In hole-doped cuprates there is now compelling evidence that inside the pseudogap phase, a charge density wave (CDW) breaks translational symmetry. In YBa2Cu3Oy (YBCO) this CDW emerges in two steps: a two-dimensional (2D) order found at zero field and up to high temperatures inside the pseudogap phase, and a 3D order that is superimposed below the superconducting transition Tc when superconductivity is weakened by a magnetic field. It has been established by NMR and x-ray measurements that these CDWs coexist at low temperatures but it raises interesting questions: Do both CDWs share the same critical doping? What is their respective impact on the Fermi surface at low temperature? We studied the doping dependence of the 3D CDW onset temperature and field using sound velocity measurements in high magnetic fields. A jump is seen in the temperature dependence of the sound velocity measured at high field, as expected for a second-order phase transition. In the figure, we compare the doping dependence of the onset temperature TCO of the 3D CDW (red circles) with the onset temperature of the 2D CDW observed by x-rays (open green triangles) and we find that both CDWs coexist at low temperature in the same doping range. In addition, the critical doping of the CDWs appears distinct from the critical point of the pseudogap, suggesting that the two phenomena are separate. The exact mechanism of the Fermi-surface reconstruction by the CDW is still debated. We assume that the sign change of the Hall effect (observed in the same doping range of YBCO where CDWs exist) is a signature of the presence of an electron pocket due to a Fermi-surface reconstruction. The facts that i) the onset of the 3D CDW barely affects the temperature dependence of the Hall coefficient and ii) the Hall coefficient changes sign at a temperature T0 (open black diamonds) which can be 20 K higher than the onset of the 3D CDW, point towards a minor role of the 3D CDW for this reconstruction.
Figure: Temperature – doping phase diagram of charge orders
in YBCO. X-ray diffraction (down green triangles) and resonant
x-ray scattering (up green triangles) give the onset temperature
of 2D CDW in zero field. The onset temperature of 3D charge
order in high fields is given by NMR (blue squares) and sound
velocity (red circles). A comparison is made with T0 (black diamonds)
the temperature of the sign change of the Hall effect,
a signature of an electron pocket in the reconstructed Fermi
surface. The solid black line is the pseudogap temperature T* in
YBCO determined from a resistivity curvature map. The dashed
black line is a guide to the eye.
High field charge order across the phase
diagram of YBCO, F. Laliberté, M. Frachet, S. Benhabib,
B. Borgnic, T. Loew, J. Porras, M. Le Tacon, B. Keimer,
S. Wiedmann, C. Proust, and D. LeBoeuf, npj Quantum
Materials 3, 11 (2018).