Micro-Raman evidence for topological charge order across the superconducting dome of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$

The doping dependence of the micro-Raman spectra of high-quality ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ microcrystals with $x=0.0\text{–}0.45$ has been investigated in the region $10\text{–}300\mathrm{K}$. The phonon at $\sim 100{\mathrm{cm}}^{-1}$ of the orthorhombic phase shows a classical soft-mode behavior up to $x=0.17$, supporting its correlation with the low-temperature orthorhombic to high-temperature tetragonal transition. In the $xx\text{−}yy$ polarization spectra of the superconducting concentrations new modes at $\sim 150$ and $370{\mathrm{cm}}^{-1}$ related to the symmetry breaking and a broad band at $\sim 280{\mathrm{cm}}^{-1}$ are attributed to the charge ordering at temperatures well above $T_c$. At all temperatures studied a correlation has been found between the doping dependence of the transition temperature and the intensity of the bands at $\sim 150$, $\sim 280$, and $\sim 370{\mathrm{cm}}^{-1}$, the intensity of the $\mathrm{La}∕\mathrm{Sr}$ mode, and the asymmetry of the apex phonon.

Figure 1

Typical Raman spectra for selected temperatures for the $x=0.03$ (a), $x=0.092$ (b), $x=0.125$ (c), $x=0.17$ (d), and $x=0.24$ (e) samples in the $y\left(zz\right)\overline{y}$ scattering geometry using the 514.5-nm excitation wavelength.

Figure 2

Typical Raman spectra for selected temperatures for the $x=0.03$ (a), $x=0.092$ (b), $x=0.125$ (c), $x=0.17$ (d), and $x=0.24$ (e) samples in the $y\left(xx\right)\overline{y}$ [or $x\left(yy\right)\overline{x}$] scattering geometry using the 514.5-nm excitation wavelength.

Figure 3

(Color online) Dependence of the energy (a) and the linewidth (b) on temperature for the soft phonon observed in $y\left(zz\right)\overline{y}$ scattering geometry spectra for the $x=0.03$, 0.092, 0.125, and 0.17 samples.

Figure 4

(Color online) The dependence of the soft phonon energy and linewidth on doping at various temperatures.

Figure 5

(Color online) The dependence on temperature of the (a) $\mathrm{La}∕\mathrm{Sr}$ and (b) apex phonon energy for the $x=0.03$, 0.092, 0.125, 0.17, and 0.24 samples.

Figure 6

(Color online) The dependence on temperature of the (a) $\mathrm{La}∕\mathrm{Sr}$ and (b) apex phonon linewidth for the $x=0.03$, 0.092, 0.125, 0.17, and 0.24 samples.

Figure 7

(Color online) The relative intensity of the $\mathrm{La}∕\mathrm{Sr}$ phonon to the apex one as a function of temperature for the $x=0.03$, 0.092, 0.125, 0.17, and 0.24 samples.

Figure 8

(Color online) Energy and linewidth dependence on temperature for the mode at $\sim 150{\mathrm{cm}}^{-1}$ observed in $y\left(xx\right)\overline{y}$ scattering geometry spectra for $x=0.092$, 0.125, 0.17, 0.20, and 0.24.

Figure 9

(Color online) (a) Energy and (b) linewidth dependence on temperature for the mode at $\sim 370{\mathrm{cm}}^{-1}$ observed in $y\left(xx\right)\overline{y}$ scattering geometry spectra for $x=0.03$, 0.092, 0.125, 0.17, 0.20, and 0.24.

Figure 10

(Color online) (a) Energy and (b) linewidth dependence on temperature for the mode at $\sim 280{\mathrm{cm}}^{-1}$ observed in $y\left(xx\right)\overline{y}$ scattering geometry spectra for the $x=0.03$, 0.092, 0.125, and 0.17 samples.

Figure 11

The dependence of the apex phonon asymmetry on doping, at various temperatures.

Figure 12

The dependence of the relative intensity La/apex, on doping at various temperatures.

Figure 13

The dependence of the relative intensities: (a) $150{\mathrm{cm}}^{-1}∕\mathrm{apex}$, (b) $370{\mathrm{cm}}^{-1}∕\mathrm{apex}$, and (c) $280{\mathrm{cm}}^{-1}∕\mathrm{apex}$ on doping at various temperatures.