Thermodynamic phase diagram of static charge order in underdoped YBa2Cu3Oy

The interplay between superconductivity and any other competing order is an essential part of the long-standing debate on the origin of high-temperature superconductivity in cuprate materials(1,2). Akin to the situation in the heavy fermions, organic superconductors and pnictides, it has been proposed that the pairing mechanism in the cuprates comes from fluctuations of a nearby quantum phase transition(3). Recent evidence for charge modulation(4) and its associated fluctuations(5-7) in the pseudogap phase of YBa2Cu3Oy, makes charge order a likely candidate for a competing order. However, a thermodynamic signature of the charge-ordering phase transition is still lacking. Moreover, whether the charge modulation is uniaxial or biaxial remains controversial. Here we address both issues by measuring sound velocities in YBa2Cu3O6.55 in high magnetic fields. We provide the first thermodynamic signature of the competing charge-order phase transition in YBa2Cu3Oy and construct a field-temperature phase diagram. The comparison of different acoustic modes indicates that the charge modulation is biaxial, which differs from a uniaxial stripe charge order.