Researchers have discovered a tetracritical point within the complex phase diagram of UTe₂, a material considered a leading candidate for topological superconductivity. Using pulse-echo ultrasound, the team at Cornell University and the University of Maryland revealed a new phase boundary marked by an unusual “upward jump” in sound velocity, evidence of a phase transition where superconducting order diminishes as temperature decreases. This finding establishes a point where two superconducting order parameters combine to form a multi-component state, demonstrating strong competition between them and offering a thermodynamic foundation for potentially topological superconductivity in UTe₂.
UTe₂: Resolving the Forbidden Triple Point with Ultrasound
This observation resolves a long-standing puzzle concerning an apparent “triple point” within the material’s complex pressure-temperature phase diagram, a point previously considered thermodynamically impossible. Researchers established this new phase boundary using pulse-echo ultrasound, revealing a transition where the loss of superconducting order occurs upon cooling, a finding that challenges conventional understanding of superconductivity in UTe₂. A “triple point” representing the intersection of two second-order phase boundaries is forbidden in thermodynamics, implying either previously undetected phase transitions or a fundamental misinterpretation of the superconducting behavior within UTe₂.
Specific-heat and magnetization measurements confirmed that all transitions observed are second order and occur throughout the bulk of the material, yet the elusive tetracritical point, requiring an additional second-order line, remained unresolved. Attempts to explain this discrepancy led to speculation about a fine-tuned superconducting transition with a vanishing specific-heat jump, potentially indicating a third-order phase transition at pressure P*.
The research demonstrates that UTe₂ exhibits a tetracritical point, a rare phenomenon where four distinct phases converge at a single point, suggesting a highly unusual and complex phase diagram. The team’s analysis indicates that if γ² < u₁u₂, the transition is second order and both transitions meet at this tetracritical point, while the continuation of the SC2 phase boundary past the critical point implies a region where the order parameters of SC1 and SC2 are simultaneously finite, with the potential for chiral topological superconductivity. The work also explores the conditions under which the transition temperature of phase 1 is influenced by the order of phase 2, deriving equations to describe this interaction.
The researchers further refined their analysis by considering the impact of pressure on the bare transition temperatures, defining = T*-α₁(p-P*) and = T* + α₂(p-P*), where represents a positive coefficient. The study validated its findings through symmetry analysis, noting that the application of a b-axis magnetic field reduces the point group symmetry of UTe₂ from to .
This reduction removes the two mirror planes containing the magnetic field vector, providing additional insight into the material’s behavior under varying conditions. “Resolving these issues has implications that go beyond simply determining the topology of the UTe₂ phase diagram,” the researchers state, establishing a thermodynamic foundation for multi-component, and potentially topological, superconductivity.
Discovery of Tetracriticality in UTe₂’s Phase Diagram
The unusual material UTe₂ displays a previously unreported phase boundary revealed through measurements of its elastic properties, establishing a critical point where four distinct phases converge. This tetracritical point, occurring at specific pressure and temperature coordinates, fundamentally alters the understanding of how superconductivity manifests within the material and provides a new thermodynamic foundation for multi-component superconductivity.
This newly mapped phase boundary extends to a tetracritical line within the broader pressure-temperature-magnetic field phase diagram of UTe₂, demonstrating a strong interplay between the two superconducting states present in the material. The measured phase diagram demonstrates 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.
Pulse-Echo Ultrasound Maps UTe₂’s Pressure-Temperature Phase Space
Regions where either SC1 or SC2 order parameters are non-zero are clearly delineated in the phase diagram, shaded red and blue respectively, while areas of coexistence are shown in purple, indicating a more detailed superconducting mechanism than previously understood. The researchers constrained a sheet of phase transitions in B-P-T space to project the phase boundary onto zero magnetic field, a stronger constraint than relying solely on zero-field transitions.
This newly defined phase space extends to a line of tetracritical points, and suggests the potential for chiral topological superconductivity, a state of matter with exotic properties potentially useful in quantum computing. The team observed an order parameter relaxation peak at the SC2 phase boundaries, marked by a solid black star on their diagrams, and found the two-component state SC1+SC2 occupies a large region of phase space extending down to zero pressure for magnetic fields greater than 12 tesla.
Upward Jump in Sound Velocity Defines SC2 Phase Exit
An unexpected reversal in sound propagation within the candidate topological superconductor UTe₂ directly identifies the point at which its second superconducting phase ceases to exist, resolving a long-standing thermodynamic puzzle. Measurements of the material’s elastic constant, c₁₁, revealed an “upward jump” in sound velocity as temperature decreased, a signature indicating the loss of superconducting order. This finding confirms the existence of a tetracritical point, designated (P*,T*), where four distinct phases converge.
Detailed analysis of c₁₁ data between 0.20 and 0.22 GPa pinpointed the unique jump, distinct from previously identified transitions at temperatures denoted as T₁ and T₂, transitions linked to the SC1 phase. The competition between the two superconducting order parameters, SC1 and SC2, is visualized through plotting the absolute values of the respective order parameters alongside the α₃₃ sound attenuation coefficient. This visualization confirms that the observed phase locking suppresses superconducting fluctuations, a consequence of the back-bending of the critical temperature line.
The researchers used pulse-echo ultrasound to resolve a 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. The authors of a prior study, Yip et al., used a positive change in sound attenuation to infer that one superconducting phase was lower in temperature than another.
Multi-Component Superconductivity Emerges Beyond P*
This emergent behavior is a fundamental shift in how superconductivity manifests within the material. Measurements of the magnetic field-temperature-pressure phase diagram definitively map this interplay, providing a thermodynamic foundation for understanding multi-component superconductivity and its potential connection to topological states. The team’s analysis goes beyond simply identifying the tetracritical point. It elucidates the dynamics governing the transition between single and multi-component superconductivity.
Ginzburg-Landau Theory Models UTe₂’s Phase Diagram
The Ginzburg-Landau (GL) theory, a standard for understanding superconductivity, has been successfully applied to model the phase diagram of UTe₂, revealing a region where two superconducting states coexist. This coexistence arises because the SC2 phase boundary extends past the SC1 boundary, creating a regime of two-component order. Analysis demonstrates that these two states interact strongly, with competition between them leading to a loss of SC2 order as temperature decreases.
The team’s calculations demonstrate that the observed phase diagram places constraints on the parameters within the model. Confirmation that the transition at the tetracritical point is second order, meaning a gradual change in the material’s properties, further validates the model.
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