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Thermodynamic phase diagram of static charge order in underdoped YBa2Cu3Oy

In the underdoped cuprate high-Tc superconductor, YBa2Cu3Oy, nuclear magnetic resonance (NMR) experiments performed at the LNCMI Grenoble, have revealed that a magnetic field, large enough to destabilize superconductivity, induces a charge order that breaks the translational symmetry of the underlying crystal structure. This experiment brought a clear explanation about the origin of the Fermi surface reconstruction inferred from quantum oscillations and Hall effect experiments performed at the LNCMI Toulouse. Now the question is whether this new phase is detrimental to superconductivity or whether it is an essential ingredient for high temperature superconductivity. Indeed, pairing can originate from the fluctuations of such a competing order that arise near a quantum critical point. To establish firmly the role of this charge order with respect to the pairing mechanism, one need to show that in the phase diagram there is a line associated with a phase transition due to the onset of charge order, ending at a quantum critical point underneath the superconducting dome.

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Figure 1 - Phase diagram deduced from the sound velocity of the longitudinal mode c11. Red circles show Bco the field onset of static charge order, black diamonds show the vortex lattice melting transition and the green diamond shows the onset of charge order deduced from NMR experiments at a similar doping.

Toulouse and Grenoble scientists took a first step towards this goal by measuring sound velocity in pulsed and static magnetic fields in underdoped YBa2Cu3O6.55. Sound velocity is a thermodynamic quantity, which is very sensitive to phase transitions, with typical resolution in the ppm range. Below about 50 K, the sound velocity shows strong anomalies as a function of magnetic field associated with the onset of charge order, thus providing the first thermodynamic signature of the charge order phase transition. This observation implies that charge order is static and three-dimensionnal. Accurate measurements of the sound velocity in static fields allow to construct the (B,T) phase diagram, which highlights the competition between superconductivity and charge order (see Fig. 1). Moreover, the tensor properties of the elastic constants offer the possibility to determine the symmetry of the order parameter. A group theory analysis of the anomalies observed in the sound velocities associated with different elastic constants, shows that the charge modulation runs along both the a-axis and the b-axis of the crystal structure. This analysis has important consequences on the topology of the reconstructed Fermi surface.

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