Probing the lattice anharmonicity of superconducting ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ via phonon harmonics

We examine coherent phonons in a strongly driven sample of optimally-doped high temperature superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$. We observe a nonlinear lattice response of the 4.5 THz copper-oxygen vibrational mode at high excitation densities, evidenced by the observation of the phonon third harmonic and indicating the mode is strongly anharmonic. In addition, we observe how high-amplitude phonon vibrations modify the position of the electronic charge transfer resonance. Both of these results have important implications for possible phonon-driven nonequilibrium superconductivity.

Figure 1

Broadband transient reflectivity of YBCO. Wavelength resolved signal at (a) 300 and at (b) 80 K, at the maximum pump fluence. Integration of $\mathrm{\Delta }\mathrm{R}$/R performed for several probe wavelengths, from 650 up to 750 nm is present in (c) and (d), for different pump fluences ($\mathrm{mJ}/{\mathrm{cm}}^2$), an offset is added to the signals to clarify.

Figure 2

Fast Fourier transform amplitude of the transient reflectivity signal after subtracting the electronic background contribution. Different pump fluences have been plotted with an offset added to clarify, from $\sim 4.5$ up to 15 $\mathrm{mJ}/{\mathrm{cm}}^2$ at 300 K (a) and at 80 K (b). The signals were calculated by adding the contributions of a broadband of wavelengths from the probe light, from 650 up to 750 nm. Inset in (b) is a zoom to show the third harmonic of the Cu vibration mode at 4.5 THz. Broadband resolved of the FFT amplitude is shown at 300 K (c) and at 80 K (d); dashed line marks the integration range of wavelengths.

Figure 3

Fluence dependence of the third harmonic signal at 13.9 THz after background subtraction (blue circles) and cubic fit (dashed line). See Supplemental Material Ref. [24] for details of the background subtraction.

Figure 4

Dependence on the amplitude and frequency of the two found coherent phonons with the pump fluence. The FFT peak amplitude is plotted at 300 K (circles), and at 80 K (squares), for the barium (a) and for the cooper mode (b). Gray solid lines are the linear fits of the experimental data. Central frequency of every mode versus pump intensity is shown for Ba (c) and for Cu (d) for the two temperatures studied. Solid lines follow the behavior of the data according to Eq. (1).

Figure 5

Probe wavelengths' dependence of the FFT peak amplitude for the barium [(a) 300 K, (c) 80 K] and copper [(b) 300 K, (d) 80 K] modes. Simulated reflectivity changes if the coherent phonon modulates the oscillator strength of the Cu-O charge transfer resonance (e) or resonance position (f). In both cases the oscillator strength or resonant energy is increased or decreased by an amount $\mathrm{\Delta }$ [24].

Figure 6

Time-dependent reflectivity at 80 K, and 14.4 $\mathrm{mJ}/{\mathrm{cm}}^2$ measured at 580 nm and 735 nm. The inset focuses on the oscillating component plotted on the same $x$ axis as the main graph by offset in $y$, with the data (square markers) fitted by the sum of two oscillations at 3.5 and 4.5 THz as described in the main text.