Theoretical Studies on Off-Axis Phase Diagrams and Knight Shifts in UTe$$_2$$: Tetra-Critical Point, d-Vector Rotation, and Multiple Phases

Abstract

Inspired by recent remarkable sets of experiments on UTe$$_2$$ 2 : discoveries of the fourth horizontal internal transition line running toward a tetra-critical point (TCP) at H = 15 T, the off-axis high-field phases, and abnormally large Knight shift (KS) drop below $$T_\textrm{c}$$ T c for $$H \parallel a$$ H ‖ a -magnetic easy axis, we advance further our theoretical work on the field (H)-temperature (T) phase diagram for $$H \parallel b$$ H ‖ b -magnetic hard axis which contains a positive sloped $$H_\textrm{c2}$$ H c2 departing from TCP. A nonunitary spin-triplet pairing with three components explains these experimental facts simultaneously and consistently by assuming that the underlying normal electron system with a narrow bandwidth characteristic to the Kondo temperature $$\sim$$ ∼ 30 K unsurprisingly breaks the particle-hole symmetry. This causes a special invariant term in Ginzburg–Landau (GL) free energy functional which couples directly with the 5f magnetic system, giving rise to the $$T_\textrm{c}$$ T c splitting and ultimately to the positive sloped $$H_\textrm{c2}$$ H c2 and the horizontal internal transition line connected to TCP. The large KS drop can be understood in terms of this GL invariance whose coefficient is negative and leads to a diamagnetic response where the Cooper pair spin is antiparallel to the applied field direction. The present scenario also accounts for the observed d-vector rotation phenomena and off-axis phase diagrams with extremely high $$H_\textrm{c2}$$ H c2 $$\gtrsim$$ ≳ 70 T found at angles in between the b- and c-axes and between the bc-plane and a-axis, making UTe$$_2$$ 2 a fertile playground for a possible topological superconductor.