Quasiparticle dynamics and in-plane anisotropy in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ near the onset of superconductivity

We report on an infrared study of carrier dynamics within the ${\mathrm{CuO}}_2$ planes in heavily underdoped detwinned single crystals of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$. In an effort to reveal the electronic structure near the onset of superconductivity, we investigate the strong anisotropy of the electromagnetic response due to an enhancement of the scattering rate along the $a$ axis. We propose that the origin of this anisotropy is related to a modulation of the electron density within the ${\mathrm{CuO}}_2$ planes.

Figure 1

$T$-dependent $R\left(\omega \right)$ for (a) $y=6.43$ and (b) $y=6.35$. Inset in (a) shows dc resistivity curves for $y=6.43$ and 6.35 crystals.

Figure 2

$T$-dependent ${\sigma }_1\left(\omega \right)$ of the $y=6.43$ YBCO along (a) the $a$ axis and (b) the $b$ axis. The circle and the square symbols represent the positions of MIR resonances and CT excitations, respectively. In the inset in (b), the ${\sigma }_1\left(\omega \right)$ with the phonon subtracted are used for the Drude fitting (the dotted lines). Note that the fits are adequate for the frequency range exceeding $\Gamma$ parameters. The symbols represent the dc resistivity values.

Figure 3

$T$-dependent ${\sigma }_1\left(\omega \right)$ of the $y=6.35$ YBCO in (a) the $a$ axis and (b) the $b$ axis. The circle and the square symbols represent the positions of the MIR resonances and the CT excitations, respectively. In the inset (b), the ${\sigma }_1\left(\omega \right)$ with the phonon subtracted are used for the Drude fitting (the dotted lines). The symbols represent the dc resistivity values.

Figure 4

Top panels: $T$-dependent $N_{\mathrm{eff},b}\left(\omega \right)∕N_{\mathrm{eff},a}\left(\omega \right)$ at (a) $y=6.30$ and (b) $y=6.43$. The square, the circle, and the star symbols correspond to the measured ${\sigma }_{\mathrm{dc},b}∕{\sigma }_{\mathrm{dc},a}$ values at 20, 80, and $150\mathrm{K}$, respectively. Low panels display the evolution of the anisotropy of the phonon modes. (c) At $293\mathrm{K}$, the frequencies of phonons positioned at the highest frequency at $y=6.30$, 6.35, 6.40, 6.43, and 6.65. (d) $y$ dependences of ${\omega }_{\mathrm{ph},a}∕{\omega }_{\mathrm{ph},b}$ and ${\left[{\sigma }_b∕{\sigma }_a\right]}_{\mathrm{optical}}\equiv {\lim }_{\omega \to 0}{\sigma }_{1,b}∕{\sigma }_{1,a}$. For $y=6.65$, we choose the value at $65\mathrm{K}$ just above $T_c$. In the inset of (b), the dotted and the solid lines represent the ${\rho }_a∕{\rho }_b$ curves at $y=6.43$ and $y=6.35$, respectively. The square $\left(y=6.43\right)$ and the circle $\left(y=6.35\right)$ symbols correspond to the $T$-dependent ${\Gamma }_a∕{\Gamma }_b$ values multiplied by 1.05 and 1.1, respectively.