Pump Frequency Resonances for Light-Induced Incipient Superconductivity in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$

Optical excitation in the cuprates has been shown to induce transient superconducting correlations above the thermodynamic transition temperature $T_C$, as evidenced by the terahertz-frequency optical properties in the nonequilibrium state. In ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$, this phenomenon has so far been associated with the nonlinear excitation of certain lattice modes and the creation of new crystal structures. In other compounds, like ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$, similar effects were reported also for excitation at near-infrared frequencies, and were interpreted as a signature of the melting of competing orders. However, to date, it has not been possible to systematically tune the pump frequency widely in any one compound, to comprehensively compare the frequency-dependent photosusceptibility for this phenomenon. Here, we make use of a newly developed nonlinear optical device, which generates widely tunable high-intensity femtosecond pulses, to excite ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$ throughout the entire optical spectrum (3–750 THz). In the far-infrared region (3–24 THz), signatures of nonequilibrium superconductivity are induced only for excitation of the 16.4- and 19.2-THz vibrational modes that drive $c$-axis apical oxygen atomic positions. For higher driving frequencies (25–750 THz), a second resonance is observed around the charge transfer band edge at approximately 350 THz. These findings highlight the importance of coupling to the electronic structure of the ${\mathrm{CuO}}_2$ planes, mediated either by a phonon or by charge transfer.

Popular Summary

To control high-temperature superconductors on ultrafast timescales, researchers have been turning to optical stimulation with far-infrared laser pulses, enabling the observation of transient superconducting correlations above the thermodynamic transition temperature. In the layered copper oxide ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$, such “incipient photoinduced superconductivity” has been associated with the large-amplitude excitation of certain optically active vibrational modes. However, similar effects in other compounds have been reported also for excitation at visible wavelengths, far from any vibrational resonance. To date, researchers have not been able to comprehensively compare the frequency-dependent photosusceptibility for this phenomenon because of a lack of a suitable optical source. Here, we present such a source and use it to probe the nature of photoinduced superconductivity in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$.

Our newly developed optical device generates widely tunable high-intensity femtosecond pulses. We use these pulses to excite ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$ across a broad spectrum of frequencies, from 3 to 750 THz. In the far-infrared region (3–25 THz), we find signatures of nonequilibrium superconductivity only with the excitation of two specific vibrational modes that involve motions of the apical oxygen atoms (those above or below the superconducting ${\mathrm{CuO}}_2$ crystallographic planes). However, a second resonance is also reported here for excitation frequencies in the visible section of the electromagnetic spectrum, peaking at approximately 350 THz.

Our findings suggest that a coupling of the incident field to the electronic structure of the copper-oxygen planes—either mediated by a phonon vibration or by direct charge transfer—might be the determining factor to induce transient superconductivity in this compound.

Figure 1

Crystal structure and equilibrium terahertz optical properties of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$. (a) Crystallographic unit cell of orthorhombic ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$. Bilayers of conducting ${\mathrm{CuO}}_2$ planes, stacked along the $c$ direction, form Josephson junctions in the superconducting state. (b) $c$-axis terahertz-frequency optical properties in the equilibrium superconducting ($T<T_C$, red curves) and normal ($T>T_C$, black curves) state. The real [${\sigma }_1(\omega )$] and imaginary [${\sigma }_2(\omega )$] parts of the optical conductivity are displayed along with the normal-incidence reflectivity $R(\omega )$ (the same data as those reported in Refs. [1, 2, 3]).

Figure 2

Transient $c$-axis optical conductivity induced by apical oxygen excitation above $T_C$. (a) Schematics of the generation processes for broadband and narrow-band excitation pulses. The signal outputs (NIR1 and NIR2) of two parallel optical parametric amplifiers were directly sent to a nonlinear crystal to generate broadband pump pulses (relative bandwidth $\mathrm{\Delta }\nu /\nu \sim 20\%$) in a difference frequency generation (DFG) process. For narrow-band generation ($\mathrm{\Delta }\nu /\nu <10\%$), the two signal outputs were linearly chirped before the DFG process (see Supplemental Material [20] for further details). (b) Equilibrium $c$-axis optical conductivity ${\sigma }_1(\omega )$ of ${\mathrm{YB}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$ at 100 K ($T>T_C$, red solid line), along with the frequency spectra of the terahertz probe (gray), broadband pump (light blue), and 19.2-THz narrowband pump (dark blue) pulses. (c) Color plots: Frequency- and time-delay-dependent complex optical conductivity measured after broadband excitation at $T=100\mathrm{K}$. Upper: Corresponding ${\sigma }_1(\omega )$ and ${\sigma }_2(\omega )$ line cuts displayed at equilibrium (gray lines) and at the peak of the coherent response ($\tau \simeq 0.5\mathrm{ps}$ time delay, blue circles). Black lines are fits to the transient spectra with a model describing the response of a Josephson plasma (see Supplemental Material [20] for details on the fitting procedure). For comparison, we also report the equilibrium ${\sigma }_2(\omega )$ measured in the superconducting state at $T=10\mathrm{K}$ (red line). Side: Frequency-integrated dissipative [$\int \mathrm{\Delta }{\sigma }_1(\omega )d\omega$] and coherent [${\omega {\sigma }_2(\omega )|}_{\omega \to 0}$] responses, as a function of the pump-probe time delay. The delay corresponding to the spectra reported in the top ($\tau \simeq 0.5\mathrm{ps}$) is indicated by a dashed line. (d) The same quantities as in (c), measured for narrow-band excitation at 19.2 THz.

Figure 3

Transient $c$-axis optical response induced by mode-selective phonon excitations above $T_C$. (a) Equilibrium $c$-axis optical conductivity ${\sigma }_1(\omega )$ of ${\mathrm{YB}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$ at 100 K ($T>T_C$, red solid line), along with the frequency spectra of the terahertz probe (gray) and of different narrow-band pump pulses, tuned to be resonant with four different optical phonons at 4.2, 10.1, 16.4, and 19.2 THz. The insets sketch the atomic motions related to each of these modes, with ${\mathrm{CuO}}_2$ layers highlighted in gray and transparency applied to quasistationary atoms (see Fig. 1 for the atom labeling). (b),(c) Complex optical conductivity ${\sigma }_1(\omega )+i{\sigma }_2(\omega )$ measured before (gray lines) and at $\tau \simeq 0.5\mathrm{ps}$ time delay (colored circles) after resonant stimulation of the phonon modes shown in (a) with $8\mathrm{mJ}/{\mathrm{cm}}^2$ pump fluence (corresponding to approximately $3\mathrm{MV}/\mathrm{cm}$ peak electric field). The black solid lines are fits to the transient spectra performed with either a simple Drude-Lorentz model for normal conductors [(b)1, (b)2, (c)1, (c)2] or a model describing the response of a Josephson plasma [(b)3, (b)4, (c)3, (c)4] (see Supplemental Material [20] for more details on the fitting procedure).

Figure 4

Evolution of the photoinduced response at $T=100\mathrm{K}$ as a function of the excitation frequency. Distinct quantities, extracted from the transient optical conductivity at $\tau \simeq 0.5\mathrm{ps}$ time delay, are displayed as a function narrow-band excitation frequency: (a) the total, frequency integrated change in optical conductivity $\int |\mathrm{\Delta \sigma }(\omega )|d\omega$, (b) the frequency integrated dissipative response $\int {\mathrm{\Delta \sigma }}_1(\omega )d\omega$, and (c) the superconducting response represented by the low-frequency limit ${\omega {\sigma }_2(\omega )|}_{\omega \to 0}$. The red shaded region represents the frequency range around the apical oxygen phonon modes, where a transient superconductinglike response could be identified. Horizontal dashed lines indicate the thermally induced increase in $\int {\sigma }_1(\omega )d\omega$ when heating the sample from 100 to 200 K (black) and the equilibrium superfluid density ${\omega {\sigma }_2(\omega )|}_{\omega \to 0}$ measured at $T=10\mathrm{K}$ (red). All data were taken with a pump fluence of $8\mathrm{mJ}/{\mathrm{cm}}^2$ (corresponding to approximately $3\mathrm{MV}/\mathrm{cm}$ peak electric field).

Figure 5

Temperature dependence of the dissipative and superconductinglike responses. Temperature-dependent (a) dissipative response $\int {\mathrm{\Delta \sigma }}_1(\omega )d\omega$ and (b) superconductinglike response ${\omega {\sigma }_2(\omega )|}_{\omega \to 0}$, measured for resonant narrow-band excitation of the lowest-frequency (4.2 THz) and highest-frequency (19.2 THz) phonon modes. The dashed lines are guides to the eye. As in Fig. 4, all data were taken with a pump fluence of $8\mathrm{mJ}/{\mathrm{cm}}^2$ (corresponding to approximately $3\mathrm{MV}/\mathrm{cm}$ peak electric field).

Figure 6

Transient $c$-axis optical response induced by high-energy charge excitation at $T=100\mathrm{K}$. (a),(b) Complex optical conductivity ${\sigma }_1(\omega )+i{\sigma }_2(\omega )$, measured at equilibrium (gray) and at $\tau \simeq 0.5$ ps time delay (colored circles) after excitation at three different pump wavelengths with approximately $8\mathrm{mJ}/{\mathrm{cm}}^2$ pump fluence. The black solid lines are fits to the transient spectra performed with either a simple Drude-Lorentz model for normal conductors [(a)1, (b)1] or a model describing the response of a Josephson plasma [(a)2, (b)2, (a)3, (b)3] (see Supplemental Material [20] for more details on the fitting procedure). (c) Pump frequency dependence of the superconducting response, represented by the low-frequency limit ${\omega {\sigma }_2(\omega )|}_{\omega \to 0}$ (red circles). The equilibrium optical conductivity ${\sigma }_1^{\text{equil}}({\omega }_{\text{pump}})$ is shown as a blue line. (d) Normalized response ${\omega {\sigma }_2(\omega )|}_{\omega \to 0}/{\sigma }_1^{\text{equil}}({\omega }_{\text{pump}})$ (red circles). The gray line is a multi-Lorentzian fit. All data for ${\omega }_{\text{pump}}<300\mathrm{THz}$ were taken with constant pump fluence ($8\mathrm{mJ}/{\mathrm{cm}}^2$) and peak electric field ($3\mathrm{MV}/\mathrm{cm}$) at a fixed pulse duration of $600\mathrm{fs}$. At ${\lambda }_{\text{pump}}=800\mathrm{nm}$ and ${\lambda }_{\text{pump}}=400\mathrm{nm}$, for which the pump pulses were $100\mathrm{fs}$ long, we report data points taken at both $8\mathrm{mJ}/{\mathrm{cm}}^2$ (approximately $7\mathrm{MV}/\mathrm{cm}$, red circles) and $1.5\mathrm{mJ}/{\mathrm{cm}}^2$ (approximately $3\mathrm{MV}/\mathrm{cm}$, empty circles), keeping either the excitation fluence or peak electric field at the same values.