Localized vibrations in superconducting $\mathrm{YB}{\mathrm{a}}_{2}\mathrm{C}{\mathrm{u}}_{3}{\mathrm{O}}_{7}$ revealed by ultrafast optical coherent spectroscopy

Localized vibrations in superconducting $YB a_{2} C u_{3} O_{7}$ revealed by ultrafast optical coherent spectroscopy

Fabio Novelli, Gianluca Giovannetti, Adolfo Avella, Federico Cilento, Luc Patthey, Milan Radovic, Massimo Capone, Fulvio Parmigiani, and Daniele Fausti

Phys. Rev. B 95, 174524 – Published 31 May 2017

Abstract

The interaction between phonons and high-energy excitations of electronic origin in cuprates and their role in the superconducting mechanisms is still controversial. Here we use coherent vibrational time-domain spectroscopy together with density functional and dynamical mean-field theory calculations to establish a direct link between the $c$ -axis phonon modes and the in-plane electronic charge excitations in optimally doped $YB a_{2} C u_{3} O_{7}$ . The nonequilibrium Raman tensor is measured by means of the broadband “coherent-phonon” response in pump-probe experiments and is qualitatively described by our model using density functional theory in the frozen-phonon approximation plus single-band dynamical mean-field theory to account for the electronic correlations. The major outcome of our experimental and theoretical study is to establish the link between out-of-plane copper ion displacements and the in-plane electronic correlations, and to estimate at a few unit cells the correlation length of the associated phonon mode. The approach introduced here could help in revealing the complex interplay between fluctuations of different nature and spatial correlation in several strongly correlated materials.

Received 10 February 2017
Revised 27 March 2017

DOI:https://doi.org/10.1103/PhysRevB.95.174524

Physics Subject Headings (PhySH)

Density functional theory Mean field theory Pump-probe spectroscopy Time-resolved infrared spectroscopy Transient absorption spectroscopy

Condensed Matter, Materials & Applied PhysicsNonlinear Dynamics

Authors & Affiliations

Fabio Novelli^1,2, Gianluca Giovannetti³, Adolfo Avella^4,5,6, Federico Cilento², Luc Patthey^7,8, Milan Radovic^7,8, Massimo Capone³, Fulvio Parmigiani^1,2,9, and Daniele Fausti^1,2,*

¹Department of Physics, Università degli Studi di Trieste, 34127 Trieste, Italy
²Sincrotrone Trieste SCpA, 34127 Basovizza, Italy
³CNR-IOM Democritos National Simulation Center and Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy
⁴Dipartimento di Fisica “E.R. Caianiello”, Universitá degli Studi di Salerno, I-84084 Fisciano (SA), Italy
⁵CNR-SPIN, UoS di Salerno, I-84084 Fisciano (SA), Italy
⁶Unitá CNISM di Salerno, Universitá degli Studi di Salerno, I-84084 Fisciano (SA), Italy
⁷Swiss Light Source, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland
⁸SwissFEL, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland
⁹International Faculty, University of Cologne, Germany

^*daniele.fausti@elettra.eu

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Vol. 95, Iss. 17 — 1 May 2017

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Figure 1
Cartoon of “delocalized” (a) vs “localized” (c) $c$ -axis phonon modes. Blue, red, yellow, and green spheres represent copper, oxygen, barium, and yttrium ions, respectively. Increasing the excitation density in a pump and probe experiment is expected to drive a larger atomic displacement for a delocalized phonon mode (b), while an increased density of similarly displaced sites for a localized phonon (d).
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Figure 2
(a) Transient reflectivity representative of the normal (red) and superconducting phase (black) at $E_{probe} = 2.2$ eV for low pump fluence. (b) Relative variation of the “incoherent” part of the reflectivity for a pump-probe delay of 0.3 ps as a function of temperature, for $Φ = 20 μ J / c m^{2}$ . (c) Same quantity as (b) but versus the pump fluence at $T = 5 K$ . In both (b) and (c) the dotted line marks zero, which is the result one would expect for no pump-induced changes to the reflectivity. (d) Amplitude of the “coherent” contribution to the transient reflectivity as a function of frequency for $T = 5$ K and $T = 120$ K at low fluence. (e) Sketch of the displacements associated with the Ba (3.5 THz) and Cu (4.5 THz) ions.
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Figure 3
(a) Amplitude of the coherent transient reflectivity (colors) at different probe energies, at $T = 5$ K, and for $Φ = 20 μ J / c m^{2}$ pump fluence. The black line is a representative cut at $E_{probe} = 2.2$ eV. (b) Amplitude (colors) in the frequency domain obtained by Fourier-transforming the time traces in (a). (c) Amplitude of the two relevant vibrational modes versus probe energy. (d) Representative traces [dashed lines in (b)] with an offset added for clarity.
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Figure 4
(a) Temperature-dependent coherent response at 4.5 THz averaged at probe energies within 2.1 eV and 2.3 eV. (b) Fluence-dependent coherent response at 4.5 THz. (c) Spectrum of the 4.5 THz oscillation as a function of temperature, normalized for the sake of comparison. (d) Normalized fluence-dependent coherent response at 4.5 THz and $T = 5$ K.
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Figure 5
(a) Density of states obtained in DMFT (red), compared with the DFT result (dashed black). (b) DMFT optical conductivity $σ_{1} (ω)$ . (c) Calculated $σ_{1} (ω)$ changes in the visible range, driven by the vibrational mode at 4.5 THz for two exemplary displacement amplitudes ( $d_{1}$ and $d_{2}$ ). (d) Energy-dependent amplitude of the Cu coherent response measured in pump-probe experiments.
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Figure 6
(a) Amplitude of the coherent response at 3.5 THz, associated with the Ba mode, averaged between 2.1 eV and 2.3 eV and normalized on the Cu response [Fig. 4]. (b) Similarly normalized Ba coherence versus fluence. In (c) we show the spectral response as a function of temperature, and in (d) the one versus pump fluence. In panels (c) and (d) most spectra maxima are normalized to 1 to allow for a visual comparison of the changing energy dispersions. This is done properly for all curves except the ones at high temperature in panel (c) (green and cyan) where the 3.5 THz mode is absent and the corresponding spectral functions are below the noise level.
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Physical Review B

covering condensed matter and materials physics

Localized vibrations in superconducting $YB a_{2} C u_{3} O_{7}$ revealed by ultrafast optical coherent spectroscopy

Fabio Novelli, Gianluca Giovannetti, Adolfo Avella, Federico Cilento, Luc Patthey, Milan Radovic, Massimo Capone, Fulvio Parmigiani, and Daniele Fausti

Phys. Rev. B 95, 174524 – Published 31 May 2017

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Physical Review B

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Localized vibrations in superconducting YBa2Cu3O7 revealed by ultrafast optical coherent spectroscopy

Fabio Novelli, Gianluca Giovannetti, Adolfo Avella, Federico Cilento, Luc Patthey, Milan Radovic, Massimo Capone, Fulvio Parmigiani, and Daniele Fausti

Phys. Rev. B 95, 174524 – Published 31 May 2017

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Localized vibrations in superconducting $YB a_{2} C u_{3} O_{7}$ revealed by ultrafast optical coherent spectroscopy