LETTERS https://doi.org/10.1038/s41563-018-0045-1 Collapse of superconductivity in cuprates via ultrafast quenching of phase coherence F. Boschini1,2*, E. H. da Silva Neto1,2,3,4, E. Razzoli1,2, M. Zonno1,2, S. Peli5,6, R. P. Day1,2, M. Michiardi1,2,7, M. Schneider1,2, B. Zwartsenberg1,2, P. Nigge1,2, R. D. Zhong 8, J. Schneeloch8,9, G. D. Gu8, S. Zhdanovich1,2, A. K. Mills1,2, G. Levy1,2, D. J. Jones1,2, C. Giannetti 5,6 and A. Damascelli1,2* 10,11 The possibility of driving phase transitions in low-density reported a non-zero pairing gap up to T ≈ 1.5 × Tc (refs ) even in condensates through the loss of phase coherence alone has the absence of macroscopic phase coherence. On heating for exam- far-reaching implications for the study of quantum phases of ple, high-resolution angle-resolved photoemission (ARPES) experi- matter. This has inspired the development of tools to control ments have shown pair-breaking scattering phenomena to emerge and explore the collective properties of condensate phases via sharply at Tc while the pairing gap is still open, suggesting a direct phase fluctuations. Electrically gated oxide interfaces1,2, ultra- connection between pair-breaking and the onset of the phase fluc- cold Fermi atoms3,4 and cuprate superconductors5,6, which are tuations12,13. In the same temperature range, non-equilibrium opti- characterized by an intrinsically small phase stiffness, are cal and terahertz experiments have given evidence for picosecond 6,14,15 paradigmatic examples where these tools are having a dra- dynamics dominated by phase fluctuations above Tc (refs ). matic impact. Here we use light pulses shorter than the inter- The present work is motivated by the idea that a light pulse nal thermalization time to drive and probe the phase fragility shorter than the internal thermalization time may be used to of the Bi2Sr2CaCu2O8+δ cuprate superconductor, completely manipulate the density of phase fluctuations in a high-Tc super- melting the superconducting condensate without affect- conductor independent of the number of across-gap charge excita- ing the pairing strength. The resulting ultrafast dynamics of tions. This would open the possibility of investigating a transient phase fluctuations and charge excitations are captured and regime inaccessible at equilibrium, where both phase fluctuations disentangled by time-resolved photoemission spectroscopy. and charge excitations are controlled by the same temperature This work demonstrates the dominant role of phase coherence and thus inherently locked. Here we demonstrate this concept in the superconductor-to-normal state phase transition and in the underdoped Bi2Sr2CaCu2O8+δ (Bi2212) superconductor 16,17 offers a benchmark for non-equilibrium spectroscopic inves- (Tc ~ 82 K) . Time- and angle-resolved photoemission spec- tigations of the cuprate phase diagram. troscopy (TR-ARPES) is used to evaluate the electronic spectral The value of the critical temperature (Tc) in a superconducting function that encodes information regarding the pair-breaking material is controlled by the interplay of two distinct phenomena: dynamics. We demonstrate that the pair-breaking scattering rate 12,13 18–20 the formation of electron pairs and the onset of macroscopic phase Γp, which is experimentally and microscopically associated coherence. While the pairing energy (Ep) is generally controlled by with the scattering of phase fluctuations, is indeed decoupled from the bosonic modes that mediate the electronic interactions7,8, the the dynamics of the pairing gap and across-gap charge excita- −2 21–23 macroscopic phase Θ depends on the stability of the condensate tions. At and above the critical fluence FC ≈ 15 μ J cm (refs ), against fluctuations and inhomogeneities. The energy scale rel- the increase of Γp is such that superconductivity is suppressed. evant for phase fluctuations can be expressed via the Ginzburg– Quantitatively, we observe that the non-thermal melting of the 2 * * 21–26 Landau theory as ħΩΘ = [ħ nS(0)a]/2m , where m is the effective condensate is achieved when Γp ≈ ħΩΘ. mass of the pairs, a is a characteristic length and nS(0) is the zero- TR-ARPES provides direct snapshots of the one-electron temperature superfluid density. In conventional superconductors removal spectral function A(k,ω) (ref. 27) and its temporal evolu- 28,29 Ep ≪ℏΩΘ and therefore Tc is determined solely by thermal charge tion due to the perturbation by an ultrashort pump pulse. The excitations across the superconducting gap, which act to reduce the spectral function A(k,ω) depends on both the electron self-energy number of states available for the formation of the superconducting Σ (ω) = Σ′ (ω) + iΣ′ ′ (ω) and the bare energy dispersion ϵk: condensate. In cuprate superconductors, the scenario is much more complex 1(Σω′′ ) since the small superfluid density pushes ħΩΘ down to a value that A(,k ω) =− (1) 5 ′′22′ is very close to the pairing energy : the low density of the quasi-two- π [(ωΣ−ϵk−+ωΣ)] [(ω)] dimensional condensate within the Cu–O planes depresses ħΩΘ as 5,9 low as ~15 meV in bismuth-based copper oxides . Several equilib- For a superconductor, Σ (ω) at the Fermi momentum k = kF can be rium measurements on underdoped cuprate superconductors have approximated well by 1Department of Physics & Astronomy, University of British Columbia, Vancouver, BC, Canada. 2Quantum Matter Institute, University of British Columbia, Vancouver, BC, Canada. 3Max Planck Institute for Solid State Research, Stuttgart, Germany. 4Department of Physics, University of California, Davis, CA, USA. 5Department of Mathematics and Physics, Università Cattolica del Sacro Cuore, Brescia, Italy. 6Interdisciplinary Laboratories for Advanced Materials Physics (ILAMP), Università Cattolica del Sacro Cuore, Brescia, Italy. 7Max Planck Institute for Chemical Physics of Solids, Dresden, Germany. 8Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, NY, USA. 9Department of Physics & Astronomy, Stony Brook University, Stony Brook, NY, USA. *e-mail: [email protected]; [email protected] 416 NATURE MATERIALS | VOL 17 | MAY 2018 | 416–420 | www.nature.com/naturematerials © 2018 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. NATURE MATERIALS LETTERS ab0.2 No pump τ = +0.5 ps φ = 36° No pump 1 to the quasiparticle recombination dynamics and the pairing gap +0.6 ps 21–23,30,31 Intensity (a.u.) closure . To then study the pairing gap dynamics, it is com- φ = 36° +1.4 ps + +4 ps ) mon to fit symmetrized energy distribution curves (SEDCs) at k = kF –1 = 45° 18,21,32 0 φ 0 (refs ). Although the emergence of a single peak in the SEDCs (Å y k at large enough excitation fluences in TR-ARPES has been inter- – preted as a signature of the pump-induced gap closure21,23, the com- –0.2 E = 0 meV E = 10 meV 0 prehensive analysis of our data presented in the following provides 0.4 0.5 0.4 0.5 –40 –20 020 clear evidence that a single peak in the SEDCs is instead related to –1 12,13,33 kx (Å ) Energy (meV) the filling of an almost unperturbed pairing gap . This provides cd consistency between transient and equilibrium studies, offering a 1 EDC MDC 1 0.55 EDC MDC 0.75 k = k –30 meV k = k –30 meV coherent picture of the electronic structure and its related dynamics. F F Intensity (a.u. ) = 15 meV Before proceeding to the detailed modelling and quantitative ΓS Γ = 6 meV P analysis of the data, we address the microscopic origins of the evo- lution of the transient spectral function. We emphasize those photo- induced modifications to the spectral function that are immediately ) Intensity (a.u. apparent, even at the level of visual inspection. In Fig. 1b we pres- = 11 meV = 20 meV ΓS ΓS = 0 meV Γ = 0 meV No pump ΓP τ = +0.6 ps 0 P 0 0 0 ent the temporal evolution of the low-fluence EDC at k = kF along 0 0 0 0 the off-nodal direction (φ =​ 36°), normalized to the momentum- –40 –40 –0.04 –0.04 integrated nodal EDC (both deconvoluted from the energy reso- E (meV) k–k (Å–1) E (meV) k–k (Å–1) F F lution broadening before the division, see Supplementary Section II). Without invoking controversial symmetrization, this procedure Fig. 1 | Ultrafast gap filling via enhancement of phase fluctuations. a, allows us to explore the spectral function and its dynamics both Equilibrium Fermi surface mapping (left panel) and differential (Pumpon− below and above the superconducting gap. The resulting curves in Pumpoff) iso-energy contour mapping at 10 meV above the Fermi level EF, Fig. 1b provide direct evidence for the particle–hole symmetry of 0.5 ps pump–probe delay (right panel). The integration energy range is the quasiparticle states across the superconducting gap in the near- 10 meV and kx is aligned along the Γ–Y direction. The dashed black and nodal region (that is, where pseudogap contributions are negligi- red lines in the right panel define the nodal and off-nodal cuts investigated ble34–36). Most importantly, the data in Fig. 1b reveal that the gap size in the present work (details in Supplementary Information). b, Off-nodal (peak-to-peak distance) remains almost constant over the entire EDC at k = kF (φ = 36°) normalized to momentum-integrated nodal EDC domain of time-delays measured. In contrast to this, we observe −2 (φ = 45°) at different pump–probe delays, F < FC fluence (FC ≈ 15 μ J cm ). a transient decrease and broadening of the quasiparticle peak on EDCs have been deconvoluted from the energy resolution broadening either side of the gap, leading to a filling of spectral weight inside before the division35 (details in Supplementary Information). c, Equilibrium the superconducting gap (analogous conclusions are reached by a 13 off-nodal (φ = 36°) normalized EDC at kF (left panel) and MDC at complementary analysis of the tomographic density of states , as E = − 30 meV (right panel).