Determine why the alternative high-field phase assignment is not realized for H parallel b

Determine why the alternative reconnection of the four phase boundaries above the tetracritical point at H_TCP = 14 T, in which the A_2 phase with Cooper-pair spin parallel to the b-axis would have the larger superfluid density, is not realized for magnetic fields parallel to the b-axis.

Background

For magnetic fields parallel to the b-axis, the paper assigns the high-field A_2 phase a smaller superfluid density than the low-field A_1 phase. However, the topology of the phase diagram above the tetracritical point does not uniquely determine this assignment: the four phase boundaries can in principle be reconnected differently. An alternative reconnection would assign the larger superfluid density to the A_2 phase with Cooper-pair spin aligned parallel to the b-axis, as occurs in the proposed phase diagrams for fields parallel to the a- and c-axes.

The paper states that experimental and thermodynamic considerations apparently favor the presented assignment but does not explain why the alternative topology is excluded. Establishing the reason would clarify the phase-boundary connectivity and the superfluid-density assignment in the high-field b-axis phase diagram.

References

However, one intriguing issue remains. Above the tetracritical point, H_TCP=14 T, the four phase boundaries meeting at the tetracritical point can, in principle, be reconnected in different ways. Consequently, it would also be possible to assign the larger superfluid density to the A_2 phase with S∥b, analogous to the cases of H∥a and H∥c. The reason why this alternative scenario is apparently not realized remains an open question for future investigation.

— Generic thermodynamics of condensates with extremely small superfluid density ---Application to UTe$_2$ and hidden second phase transition---  (2609.19834 - Machida, 17 Sep 2026) in Section “Construction of overall phase diagrams under P=0,” subsection “H∥b-axis”