Thermodynamic Discovery of Tetracriticality and Emergent Multicomponent Superconductivity in UTe$_2$

Abstract

The candidate topological superconductor UTe$_2$ exhibits a complex phase diagram with multiple superconducting states, yet the nature of their coexistence has remained a central mystery. In particular, the apparent intersection of two second-order phase boundaries at a ``triple point'' in the pressure-temperature phase diagram is thermodynamically forbidden, suggesting either hidden phase transitions or a fundamental misunderstanding of the superconductivity in UTe$_2$. Here, we use pulse-echo ultrasound to resolve this puzzle by discovering a new phase boundary that is characterized by a unique ``upward jump" in the sound velocity -- direct thermodynamic evidence for a phase transition where superconducting order is lost upon cooling. Our results establish $\left(P^{\star},T^{\star}\right)$ as a tetracritical point, beyond which the ambient and pressure-induced superconducting order parameters form a multi-component state. We use the measured phase diagram to demonstrate that strong competition between the two superconducting order parameters drives the loss of order on cooling, and leads to phase locking that suppresses superconducting fluctuations. These findings provide the definitive magnetic field-temperature-pressure phase diagram of UTe$_2$, and establish a thermodynamic foundation for multi-component -- and potentially topological -- superconductivity.