P9 Raman Study of Competing Ordering Phenomena in the Cuprates

Inelastic scattering of light (Raman effect, Fig. 1+Fig. 2) is complementary to neutron and optical spectroscopy. By photons, phononic, magnetic and charge excitations can be probed. With visible light the momentum transfer q is close to 0. However, by using polarized light excitations with different symmetries can be projected out separately. In the case of phonons, vibrations with specific eigenvectors can be observed for a given combination of light polarizations.

Fig. 1: Typical Raman set up. The green laser light is coming in on the lower left. Different polarization states can be selected before the photons enter the cryostat from below. The light scattered from the sample is collected with an objective lens and focussed on the entrance slit of the spectrometer on the right hand side of the figure. The Raman light is detected with a CCD camera.		Fig 2: Schematic view of an inelastic light scattering experiment. High energy photons (blue) hit the sample (yellow). Part of the energy is absorbed (red) and a photon with lower energy (green) scatters off the sample. Usually all photons have well-defined polarization states.

For spin and charge excitations symmetry-related form factors become effective. This translates into a sensitivity in momentum space. For the cuprates, the diagonals and the principle axes of the Brillouin zone can be accessed independently by crossed polarizations at 0 or 45°, respectively, in the coordinate system of the CuO₂ planes (Fig. 2).

Fig. 3: Relationship between light polarizations and sensitivity in momentum space. Spectra measured at B1g (dx2-y2) symmetry (left) and B2g (dxy) symmetry (right) are mainly sensitive along the principal axes and the diagonals of the Brillouin zone, respectively. The polarizations are indicated by arrows in the CuO2 plaquette.

We are mainly interested in charge excitations. Then the Raman response is similar to a conductivity with momentum resolution, i.e. different parts of the Fermi surface can be projected out as indicated in Fig. 3. In this way the momentum dependence of the electron dynamics both in the superconducting and in the normal state could be mapped out. AboveT_c, the B_1g spectra are strongly suppressed with decreasing carrier concentration indicating incipient localization along the principle axes below p = 0.22 holes/CuO₂. It became clear that the energy gap below T_c is best compatible with d-wave symmetry (B_1g, see Fig. 3). Recently, fluctuating charge order best described in terms of an incipient charge density wave (CDW) was observed. The effect sets in around optimal doping (maximal T_c) in La_2-xSr_xCuO₄ and manifests itself as a peak at very low but finite energy in B_1g symmetry. In the compounds with high T_c such as YBa₂Cu₃O_6+x the additional response is found only below the onset point of superconductivity at approximately p = 0.05. Here, similarly as in La_2-xSr_xCuO₄ at low doping, the low-energy mode appears in B_2g symmetry indicating the charge density to be modulated along the diagonal of the CuO₂ plane  Various discontinuous changes in the spin, charge, and vibrational spectra (Fig. 4) occurring at p = 0.05 are driven by the reorientation of the superstructure.

Fig. 4: Raman response χ''μ(p,W) of YBa2Cu3O6+x at high (a,b) and low (c,d) energy transfers. 8000 cm-1 corresponds to 1 eV. Temperatures and doping levels are indicated in the upper right inset of (a). As indicated, areas around the M point and the center of the quadrant are projected out in B1g and B2g symmetry, respectively. Spin, charge, and phonon responses change discontinuously across the onset of superconductivity: (a) the 2-magnon peak moves down by 10%, (inset of c) the intensity of the B1g phonon decreases by a factor of 2 signaling an increase of the electron-phonon coupling by a factor of 5, (d) the B2g spectrum is fully gapped at zero doping. At finite doping a low-energy peak appears originating from diagonal fluctuating charge order. Above the onset of superconductivity at p = 0.05 all low-energy peaks disappear and the Raman response is fully compatible with optical transport.

In the project we plan to extend the experiments to new samples in particular to the electron doped side of the phase diagram. The main focus will be placed on charge ordering at low doping and its relationship to the antiferromagnetism and superconductivity. The purpose is to better understand the origin of the charge-ordering instability and its connection to other phases. In this context, we also wish to clarify whether or not charge ordering leads to time reversal symmetry breaking. At the transition to the superconducting state the spectra are modified over energy ranges much larger than the gap. In spite of the absence of a "Raman sum rule" the renormalization of the spectra can be studied now with an accuracy better than 1%. Hence, the temperature dependence of the different symmetries will be investigated up to energies of approximately 1.5 eV.

In general, all results be compared with those from the other experiments on a quantitative basis. This is now much more precise than in earlier attempts since the very same set of samples will be used. The purpose is to compare the differences between single-particle and two-particle methods and to study the renormalization effects due to the interaction between the electrons. This can finally lead to a better understanding of the high transition temperatures in the cuprates.

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