a))areusedtodefinethepositionoftheplanes.(e)theinplaneow CuWObucklingincreasesby5%bothalongaandbatoxygendeficientsites. 14

15 Online$OnlyMethods ExperimentalDetails ThexWraydiffractionmeasurementswerecarriedoutwith6.7keVpulsesattheXWrayPump Probe(XPP) beamline of the Linac Coherent Light Source(LCLS). The energy of the xwrays was selected using a channelwcut Si (111) monochromator with a resolution of 1 ev. The diffractionfromeachpulsewasrecordedindividuallywithoutaveragingusingadiode. ShotW towshotnormalizationtotheintensitymonitorafterthemonochromatorwasusedtocorrect the detected signals for intensity and wavelength fluctuations of the xwray pulses. The experimentwascarriedoutingrazingincidencegeometrywithanangleof5 betweenthexw raysandthesamplesurface. The YBa2Cu3O6.5 sample was excited with midwinfrared pulses pulses of ~3 fs duration, generated by optical parametric downwconversion and differencewfrequency generation of nearwinfrared pulses from a TitaniumWSapphirelaser. These pulses were tuned to 15µm wavelengthwith2µmbandwidth,chosentobeinresonancewiththeb1uphononmode.the measurementwascarriedoutatarepetitionrateof12hz,whiletherepetitionrateofthe midwinfrared pulseswassetto6 Hz. This allowed measuring the equilibrium and excited stateforeachtimedelaytocorrectforanydriftsofthefreeelectronlaser. StructureFactorCalculations Todeducetheamplitudes oftheatomicdisplacementsalongtheeigenvectors oftheag coordinatesfromthechangesinscatteredintensity~ wecalculatedthecorresponding modulation of the structure factors. Specifically, we quantified = exp( ), withbeingthereciprocallatticevectorofthecorrespondingdiffractionpeak,fjtheatomic scattering factor and rj the positions of the jwth atom in the unit cell. By calculating the structure factors for the equilibrium atomic positions = () and the transient structure = () + ", the relative change in diffracted intensity was evaluated as / = /. ThechangesinsignalamplitudearecalculatedforAgamplitudes aspredictedbydensity functionaltheorycalculationsforacertaininfraredamplitude andcomparedwiththe experimentalfindingstodeterminethequantitativevalues. 15

16 Densityfunctionaltheorycalculations The phonon modes and the nonlinear phonon couplings were obtained using density functional theory calculations with planewwave basis sets and projector augmented wave pseudopotentials 2,21 as implemented in the VASP software package 22. The local density approximationwasusedfortheexchangeandcorrelations.weusedacutwoffenergyof95 ev for planewwave expansion and a4 8 4kWpoint grid for the Brillouin zone integration during selfwconsistency. We used the experimental lattice parameters of the YBa2Cu3O6.5 OrthoWII structure, but relaxed the internal coordinates. The interatomic force constants werecalculatedusingthefrozenwphononmethod 23,andthePHONOPYsoftwarepackagewas usedtocalculatethephononfrequenciesandnormalmodes 24.Afterthenormalmodeswere identified,totalenergycalculationswereperformedasafunctionofinfraredqirandraman phononmodeqramplitudestoobtaintheenergysurfaces.thenonwlinearcouplingbetween theirandramanmodeswereobtainedbyfittingtheenergysurfacestothepolynomial: = 1 2 " " " " CouplingstrengthsoftheAgtotheB1umodes TheenergypotentialofanAgRamanmodeinthepresenceofacubicnonWlinearcouplingto aninfraredmodeis = " ".Atequilibrium,whentheIRmodeisnot excited,thepotentialoftheramanmodehasaminimumatqr=becausethestructureis stableatequilibrium.however,whentheirmodeisexcitedexternally,theminimumofthe Ramanmodeshiftsbyanamount " " /.TheminimaoftheAgmodesenergypotentials asobtainedfromdftcalculationsforafrozendisplacementoftheb1umodeof.14a are reportedinextendeddatatable1.themodedisplacementsaregiveninamplitudes of thedimensionlesseigenvectorsofthemodeandhavetheunita,withubeingtheatomic massunit.theatomicdisplacementsduetoanamplitude ofamodeisgivenby =,where isthedisplacementofthejwthatom, isthemassofthisatom,and isthe correspondingcomponentofthenormalwmodevector.notethat isnormalizedand dimensionless. 16

17 ThestaticcrystalstructureofYBa2Cu3O6.5(OrthoWII)isgiveninExtendedDataTable2.The latticeconstants are (a= A, b =3.8722A, c =11.725A ) as determined bysingle crystalxwraydiffractionat1k.thelightinduceddisplacementsoftheatomicpositionsat peakchangeindiffractedintensityarereportedinextendeddatatable2. Transientcrystalstructure Changestotheelectronicstructure The changes of the electronic structure due to the lightwinduced distortions were studied using the generalized fullwpotential method within the local density approximation as implementedinthewien2kpackage 25.ThemuffinWtinradiiof2.35,2.5,1.78,and1.53bohrs wereusedfory,ba,cu,ando,respectively,anda2 4 12kWpointgridwasusedforthe Brillouinzoneintegration.Theplanewavecutoffwassetat "# = 7.,where "# isthe planewavecutoffandisthesmallmuffinwtinradius,i.e.1.53bohrs.thedensityofstates (DOS) was generated with a kWpoint grid. Calculations are presented for the equilibrium structure and the transient displaced structure for three B1u amplitudes: the amplitude.3 A as determined here, the amplitude.8 A as estimated in the experimentofreference1and11aswellasalargeramplitudeof1.2a. Our calculated electronic structure of the equilibrium YBa2Cu3O6.5 (orthowii), shown in Figure2ofthemaintext,issimilartotheonecalculatedpreviously 26,27.Thebandsnearthe Fermi level are derived from the Cu 3d" states from both the planes and chains. The four bands that disperse highly along the path Γare due to the planar Cu states.thebroadbandthatdispersesverylittlealong isduetothecu statesfrom thefilled chain. The oxygen deficient chains that control the hole doping give rise to fairly flatelectronicbandswithdominantcu " and " characterthatareveryclosetothefermi level at the point. The electronic structure calculations predict some hybridization between these bands and the planar Cu bands that creates an antiwcrossing nearin the equilibrium structure, this antiwcrossing is close to the Fermi level, giving rise to pockets withunfilledchaincucharacterinthefermisurface.(seeextendeddatafigures4and5). Thedisplacementsduetothenonlinearcouplingscausenoticeablechangestotheelectronic structurearoundthefermilevel.therearethreemaineffects: (i) The lightwinduced displacements reduce the width of the planar Cu bands, which leadstoanincreaseintheplanarcucontributiontothedosatthefermilevel. (ii) The atomic displacements cause a charge transfer from the planes to the oxygen deficientchains.astheunfilledcuchainbandslowerinenergyandmovebelow thefermilevelwithincreasinglightwinduceddisplacements,theplanarcustates increase in energy, becoming more unoccupied. I.e., there is an effective hole doping of the planar Cu states due to the lightwinduced displacements (see ExtendedDataFigure6). 17

18 (iii) Thechangesintherelativeoccupationsofthebandsalsocauseatopologicalchange in the Fermi surface. The lightwinduced displacements increase the filling of the unfilled chain Cu bands, which decreases the size of the pockets in the Fermi surface. Above a threshold of.8a, the oxygen deficient chain Cu bands become fully filled and the Fermi surface consists solely of twowdimensional planarcuandonewdimensionalfilledchaincusheets. Quarticordercoupling Toverifythatthenonlinearphononcouplingisdominatedbythirdorder,asdiscussedinthe maintext,wecheckedforsignalsfromthenext(fourth)order,describedbytheterm " inthenonlinearhamiltonian: " = 1 2 " " " Asnotedinthetext,whenthedirectlydriveninfraredmodeisofB1usymmetry,thirdorder coupling is nonzero only to modes of Ag symmetry. However, coupling to any mode Qj is allowedthroughq 2 Q 2 coupling,inparticulartoinwplanebgmodes. NotefirstthatsmallamplitudeB1uexcitationswouldsimplyrenormalizethefrequencyofa secondmodeqj.thiscandirectlybededucedfromtheequationofmotion,wherethedriving forceisgivenbythecouplingterm ",whichislinearinqj = 2 " UponQIRdisplacement,theanharmonicallycoupledmodeexperiencesarenormalizationof itsfrequency = 1 2 " /. However, above a thresholdwamplitude ", the frequency of the second mode Qj becomes imaginary 3 andthelatticebecomesunstable.importantly,suchinstabilitycantakeplacein two directions, depending on the random instantaneous state of the system (mode amplitudeqjanditsvelocitydqj"/dt.thismanifestsinachangefromaparabolictoadouble wellenergypotentialasshownintheextendeddatafigure1. Hence, fourth order effects need to be identified by analyzing the diffraction of each individualxwraypulse,whereastheunsortedaverageisexpectedtobezeroevenifquartic 18

19 couplingissizeable.intheexperiment,wesortedallpositiveandnegativedeviationsfrom theaveragesignalofallshotstoobtaintheq 2 Q 2 responseataspecifictimedelay.averaging them separately and subtracting negative from positive deviations then gives the intensity changesfromq 2 Q 2 only. TimeWresolvedxWraydiffractionwasmeasuredforfourBraggreflections,sensitivetoAgand tob2gdisplacements.theresultsoftheseexperimentsareshowninextendeddatafigure2. Within our resolution, we find no evidence of quartic contributions. The amplitude of the infraredmotionisbelowthethresholdbeyondwhichfourthordercouplinginduceslattice displacements. 19

20 ReferencesOnline$OnlyMethods 2 P.E.Blöchl,ProjectoraugmentedWwavemethod,Physical"Review"B5,17953(1994). 21 G.KresseandD.Joubert,FromultrasoftpseudopotentialstotheprojectoraugmentedW wavemethod,physical"review"b59,1758(1999). 22 G.KresseandJ.Furthmüller,EfficientiterativeschemesforabinitiototalWenergy calculationsusingaplanewwavebasisset,physical"review"b54,11169(1996). 23 K.Parlinski,Z.Li,andY.Kawazoe,FirstWPrinciplesDeterminationoftheSoftModeinCubic ZrO2,Physical"Review"Letters78,463(1997). 24 A.Togo,F.Oba,andI.Tanaka,FirstWprinciplescalculationsoftheferroelastictransition betweenrutilewtypeandcacl2wtypesio2athighpressures,physical"review"b78,13416 (28). 25 P.Blaha,K.Schwarz,G.Madsen,D.Kvasnicka,andJ.Luitz,WIEN2k,AnAugmentedPlane Wave+LocalOrbitalsProgramforCalculatingCrystalProperties(K.Schwarz,Tech.Univ. Wien,Austria,21). 26 A.CarringtonandE.A.Yelland,BandWstructurecalculationsofFermiWsurfacepocketsin orthowiiyba2cu3o6.5,physical"review"b76,1458(r)(27). 27 I.S.Elfimov,G.A.Sawatzky,andA.Damascelli,TheoryofFermiWsurfacepocketsand correlationeffectsinunderdopedyba2cu3o6.5physical"review"b77,654(r)(28). 2

21 a 15 b 15 V R (a.u.) 1 5 V j (a.u.) Q R amplitude (a.u.) Q j amplitude (a.u.) ExtendedDataFigureandTableLegends ExtendedDataFigure1 Nonlinearlatticedynamicsinthelimitofcubicandquarticcoupling.Dashedlines:PotentialenergyofamodeQasafunctionofmodeamplitude.a)A static distortion " shifts the potential of all modes QRthat are coupled through a " coupling,(solidline)displacingtheequilibriumpositiontowardsanewminimum.b)dueto quartic " coupling,theenergypotentialofacoupledmodeqjisdeformedsymmetrically upon static distortion ". The frequency of the mode first softens until it is destabilized, whichmanifestsinadoublewellpotential(solidline). 21

22 (211) 1K.4 (14) 1K di/i in %.2. di/i in % time in ps time in ps (211) 1K.4 (24) 1K di/i in %.2. di/i in % time in ps time in ps 2 4 Extended Data Figure 2 Changes in diffracted intensity of specific Bragg reflections fromfourthordercouplingfordifferenttimedelaysbetweenpumpandprobepulse. Wefindnoevidenceoflatticedistortionsoriginatingfromfourthordercontributionstothe phonon coupling. The amplitude of the infrared mode QIR is below the threshold beyond whichfourthordereffectsdestabilizecoupledphononmodes.theerrorbarsareextracted fromthemeasurementsas1wσ(67%)confidenceinterval. 22

23 A g cm 1 A g cm 1 A g cm 1 A g cm 1 A g cm 1 A g cm 1 A g cm 1 A g cm 1 A g cm 1 A g cm 1 A g cm 1 B 1u cm 1 ExtendedDataFigure3 PhononmodesofOrtho$IIYBa2Cu3O6.5.Shownaresketchesof the resonantly excited B1u mode and all 11 Ag modes to which the coupling strengths (reportedinextendeddatatable1)havebeencalculated. 23

24 a 2 b 2 Energy (ev) 1 E F Energy (ev) 1 E F 1 1 Γ X S Y Γ Z Γ X S Y Γ Z ExtendedDataFigure4 Bandstructureoftheequilibrium(blackline)andtransientcrystal structure. The band structure is plotted along Γ,,.5,,.5,.5,,.5, Γ,, Z(,,.5) a) for.8 A, which is the amplitudeestimatedforthegeometryofreference1and11andb)1.2a B1u. 24

25 π b π b k y k y π π b π k π b π x k π a a a x a ExtendedDataFigure5 kz=cutofthefermisurfaceoftheequilibrium(blackline) andtransientcrystalstructure(reddashedline).intheequilibriumstructure,thebands of the unfilled chain Cu give rise to pockets in the Fermi surface. The light induced displacements shift the density of states of these bands to lower energies, increasing the filling andreducingthepockets. Above a threshold of.8a, the oxygen deficient chain bands become fully filled, the pockets close and the Fermi surface consists solely of twow dimensionalplanarcuandonewdimensionalfilledchainstates.thefermisurfaceisshown inthedisplacedstateforb).8a andb)1.2a B1uamplitude. 25

26 a b DOS (a.u.) Empty chain Cu Equilibrium.3 B1u.8 B1u 1.2 B1u DOS (a.u.) Inplane Cu empty chain Equilibrium.3 B1u.8 B1u 1.2 B1u Energy (ev) Energy (ev) c d DOS (a.u.) Filled chain Cu Equilibrium.3 B1u.8 B1u 1.2 B1u DOS (a.u.) Equilibrium.3 B1u.8 B1u 1.2 B1u Energy (ev) Energy (ev) ExtendedDataFigure6 ChangesinthedensityofstatesintheCuO2planeandtheCu O chains. These are obtained from a projection of the density of states onto the copper muffinwtin spheres. a, b, In the lightwinduced state, the density of states of the OWdeficient chainlowersinenergy(a),whereastheoppositeeffectisobservedforthecuintheplane below (b). This corresponds to charge transfer from the planes to the chains. c, d, The density of states of the filled chain Cu is not strongly affected(c). The bands of the planar Cuatoms narrow, which leads to an increase in the density of states near the Fermi level both at sites with filled (d) and empty chains (b). The effect is already visible for a QB1u amplitude of.3a (blue) but becomes more prominent for larger displacements of.8a (purple)and1.2a (green). 26

27 Mode Displacement Ag14.2 Ag15.31 Ag21.38 Ag29.23 Ag39. Ag52.7 Ag53. Ag61.7 Ag63.7 Ag65.1 Ag74.2 A u ExtendedDataTable1 Modedisplacements A EnergypotentialminimaoftheAg modesasobtainedfromdftcalculationsforafrozendisplacementoftheb1umodeof.14a,whichcorrespondstoachangeinapicaloxygen copperdistanceof2.2pm. 27

28 Equilibrium Structure (Å) Displacements (pm).3å u Displacements (pm).8å u Displacements (pm) 1.2Å u Atom x y z x y z x y z x y z Y Y Ba Ba Ba Ba Cu Cu Cu Cu Cu Cu O O O O O O O O O O O O O Extended Data Table 2 Equilibrium structure of YBa2Cu3O6.5 and light induceddisplacements. Atomic positions are given in Ångström (x,y,z), thelightwinduced atomic displacementsinpm. 28