Generic thermodynamics of condensates with extremely small superfluid density ---Application to UTe$_2$ and hidden second phase transition---

Abstract

Motivated by recent experimental findings on UTe$_2$ via NMR and specific heat experiments, we theoretically explore the thermodynamic signatures of condensates with small superfluid density and characterize their physical properties. We identify the hidden superconducting phase $A_2$ composed of spin-up Cooper pairs at lower temperature ($T$) and field ($H$) under ambient pressure of UTe$_2$ and show that $A_2$ reappears at higher $H$ for all three principal field directions, $a$, $b$, and $c$-axis. The phase transition lines from the $A_1$ phase with spin down pairs to the $A_2$ phase in the $H$-$T$ plane are all horizontal in common, implying a universal physical origin due to the originating from the magnetic-energy gain of the spin-up pairing state with increasing magnetic field. This multiple-phase diagram is extended to these under pressure ($P$), resulting in a simple picture based on non-unitary spin-triplet pairing symmetry $^3B_{3u}$, which enables us to consistently capture the evolution of the superconducting phases throughout the entire $H$-$T$-$P$ phase space.