Amplification of Superconducting Fluctuations in Driven ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$

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Amplification of Superconducting Fluctuations in Driven ${YBa}_{2} {Cu}_{3} O_{6 + x}$

A. von Hoegen, M. Fechner, M. Först, N. Taherian, E. Rowe, A. Ribak, J. Porras, B. Keimer, M. Michael, E. Demler, and A. Cavalleri

Phys. Rev. X 12, 031008 – Published 13 July 2022

Abstract

In cuprate high- $T_{c}$ superconductors, resonant excitation of certain lattice vibrations has been shown to induce transient terahertz reflectivity features suggestive of nonequilibrium superconductivity above the critical temperature $T_{c}$ . A microscopic mechanism for these observations is still lacking. Here, time-resolved measurements of scattering-angle- and polarization-dependent second-harmonic generation in driven ${YBa}_{2} {Cu}_{3} O_{6 + x}$ reveal a three-order-of-magnitude amplification of a 2.5-THz electronic mode, which is unique because of its symmetry, momentum, and temperature dependence. A theory for amplification of finite-momentum Josephson plasma polaritons, which are assumed to be well formed below $T_{c}$ but incoherent throughout the pseudogap phase, explains all these observations. A theoretical solution for the Fresnel-Floquet reflection that starts from the coherently oscillating Josephson plasma polaritons provides a possible mechanism for the nonequilibrium superconductorlike terahertz reflectivity reported earlier. Beyond the immediate case of cuprates, this work underscores the role of nonlinear mode mixing to amplify fluctuating modes above the transition temperature in a wide range of materials.

Received 7 March 2022
Revised 24 May 2022
Accepted 10 June 2022

DOI:https://doi.org/10.1103/PhysRevX.12.031008

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Phonons Superconducting fluctuations Superconductivity

High-temperature superconductors

Photoexcitation Ultrafast pump-probe spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. von Hoegen¹, M. Fechner¹, M. Först¹, N. Taherian¹, E. Rowe¹, A. Ribak¹, J. Porras², B. Keimer², M. Michael³, E. Demler³, and A. Cavalleri^1,4,*

¹Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
²Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
³Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
⁴Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom

^*andrea.cavalleri@mpsd.mpg.de

Popular Summary

Enhancing desirable functional properties, such as magnetism, ferroelectricity, or superconductivity, of quantum materials is a major goal of modern condensed-matter physics. Optical excitation has proven especially fruitful in this regard. One of the most striking and yet unclear demonstrations of this class of phenomena is “light-induced superconductivity” in high-temperature cuprate superconductors, observed far above the equilibrium critical temperature when certain lattice vibrations (optical phonons) are driven to large amplitude by intense midinfrared light pulses. Here, we use time-resolved nonlinear optical spectroscopy to explore this phenomenon in the family of underdoped bilayer ${YBa}_{2} {Cu}_{3} O_{6 + x}$ .

We find that the driven optical phonons amplify Josephson plasma waves—collective oscillations of superconducting Cooper pairs of electrons between the ${CuO}_{2}$ layers of this material. Importantly, the amplification was observed throughout the pseudogap phase, a regime of unusual electronic properties that are often connected to fluctuating superconductivity, a precursor to the well-defined superconducting state below the critical temperature.

This result confirms in a new way that superconducting fluctuations exist throughout the pseudogap phase. In addition, we provide a theory for the amplification of these fluctuations and, connected to it, a theory for the previously reported signatures of light-induced superconductivity in the transient terahertz reflectivity.

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Vol. 12, Iss. 3 — July - September 2022

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Figure 1
(a) Schematic of the pump-probe geometry. The 800-nm near-IR probe (gray) and CEP stable mid-IR (MIR) pump (yellow) pulses were polarized along the ${YBa}_{2} {C u}_{3} O_{6.48}$ crystal’s $c$ -axis and perpendicular to the ${CuO}_{2}$ planes. The resonantly excited apical oxygen vibrations are shaded in yellow. Light at the fundamental (gray arrow) and second-harmonic (red arrow) frequency is reflected from the sample. (b) Time-resolved changes of the linear reflectivity at 800-nm wavelength, showing coherent modulations due to fully symmetric Raman phonon modes. (c) Time-resolved second-harmonic intensity at 400-nm wavelength (red circles) and a numerical fit to the nonoscillatory component of the signal (dashed line). The data in (b) and (c) are shown for 5-K base temperature and 7-MV/cm peak excitation field.
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Figure 2
(a),(b) Coherent SH signal at the lowest excitation field ( $E = 0.3 MV / cm$ ) and the corresponding Fourier amplitude spectrum at $T = 5 K$ , well below the critical temperature $T_{c} = 48 K$ . The high-frequency oscillations at 17 and 20 THz (yellow peaks) are coherent symmetry breaking apical oxygen vibrations, resonantly driven by the excitation pulse. (c),(d) Coherent SH response at higher excitations fields ( $E = 0.5 MV / cm$ ) at the same temperature. The peaks at $ν_{1} = 2.5 THz$ and $ν_{2} = 14.5 THz$ (red and magenta) are ascribed to coherent oscillations of Josephson plasma waves. (e),(f) The coherent SH response at significantly stronger excitations ( $E = 7 MV / cm$ ) show the same coherences of (c) and (b), with additional modes drawn as gray peaks. These additional peaks are dominated by those at 8.6 and 10.5 THz and label additional phonons nonlinearly coupled to the resonantly driven lattice modes. (g) Measured amplitude of the amplified low-frequency JPP $J_{1}$ and the amplified phonon amplitude $Q_{amplified}$ plotted as a function of the driven apical oxygen vibration amplitude $Q_{drive}$ . All quantities were extracted from the same time trace, for different strengths of the midinfrared excitation field. The dashed line is an exponential fit $A (Q_{drive}) = a \cdot (e^{α Q_{drive} - β} - 1)$ to the data, where the gain factor $α$ is determined by the strength of the coupling between the driven phonon and the JPP and $β > 0$ is the amplification threshold. Error bars represent the standard deviation $σ$ of the amplitudes extracted by numerical fits. (h) Full temperature dependence of the JPP peaks in (d) (shaded area) for ${YBa}_{2} {Cu}_{3} O_{6.48}$ (red) and ${YBa}_{2} {Cu}_{3} O_{6.65}$ (dark red). The lines are fits to the data with a mean-field approach $\propto \sqrt{1 - T / T^{'}}$ , yielding $T^{'} = 380 K$ for ${YBa}_{2} {Cu}_{3} O_{6.48}$ and $T = 280 K$ for ${YBa}_{2} {Cu}_{3} O_{6.65}$ . The dashed line is the temperature dependence of the equilibrium low-frequency Josephson plasma resonance in ${YBa}_{2} {Cu}_{3} O_{6.5}$ , which disappears at $T_{c}$ . (i) Temperature dependence of the amplitude of the nonlinearly coupled infrared active phonons at 8.5 and 10 THz. Their temperature dependence from equilibrium infrared measurements in ${YBa}_{2} {Cu}_{3} O_{6.5}$ , taken from Ref. [28], is shown as a dashed line. The data in (h) and (i) were recorded at an excitation peak field of $\sim 7 MV / cm$ . Error bars represent the standard deviation $σ$ of the amplitudes obtained by repeating the experiment under equivalent conditions.
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Figure 3
(a) Schematic of the SH polarimetry geometry. The polarization angle $φ$ of 800-nm near-infrared probe pulses (gray) is controlled by rotating a $λ / 2$ waveplate. The reflected second-harmonic light (red arrow) passes through an analyzer to measure the different polarization components individually. (b) SH signal as a function of polarization angle and pump-probe time delay, measured at room temperature. (c)–(e) Normalized polarimetry signal of the driven phonons (yellow dots), amplified phonons (gray dots), and amplified JPPs (red and blue dots) for an analyzer oriented along the crystal’s $c$ axis, at one time delay $t = 150 fs$ . The SH polarimetry signal of the two sets of phonons can be reproduced by a fit to a second-harmonic tensor with $m m 2$ point group symmetry (dashed line) and the phase of the oscillations is polarization angle $φ$ independent. The polarimetry signal of the amplified JPP agrees with a fit to a point group of lower symmetry (dashed line), in which at least two mirrors are lost. The phase of the coherent oscillations is periodically modulated with polarization angle $φ$ , indicated by the red and blue color coding. The SH polarimetry data were recorded at room temperature with a peak field strength of $\sim 5 MV / cm$ .
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Figure 4
(a) Schematic of the collinear geometry, where pump and probe beams are aligned collinear to excite the sample at an incidence angle $α$ to the surface normal. The specular linear reflection at 800 nm (gray arrow) obeys Snell’s law and leaves the sample with the same angle $α$ . A finite-momentum transfer, due to scattering of propagating modes, appears as a deflection $Δ θ$ from the specular deflection (red arrows). (b)–(d) Momentum distribution of the driven phonons, amplified phonons, and amplified JPPs, measured at room temperature. Panel (d) shows the raw data (light red) together with deconvolved data (dark red), using the measured Gaussian profile of the $q = 0$ pump electric field induced SH response. The gray shaded areas denote the maximum accessible momentum of the experiment. For all the raw data in (b)–(d), error bars represent the standard deviation $σ$ of the amplitudes extracted from numerical fits to the time-resolved second-harmonic intensity changes. The error bars of the deconvolved data (d) are determined from the deviation of the least squares fit, used in the deconvolution, to the raw data points (see Supplemental Material [24]). The data were recorded at room temperature with a peak field strength of $\sim 5 MV / cm$ .
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Figure 5
(a) Dispersion of the interbilayer ( $J_{1}$ ) and intrabilayer ( $J_{2}$ ) JPP modes along the in-plane momenta $q_{x}$ and $q_{y}$ in ${YBa}_{2} {Cu}_{3} O_{6.5}$ . The red lines are a cut through the $q_{y} = 0$ plane. The apical oxygen phonon mode at 17 THz (yellow) does not disperse along either direction. The three-wave scattering process is sketched as red and blue arrows and results from a numerical simulation in response to the resonant drive of the apical oxygen phonon at $q = 0$ are shaded in the same colors. The response vanishes along $q_{y}$ , parallel to the light propagation direction. (b) Detailed insight into the simulation results along $q_{x}$ for $q_{y} = 0$ . The driven phonon with zero momentum excites a pair of JPPs, $J_{1}$ and $J_{2}$ , with opposite wave vectors $q_{JPP}$ and frequencies that add up to the phonon frequency. The two processes for mirrored momentum transfer are shown as red and blue arrows, respectively. (c) Amplitude of the JPPs obtained integrating along the vertical frequency axis of (b). The amplitude is zero for $q_{x} = 0$ , and peaks at $q_{x} = \pm 200 {cm}^{- 1}$ . (d) Sketch of the two JPPs at $q = 0$ , with the supercurrents oscillating in phase ( $J_{1}$ ) or out of phase ( $J_{2}$ ) for the low- and high-frequency mode, respectively. The thicknesses of the arrows indicate the supercurrent strengths within and between the bilayers. (e) Simulated excitation-strength dependence (dashed line) of the low-frequency 2.5-THz oscillations, together with the experimental data (dots) from Fig. 2. (f),(g) Sketch of the real-space symmetries of the finite-momentum amplified JPP ( $m$ or lower) and the driven apical oxygen vibration ( $m m 2$ ). The in-plane currents (black arrows) and the resulting finite-momentum JPP (red and magenta lines) break the $x, z$ and $y, z$ mirror planes. The optical $B_{1 u}$ -symmetry phonons break the $x, y$ mirror plane only.
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Figure 6
(a) Two counterpropagating JPPs with in-plane momentum $q_{JPP}$ periodically modulate the superconducting order parameter $θ (x, t)$ along the $x$ axis. (b) Resulting spatial and temporal (shaded gray) modulation of the superfluid density $ρ_{s} (x, t)$ around its equilibrium value $ρ_{s, 0}$ . The zero-momentum temporal modulation proceeds at twice the Josephson plasma frequency $2 Ω (q_{JPP})$ . (c) Frequency-momentum diagram of the parametric amplification that drives the terahertz emission. The two counterpropagating JPPs (red and blue shaded regions) add in energy and momentum to emit two $q_{x} = 0 THz$ photons, each of frequency $Ω (q_{JPP})$ . (d),(e) Calculated photoinduced (red) and equilibrium (gray) terahertz reflectivity below $T_{c}$ and the normalized reflectivity changes $Δ R (ω, t) / R_{0}$ , respectively. The finite-momentum JPP induces a second plasma edge at a frequency close to $Ω (q_{JPP})$ and overall enhancement of the reflectivity above the equilibrium plasma edge. (f),(g) Calculated photoinduced (red) and equilibrium (gray) terahertz reflectivity above $T_{c}$ and the normalized reflectivity changes $Δ R (ω, t) / R_{0}$ , respectively. Excitation of the apical oxygen vibration leads to the appearance of a plasma edge at a frequency close to $Ω (q_{JPP})$ , which is clearly visible in the normalized reflectivity changes $Δ R (ω, t) / R_{0}$ . Panels (h)–(k) show the same features, observed experimentally in time-resolved terahertz reflectivity measurements after resonant excitation of apical oxygen oscillations (Ref. [14]).
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Physical Review X

Amplification of Superconducting Fluctuations in Driven YBa2Cu3O6+x

A. von Hoegen, M. Fechner, M. Först, N. Taherian, E. Rowe, A. Ribak, J. Porras, B. Keimer, M. Michael, E. Demler, and A. Cavalleri

Phys. Rev. X 12, 031008 – Published 13 July 2022

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Amplification of Superconducting Fluctuations in Driven ${YBa}_{2} {Cu}_{3} O_{6 + x}$