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Michael , cuprates di Weber edric ´ | lrfs optics ultrafast a,San and Spain; ´ ıan, d,1 C c rbe,btrather but problem, g e | ihl swl nttto hscladTertclCeity nvriyo epi,D-04103 Leipzig, of University Chemistry, Theoretical and Physical of Institut Ostwald Wilhelm hita Bernhard Christian , wgt Acharya Swagata , electron–phonon i etrfrCmuainlQatmPyis h ltrnIsiue e ok Y10010 NY York, New Institute, Flatiron The Physics, Quantum Computational for Center d doi:10.1073/pnas.1919451117/-/DCSupplemental at online information supporting contains article This 1 pairs particle–hole the photodoping the in by underlying accomplished dynamics was the This on IMT. details preliminary revealed has the (13). and them freedom between uncover of forces to degrees mutual strategy microscopic promising various a of relevance as ultra- the evolved with have (12) behavior of probes real-time fast out their systems monitoring complex and driving equilibrium disentangling particular, spectro- In in novel techniques. of progress development scopic the experimental on time, relies interactions same (5, intricate computers the avail- modern At on becoming tractable are 11). problem methods the difficult render powerful that now notoriously able only are and correlations handle, strong to with deal that puz- descrip- theoretical a tions First-principles solids (10). these understand to renders case also zling it theories physics, new correlated-electron benchmark in to candidates excellent cuprates makes oeiaie ies . C BY-NC-ND) (CC 4.0 NoDerivatives License distributed under is article access open This interest.y competing no University. declare y Stanford authors Z.-X.S., The and Technology; of Institute Massachusetts R.C., E.B., paper.Reviewers: and the data; wrote analyzed C.W. F.C. and and E.S., T.B., A.R., E.B. C.B., S.A., research; M.A.S., E.B., performed C.W. research; and designed A.R., C.W. M.v.S., and E.P., F.L., A.R., M.A.S., E.B., contributions: Author was response Drude fs) low-energy 150 the to of (40 rise timescale fast the extremely with The associated contin- 15). delayed (14, a probe with spectrum uum absorption optical the in change owo orsodnemyb drse.Eal ne.ui@pdmgd,cedric. [email protected] [email protected], or Email: [email protected], addressed. be may correspondence whom To h f cl oyehiu F Polytechnique Ecole o lrfs wthn eie tro temperature. room at of devices design switching potential geometrical ultrafast technological for with the insulators, transition. toward Mott phase in way states this metallic the in pave sup- lattice the results turn, the Our along in of involvement This, displaced the modes. is ports vibrational structure specific of crystal coordinates its when met- toward allization La unstable insulator is superconductivity, correlated calculations high-temperature the theoretical that and unveil we spectroscopy to Here, laser role. dominant ultrafast the play use which to in thought are insulators, Mott the of is transition interest insulator-to-metal significant materi- attracts the complex that transformation of phase comprehension A the als. in phase a crucial in is freedom of transition degrees different of role the Elucidating Significance ´ aoBoSetocp ru,Dpraet eF de Departamento Group, Spectroscopy Nano-Bio h plcto futaatmtost noe cuprates undoped to methods ultrafast of application The interactions different of character intertwined this While hmsBrumme Thomas , akvnSchilfgaarde van Mark , CuO 2 lnswt hr ae us hl oioigthe monitoring while pulse laser short a with planes g oi tt hmsr ru,Lbrtr o Multiscale for Laboratory Group, Chemistry State cl oyehiu F Polytechnique Ecole ´ ed ´ rl eLuan,C-05Lausanne, CH-1015 Lausanne, de erale ´ c,e veiaSheveleva Evgeniia , . y d raieCmosAttribution-NonCommercial- Commons Creative arzoCarbone Fabrizio , d y eateto hsc,King’s Physics, of Department . y ed ´ rl eLuan,CH-1015 Lausanne, de erale ´ https://www.pnas.org/lookup/suppl/ NSLts Articles Latest PNAS 2 CuO sc eMateriales, de ´ ısica f 4 , rcro to precursor , a , | f8 of 1

PHYSICS found to be imprinted onto the dynamical evolution of the opti- Results cal charge-transfer (CT) excitation in the visible range. Within Crystal Structure and Equilibrium Optical Properties. As a model 200 fs from its formation, the mobile charges freeze into local- material system we study La2CuO4 (LCO), one of the sim- ized midgap states owing to the concomitant action of polar plest insulating cuprates exhibiting metallicity upon hole . lattice modes and spin fluctuations (16). Finally, the self-trapped In this solid, the 2D network of corner-sharing CuO4 units is carriers release energy in the form of heat over a picosecond accompanied by two apical O atoms below and above each CuO4 timescale. plaquette. As a result, the main building blocks of LCO are Despite their pioneering contribution, these works have left CuO6 octahedra (Fig. 1A) that are elongated along the c axis due several fundamental questions unanswered. First, the use of to the Jahn–Teller distortion. The unit cell of LCO is tetragonal cuprate thin films has hindered the study of the charge dynamics above and orthorhombic below 560 K. A simplified scheme of the c along the crystallographic axis. Hence, it is unknown whether electronic is shown in Fig. 1 B, Left. An energy the transient metallic state has a purely 2D nature or whether gap (∆CT ) opens between the filled O-2p band and the unoc- it also involves a certain degree of interlayer transport. Further- cupied Cu-3d upper Hubbard band (UHB), thus being of the more, the high temperature employed in these experiments has d masked the observation of possible bosonic collective modes that CT type. In contrast, the occupied Cu-3 lower Hubbard band cooperate with the charge carriers to induce the IMT. (LHB) lies at lower energy. Here we combine ultrafast optical spectroscopy and first- First, we present the optical properties of LCO in equilibrium. principles calculations to unravel the intricate role of the Fig. 1C shows the absorptive part of the optical conductivity electron–phonon coupling in the stability of the insulating state (σ1), measured via ellipsometry. The in-plane response (σ1a , of a prototypical cuprate parent compound. By measuring the solid violet curve) is dominated by the optical CT gap at 2.20 eV nonequilibrium response of different elements of the optical con- (17, 18). This transition is a nonlocal resonant that ductivity tensor, we reveal that rapid injection of particle–hole extends at least over two CuO4 units. The strong coupling to pairs in the CuO2 planes leads to the creation of a three- the lattice degrees of freedom causes its broadened shape (18– dimensional (3D) metallic state that has no counterpart among 20). As such, this optical feature can be modeled as involving the chemically doped compounds and is accompanied by a com- the formation of an electron– and a hole–polaron, cou- plex motion of the ionic positions along the coordinates of fully pled to each other by a short-range interaction (18, 21). At symmetric modes. The information gleaned from our experiment higher energy (2.50 to 3.50 eV), the in-plane spectrum results about the that strongly couple to the mobile charges from charge excitations that couple the O-2p states to both the is supported by a state-of-the-art theoretical framework that Cu-3d states in the UHB and the La-5d/4f states. In contrast, unveils a striking instability of the insulating state against the the out-of-plane optical conductivity (σ1c ) is rather featureless displacement of the same lattice modes. These findings indicate and its monotonic increase with energy is representative of a that the light-induced IMT in cuprates cannot be interpreted as particle–hole continuum. This spectral dependence reflects the a purely electronic effect, calling for the involvement of inter- more insulating nature of LCO along the c axis, which stems twined degrees of freedom in its dynamics. More generally, these from the large interlayer distance between neighboring CuO2 results open an avenue toward the phonon-driven control of the planes. As a consequence, over an energy scale of 3.50 eV, IMT in a wide class of insulators in which correlated electrons charge excitations in equilibrium are mainly confined within each are strongly coupled to fully symmetric lattice modes. CuO2 plane.

A B C 1.6 3

Exp. UHB The. ) 1.2 1c -1

2 (10 UHB Energy (eV) Energy (eV) cm

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Fig. 1. (A) Crystallographic structure of La2CuO4 in its low-temperature orthorhombic unit cell. The Cu atoms are depicted in black, the O atoms in red, and the La atoms in violet. The brown shading emphasizes the CuO6 octahedron in the center. (B) Schematic representation of the interact- ing density of states in undoped insulating (Left) and photodoped metallic (Right) La2CuO4. The O-2p, lower Hubbard band (LHB), upper Hubbard band (UHB), and (QP) peak are indicated. In the insulating case, the optical charge-transfer gap (∆CT) is also specified. The blue arrow indicates the 3.10-eV pump pulse, which photodopes the material and creates particle–hole pairs across the charge-transfer gap. The multicolored arrow is the broadband probe pulse, which monitors the high-energy response of the material after photoexcitation. (C) Real part of the optical conductivity at 10 K, measured with the electric field polarized along the a axis (violet solid curve) and the c axis (brown solid curve). The shaded area represents the spectral region monitored by the broadband probe pulse in the nonequilibrium experiment. The theory data for the in-plane response are shown as a violet dashed curve. The a-axis response comprises a well-defined peak in correspondence to the optical charge-transfer gap around 2.20 eV and a tail extending toward low energies down to 1.00 eV. In contrast, the c-axis response is featureless and increases mono- tonically with increasing energy, as expected from a particle–hole continuum. Exp. and The. in C refer to the experimental and theoretical results, respectively.

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Energy (eV) Energy (eV) 2 Fig. CuO A 1.9 2.1 2.3 2.5 1.8 2.0 2.2 2.4 and (A ∆σ x A 2 ph and B 1 1a 0 0 lns eepoea xiainrgm between regime excitation an explore We planes. ttredfeetpm–rb iedly uigters 01 n .7p)adterlxto 15 s ftersos.( response. the of ps) (1.50 relaxation the and ps) 0.17 and (0.10 rise the during delays time pump–probe different three at and ∼ ln the along oo-oe aso h ifrnilotclcnutvt (∆σ conductivity optical differential the of maps Color-coded B) and ) Probe ||a Pump ||a Probe ||c Pump ||a ,w bev infiatyreduced significantly a observe we (A), polarization probe in-plane For atom. copper per photons 0.06 B B .Ulk rvoseprmns(4 5 22), 15, (14, experiments previous Unlike ). 1 1 hw rmtcsprsinadso eoeywtotceryvsbechrn siltos ml ekeegsi h ieo the of rise the in emerges peak small A oscillations. coherent visible clearly without recovery slow and suppression dramatic a shows ) Time delay(ps) Time delay(ps) , hwtesetotmoa vlto fthe of evolution spectro-temporal the show c ,poooigpril–oepisinto pairs particle–hole photodoping Left), ai (∆σ -axis a and 2 2 c xs ahtmoa rc eut rmteitgainoe h nrywno niae ytesae ra in areas shaded the by indicated window energy the over integration the from results trace temporal Each axes. -50 -5 1c 3 3 enwrva o hs opti- these how reveal now We 0 ifrnilotclconductiv- optical differential ) 0 5 50 4 4 B , Inset Right -60 -20 20 -3 -1 1 .Teoto-ln rc (F trace out-of-plane The ). 1.9 1.8 n shaded and 1.50ps 0.17 ps 0.10 ps C and 2.0 Inset Energy (eV) 2.1 Energy (eV) D. ). w rsalgahcae n ou ntednmc ls to close dynamics the on focus and axes crystallographic two eso htti upesdbcgon skyt unraveling to LCO. key of is dynamics intricate background the on suppressed Here information this counterpart. invaluable in-plane that its show one than we and smaller featureless magnitude is of system response order the The while equilibrium. picoseconds to into for thermalizes relaxes persists and that plateau spectrum negative whole a the over drops weakly intensity increased and increase). temperature 2C lattice the the Fig. by (compare in produced and ps timescale 1.50 femtoseconds picosecond at the hundred curve on several dominant after shape becomes derivative-like arises first the gradually causes that latter the heat- several particular, lattice to In and in-plane states, ing. due of midgap energy in emergence localization low ultrafast charge the metallicity, to are high which from among 2.00- redistribu- processes, weight pump-induced to spectral the 1.80- of from the stems tion behavior in this values 15), 2 (14, positive (Fig. to range increase eV delayed its to in reduction sudden 1 2.2 out-of- (B) and in-plane (A) and polarization pump in-plane with K 10 at ) is,w opr h eprleouinof evolution temporal the compare we First, modifies also process photodoping same The netn atcehl ar nthe in pairs particle–hole Injecting 2.3 hw la inlta iistefs npaersos,btrelaxes but response, in-plane fast the mimics that signal clear a shows ) .A .0p,acosvrbtenardcdadan and reduced a between crossover a ps, 0.10 At D). 1.50ps 0.17 ps 0.10 ps 2.4 ∆σ 2.5 1c F E mre rud20 V usqety the Subsequently, eV. 2.00 around emerges A -50 -3 -2 -1 ∆σ 0 0 and 1a C 0 0 ls oteotclC xiainand excitation CT optical the to close and .A xlie npeiu studies previous in explained As ). ∆σ 1 1 and ∆σ 1a Time delay(ps) Time delay(ps) ∆σ 1 in npht ftesm data same the of Snapshots D) CuO bv h pia Teg at edge CT optical the above 1 NSLts Articles Latest PNAS i.S2 Fig. Appendix, SI scnieal ekrand weaker considerably is 2 2 2 lnspoue a produces planes -0.2 0.4 E ∆ ∆ Time delay(ps) and 3 3 Time delay(ps) σ σ 0.0 0.8 1c 1 F ln the along Temporal ) Fg 2 (Fig. 0.2 1.2 C | and 4 4 f8 of 3 0.4 1.6 C D. B

PHYSICS zero time delay. Fig. 2E displays a representative trace of ∆σ1a Dynamics of the Collective Modes. As a next step, we search for obtained through integration around the optical CT feature. possible collective modes that strongly couple to the mobile car- The intensity drops within ∼0.17 ps, a timescale that is signif- riers and clarify their involvement in the IMT. In this respect, we icantly longer than our resolution (∼0.05 ps). The subsequent note that the lack of a significant background in ∆σ1c uncovers relaxation spans tens of picoseconds. A close inspection around a pronounced oscillatory pattern that emerges from the rise of zero time delay (Fig. 2 E, Inset) reveals a resolution-limited the response and persists during its decay (Fig. 2 F , Inset). This signal that emerges only partially before being buried under coherent beating is due to collective modes displaced through the pronounced intensity drop. Fig. 2F shows the out-of-plane the delocalized carrier density (28, 29). Similar oscillations also response (integrated over the low-energy region of Fig. 2D), appear in the a-axis polarization channel (Fig. 2E), but the which shares important similarities with the in-plane signal: The contrast to resolve them is lower owing to the huge relaxation intensity suppression is also complete within ∼0.17 ps and com- background. prises a resolution-limited feature that perfectly mirrors the one We assign the modes coupled to the in-plane charge density by along the a axis. This signal cannot originate from a leakage applying a Fourier transform analysis to the original background- of the other probe polarization channel, as the shape of the free transient reflectivity data to maintain high accuracy. The ∆σ1c spectrum has no fingerprint of the in-plane CT exciton. results, shown in Fig. 3 A and B, reveal that five bosonic exci- Furthermore, since the resolution-limited temporal response is tations (labeled as Ag (1 − 5)) participate in the nonequilibrium observed only in LCO and over a broad spectral range away from response. Their energies match those of the five Ag phonons the pump photon energy, it cannot be a pump-induced artifact reported in orthorhombic LCO by spontaneous Raman scatter- (SI Appendix, section S4). Conversely, the combination of high ing (25). We characterize their eigenvectors by calculating the time resolution and a continuum probe allows us to ascribe this phonon spectrum of LCO via density-functional theory (Mate- feature to the signature imprinted onto the optical CT energy rials and Methods). Fig. 3C shows the involved ionic displace- scale by a light-induced metallic state. ments in the first half cycle of the different Ag phonons. Modes This conclusion naturally emerges through direct inspection Ag (1) and Ag (2) exhibit staggered rotations of CuO6 octahedra. of our spectro-temporal response. Previous pump–probe mea- In particular, Ag (1) is the soft phonon of the orthorhombic- surements covering the 0.10- to 2.20-eV range identified an to-tetragonal transition. Ag (3) and Ag (4) present large c-axis ultrafast transfer of spectral weight from the above-gap to the displacements of the La atom, which in turn modify the La– below-gap region, with the establishment of Drude conductiv- apical O distance. The only difference between them lies in the ity within the CuO2 planes (15). Due to this spectral weight displacement of the apical O: While its out-of-plane motion is transfer, the high-energy region of the spectrum becomes sen- the same, its in-plane motion occurs in the opposite direction. sitive to the buildup and relaxation dynamics of the itinerant Finally, Ag (5) is the breathing mode of the apical O. The Fourier carrier density. The transient metallic behavior manifests itself transform indicates that all phonons modulate the out-of-plane with a pulsed signal that modifies the optical CT gap feature response (Fig. 3B, brown curve), whereas only Ag (1), Ag (3), and decays within 150 fs from the arrival of the pump pulse. and Ag (4) are unambiguously resolved in the in-plane signal The sign and shape of the transient metallic response depend on (Fig. 3B, violet curve). Furthermore, since Ag (1), Ag (2), and the nature of the optical nonlinearities induced by the delocal- Ag (4) are characteristic phonons of orthorhombic LCO (25), ized carriers on the high-energy scale. In this respect, the sharp their presence denotes that the trajectory followed by the lat- feature that we observe in our temporal traces in Fig. 2 E and tice after photodoping does not evolve through the structural F is in excellent agreement with the evolution of the in-plane . Finally, no modes with symmetry other than Drude conductivity found in these previous experiments. More Ag appear in our data. While this result is natural when the importantly, the rise of ∆σ1c in our data closely mimics that probe is c-axis polarized because of symmetry arguments, more in ∆σ1a , indicating that the metallic state has an unexpected noteworthy is the in-plane probe polarization case. According 3D character. Quantitative information is obtained through a to Raman selection rules, modes of B1g symmetry should also systematic global fit analysis of the temporal dynamics along emerge in this polarization configuration (30). Their absence both crystallographic axes. An accurate fit is accomplished only can be attributed either to the short lifetime of the B1g compo- through a model based on that proposed in ref. 15. A Gaussian nent of the real charge-density fluctuation driving the coherent function representing the metallic state captures the fast-varying lattice response (28) or to a weak Raman cross-section in the signal during the rise of the response, whereas a subsequent probed spectrum. multiexponential relaxation comprises contributions from charge To establish which Ag modes preferentially couple to the localization in midgap states and lattice heating effects. Details in-plane photodoped carriers, we also excite LCO with a light are given in SI Appendix, section S6; here we present only fits field polarized along the c axis. Despite keeping the carrier to the traces in Fig. 2 E and F, which are overlapped as dashed excitation density constant, this pump scheme causes a smaller black lines. drop in the transient signal amplitude and a weaker modu- Besides leaving a characteristic signature in the time domain, lation depth due to the coherent lattice modes (SI Appendix, the 3D metallic state also influences the ultrafast spectral Fig. S7). Fourier transforming the background-free data (Fig. 3 response of LCO. A similar behavior appears in both the absorp- A and B, green curves) establishes that only Ag (1) and Ag (2) tive and dispersive components of ∆σa and ∆σc (SI Appendix, are efficiently triggered by the out-of-plane electronic density, Figs. S10 and S11), but with a time lag between the two direc- whereas Ag (3) and Ag (4) are strongly suppressed compared to tions. This suggests that the optical nonlinearities induced by the the in-plane photoexcitation scheme. This suggests that periodic itinerant carriers onto the high-energy optical response of LCO structural elongations and compressions of the CuO6 octahe- follow distinct dynamics along the a and the c axis. dra along the c axis through the La atom are favorably trig- We stress that this 3D metallic state in photodoped LCO is gered by photodoping charges within the CuO2 planes. This significantly different from the case of chemically doped LCO aspect can be explained by noting that excitation across the (26). In the latter, 3D metallicity is suppressed up to doping lev- optical CT gap promotes electrons in the UHB and holes in els as high as p = 0.12 (i.e., well above our photodoping density), the O-2p band, thus locally removing the Jahn–Teller distor- and only in overdoped samples a well-defined Drude response tion on the CuO6 octahedra. In the past, this picture has been is observed (27). In contrast, our findings break the scenario explored theoretically for chemical (hole) doping, showing how of an ultrafast IMT solely governed by 2D in the the apical O approaches the Cu2+ ions to gain attractive elec- CuO2 planes. trostatic energy. Consistent with this idea, the dominant mode

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To the LCO. influence of also can properties coordinates mode rel- the lattice along is evant to displacements us that ionic the motivates motion whether This theoretically structural carriers. study delocalized complex the a to by coupled strongly accompanied is LCO of Tran- Insulator-to-Metal the sition. in Coupling Electron–Phonon the of Role Jahn–Teller the the of along destabilization atoms the distortion. api- follows La likely the the that of motion and displacements O coherent occurs involves cal motion in-plane experiment its same, our the is in motion out-of-plane its While O: apical the of ( displacement symmetric the Mode totally in direction. lies opposite of them the set between in a difference only of The presence distance. the O show CuO of polarizations rotations Different staggered involve curves). in green the asterisks and The (C brown structure. the crystal for orthorhombic eV the 2.20 to 1.80 and in indicated adn tal. et Baldini acltdegnetr ftefiemdsof modes five 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aeil and (Materials DMFT) + xs .. noscillating an i.e., axis, A g B ymty lc tm ee oC,rdaost ,advoe tm oL.Modes La. to atoms violet and O, to atoms red Cu, to refer atoms Black symmetry. niaetepoo nrymaue ysotnosRmnsatrn 2) .. rirr units. arbitrary a.u., (25). scattering Raman spontaneous by measured energy phonon the indicate A g 2 A (2) g 3 and (3) A g 4 rsn large present (4) g 3 A (3) h aain data The A. es u prahi ufiinl outt lcdt h effect the the on in elucidate shown motions to results, ionic robust Neverthe- sufficiently different S15). is of Fig. approach Appendix, our (SI less, spectrum experimental resulting the current the Our and (33). corrections bandwidths tex small very of cru- QSGW presence becomes the corrections in vertex cial screening electron–hole conductivity of optical use equilibrium the the of insulating Cap- along onset displacements. out-of-plane correct lattice same the the the turing against how reacts test LCO of and state response optical axis the than other in response symmetries an Drude with broad metal a func- bad and spectral tion a single-particle the into in evolves peak system the quasiparticle incoherent The S14). of and each S13 Figs. along the along metallization displacements net induce 0.04 Surprisingly, that results. values by observe similar LCO smaller yield we displacement of However, lattice cell coordinates. frozen of unit phonon the different displacing along upon spec- obtained show we tra conductivity, optical the on motions ionic different elec- whereas the S16 results, important affect 4 representative first Fig. motions insulator. some a atomic correlated this specific represents of properties how it tronic elucidate state, to ground coupling step electronic electron–phonon method the the on adiabatic in only this information While provide modes. can Raman-active relevant of c CuO rvd h ulaayi.T mhsz h mato the of impact the emphasize To analysis. full the provide ai ipaeet fteL tm hc ntr oiyteLa–apical the 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Appendix, SI ncnrs,mdswith modes contrast, In . svoe uvs confirm curves, violet as NSLts Articles Latest PNAS A g hnnmdsof modes phonon ) A A IAppendix , SI g 1 and (1) − A g C | modes shows f8 of 5 A g (2) c A ˚ -

PHYSICS ABC

Fig. 4. (A − C) Many-body calculations of the in-plane optical conductivity for the La2CuO4 unit cell. Comparison between the response for the undisplaced structure (brown curve) and the response for the structure displaced by 0.04 A˚ along the phonon coordinates is indicated (violet curves). For displacements along totally symmetric modes (an example is shown in A), a metallic state emerges and gives rise to Drude spectral weight below ∼1.00 eV. In contrast, for displacements along Bg modes (examples are given in B and C), there is no metallization and hence no impact on the low-energy spectral weight inside the optical charge-transfer gap.

the trends reported for the Ag modes, establishing that displace- tors [i.e., devoid of coexisting charge-orbital orders (34–36) and ments along their eigenvectors cause net metallization also along not lying in proximity to a structural transformation (37–39)]. the c axis. These findings have three important implications: As such, this IMT can be extended to a wide class of corre- 1) The spectral region covered by our experiment is sensitive lated solids (e.g., NiO, iridates, etc.). Moreover, in the specific to the displacements of modes with any symmetry, ruling out case of cuprates, our data enrich the debate around the role the possibility of a weak Raman cross-section behind the lack and structure of the electron–phonon interaction (7, 9, 40–46). of B1g modes in our experiment; 2) displacements along the In particular, an old puzzle in the field regards the evolution of coordinates of modes with a fully symmetric representation can the quasiparticle-like excitations from the undoped Mott insu- induce an IMT; and 3) the lattice-driven metallic state has a lator to the doped compounds (19, 47). This problem is closely 3D nature. related to the correct identification of the chemical potential and Let us discuss the possible contributions that can explain its behavior upon hole or electron doping. A possible solution of the observed metallicity in the Ag -displaced structures: effec- this paradox was proposed by noting that the coherent quasipar- tive doping, change of screening, and modification of orbital ticle scenario fails to describe the Mott insulating state and that a overlaps. Regarding the doping into Cu-3d states, displacements Franck–Condon type of broadening contributes to the lineshape along the coordinates of all Raman-active modes (except B3g ) of the main band in the single-particle excitation spectrum (19). lead to an increase in the hole density in the d states relative In the Franck–Condon scenario, the true quasiparticle peak at to the undisplaced case (SI Appendix, Table S2). In the case of half filling has a vanishingly small weight and the spectrum is the Bg modes, this effective doping yields ∼ 0.4% holes for B1g , dominated by incoherent sidebands due to shake-off excitations ∼ 0.3% holes for B2g , and ∼ 1.5% electrons for B3g . In the case stemming from the coupling between the electrons and bosonic of the Ag modes (except Ag (1)), the hole doping reaches val- collective modes. ues larger than ∼ 3%. It appears that all of the Raman-active Our results add significant insights to this long-standing prob- modes that cause significant effective doping in Cu-3d induce lem. First, the combination of our equilibrium optical data a transfer of spectral weight to lower energies, leading to weak and calculations reinforces the idea that polar lattice modes metallization. Enhanced screening in the displaced structures cooperate with the electronic correlations to freeze quasiparti- could also lead to the breakdown of the insulating state via cles and stabilize the insulating state of LCO (14–16, 22, 48). modified effective Hubbard U and CT energies. However, our This is evidenced by the tail of optical spectral weight extend- estimates of the CT energy for the displaced structures show ing down to 1.00 eV in Fig. 1C , at odds with the 1.80-eV very small variation compared to that of undisplaced LCO (SI electronic-only gap retrieved by our simulations. This discrep- Appendix, Table S1). While these changes are typically larger ancy can be explained by noting that our theory does not for modes that lead to metallization, the rather small modifica- account for either the electron–phonon or the electron–hole tion of the CT energy alone is unlikely to cause the loss of the interactions. As such, the tail emerging below 1.80 eV in σ1a insulating state. Finally, by the principle of exclusion, the orbital is most likely due to the interplay between excitonic states and overlaps and thus the hopping integrals between Cu-3d and O-2p polar lattice modes (49). This observation would clarify why orbitals remain as the main explanation for the emerging metallic the energy gap (and the barrier to metallicity) relevant to the state, due to their high sensitivity to certain lattice displacements. transport and thermodynamic properties of insulating cuprates While we do not explicitly compute values for renormalized hop- is much smaller that the optical CT gap (for LCO the trans- pings here, the momentum-resolved spectral functions for the port gap is estimated around 0.89 eV, at the onset of the tail displaced structures (SI Appendix, Fig. S13) strongly suggest that in σ1a ) (50–52). The same polar lattice modes would also be modified hoppings are indeed the most important ingredient in responsible for the charge–phonon coupling revealed by the the observed metallization. previous photodoping experiments on LCO (14, 15), shaping the structure of the midinfrared absorption bands (16). On Discussion top of this, our study uncovers that (real) Raman-active lat- The fundamental and technological implications of our results tice displacements can instead induce quasiparticle delocaliza- are noteworthy. On the theory side, we have reported a hitherto tion and trigger an IMT. Taken together, these results con- undetected type of IMT, which applies to pure Mott/CT insula- stitute additional proof for the role of the crystal lattice in

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Sciences P020194/1); Physical UK by National and UK the (Engineering supported (ARCHER) Hub and were Resource Service End C.W. High Supercomputing and Computing from For M.v.S., division Research 200020-172611. funding Grant a Advanced S.A., acknowledge by is C.B. resources, (SNSF) Foundation and Institute computational F.L., Science Flatiron National E.S., Grupos Swiss con- The Foundation. the [AIM]), and systems.” Simons dynamics Matter the quantum induced of of correlated “Light Imaging of A.R. SFB925 trol and (Advanced and T.B. Excellence (IT1249-19), 2558/2-1). (ERC-2015-AdG694097), Consolidados of Council (SE Cluster Research program European Forschungsgemeinschaft the the Noether by Deutsche (NCCR-MUST). Emmy supported Technology the were the and by through Science support (DFG) Ultrafast acknowledges Molecular Competence M.A.S. - of Center Research National the in from support acknowledge F.C. and E.B. Jos Georges, ACKNOWLEDGMENTS. the ionic for the shifts conductivity considered density- the of 0.04 optical of was from amplitude the displacement largest calculated As The computed structures. fields rigid cores. displaced we different vector 64 small Finally, phonon over theory. a the averaged functional along considered were LCO we in statistics positions step, the and second 10 core a with per performed was steps were energy, Carlo responses kinetic single-particle in the the converged than self-energy 16 slowly ical a more 4 on much Σ a performed k on was with calculated self- potential Charge varies problem. QSGW which impurity Monte static correlated quantum the 16 the continuous-time hybridization solve on the exact to consistency used locally (68) (66), We solver the fluctuations. 64/Cmca Carlo of spin group local flavor space the expansion with of nonmag- treatment phase for tive orthorhombic calculations QS the the the out within in carried LCO We subspace. netic correlated the to QSGW the with at bined available package freely Questaal at now the is in code LDA implemented Our Questaal as for (The (5), typical calculations (65). DMFT (∼1%), calculation and volume phonon ory the reduced to slightly respect experimen- prior a with The relaxed thoroughly. in was convergence calculations. checked (64) resulted The been cell Ry. which unit has 0.002 primitive parameters of tal these smearing all Gaussian to a and 0 <10 emdldteotcldt fLOb obnn h QSGW the combining by LCO of data optical the modeled We × 0fs. ∼50 × µm GW β 6kms,flycnegn h hre h Wsl-nry(Σ self-energy GW The charge. the converging fully k-mesh, 16 bru oaecytladdrce oadtesml ne nor- under sample the toward directed and crystal borate -barium −5 )Teprmgei MTwscom- was DMFT paramagnetic The https://github.com/tkotani/ecalj/.) 7 A. × ˚ × mlmnainwsaatdfo h rgnleajpackage, ecalj original the from adapted was implementation y usqetDF acltoswr trtd n h dynam- the and iterated, were calculations DMFT Subsequent Ry. 87 oezn,adFriAystaa o nihfldiscussions. insightful for Aryasetiawan Ferdi and Lorenzana, e ´ 7 GW cnee okos–ak(3 lcrnmmnu grid electron-momentum (63) Monkhorst–Pack Γ-centered o h upad23 and pump the for µm MTapoc 6) MTpoie nonperturba- a provides DMFT (67). approach DMFT + × 4 ocaatrz h atc oe fLO eper- we LCO, of modes lattice the characterize To d Cu-3 local via × eaegaeu oAtoyJ egt,Antoine Leggett, J. Anthony to grateful are We -ehadcnegdwt m hnein change rms with converged and k-mesh 4 5t 0ieain.Tecluain for calculations The iterations. 20 to ∼15 Γ rjcoso h onSa space Kohn–Sham the of projectors on fteBilunzn using zone Brillouin the of point µm NSLts Articles Latest PNAS × http://www.questaal.org. 23 o h probe. the for µm 8 unu Monte quantum | f8 of 7 the- 0 × ),

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