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

TL;DR

This study uncovers a tetracritical point in UTe$_2$, revealing a complex multi-component superconducting phase diagram driven by competition between order parameters, supported by thermodynamic ultrasound measurements and Ginzburg-Landau theory.

Contribution

It provides the first thermodynamic evidence for a tetracritical point and multi-component superconductivity in UTe$_2$, clarifying the phase diagram and underlying mechanisms.

Findings

Discovery of a new phase boundary via ultrasound measurements.

Identification of a tetracritical point in the phase diagram.

Theoretical modeling of phase competition and locking effects.

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 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 re-entrant phase transition. Our results establish $\left(P^{\star},T^{\star}\right)$ as a tetracrtical point, beyond which the ambient and pressure-induced superconducting order parameters form a multi-component state. We use the measured phase diagram to construct a Ginzburg-Landau theory that shows that strong competition between the two superconducting order parameters drives the re-entrance and leads to phase locking that suppress superconducting fluctuations. These findings provide the definitive magnetic field-temperature-pressure phase diagram and establish a thermodynamic foundation for multi-component -- and potentially topological -- superconductivity in UTe$_2$.