Bulk signatures of re-entrant superconductivity in UTe$_2$ from ultrasound measurements

TL;DR

The paper delivers bulk evidence for the field-reentrant SC3 phase in $UTe_{2}$ by performing pulsed-field ultrasound up to $80$ T at a tilt of $\theta_{b-c}=30^{\circ}$ and monitoring the $c_{11}$ mode, revealing a bulk signature of superconductivity that correlates with the phase boundaries set by $H_m$ and $H_{c2}$. It reports an upper critical field of $H_{c2} \approx 65$ T at $0.5$ K and a bulk superconducting state extending up to $T \approx 2$ K for fields above the metamagnetic transition, accompanied by hysteresis and excess attenuation across the entire SC3 phase. The frequency-dependent ultrasound response and analysis with LK relaxation and TAFF models suggest vortex pinning to lattice defects and unconventional vortex dynamics; however, neither model fully accounts for the observed magnitude and frequency dependence, implying more complex vortex physics or inhomogeneous pinning in high-field SC3. Overall, the work establishes SC3 as a bulk mixed state in $UTe_{2}$ and highlights distinctive vortex dynamics under re-entrant high-field superconductivity, with implications for understanding spin-triplet pairing and high-field superconducting phases in correlated electron systems.

Abstract

We report bulk ultrasound measurements up to 80 T and down to 0.5 K of the field re-entrant superconducting phase of the unconventional superconductor UTe$_2$. Clear bulk signatures of superconductivity are observed in the longitudinal elastic mode $c_{11}$ for fields applied at a tilt angle of $θ_{b-c} =30^\circ$ from $b$-axis. We confirm an upper critical field of $H_{\rm c2}\approx65$ T at 0.5 K and bulk superconductivity which survives up to $T\approx 2$ K for fields above the metamagnetic transition. The $c_{11}$ mode has propagation and displacement vectors along the $a$-axis, and for fields applied at a tilt angle of $θ_{b-c} =30^\circ$, this mode is sensitive to the elasticity of the vortex lattice. The anomalies observed in $c_{11}$ are in part reminiscent of superconducting vortices pinned to lattice defects. Nonetheless, an excess attenuation, with respect to the normal state, is observed throughout the entire superconducting phase, suggesting unusual vortex dynamics and pinning in the field re-entrant superconducting phase of UTe$_2$.

Figures (18)

• Figure 1: Phase diagram of SC3 phase of UTe2 for $H$ applied with $\theta_{b-c} =30^\circ$. The metamagnetic transition $H_{\rm m}$ is shown in green diamonds and $H_{\rm SC}$ is shown in black circles (see sound velocity data in Fig. \ref{['c11_SC']}a). The color code represents the amplitude of the hysteresis loop in the sound attenuation $\Delta \alpha$ shown in Fig. S13 in Ref. [28].
• Figure 2: (a) Field dependent relative change of sound velocity ${\Delta v}/{v}$ in the $c_{11}$ mode for a field orientation of $\theta_{\rm b-c}=30^\circ$ for temperatures ranging from $0.49-2.28$ K. Curves are shifted vertically for clarity. $H_{\rm SC}$ (fig. \ref{['Phase']}) is a kink in the field decreasing curve shown by black arrows. Kinks is best observed in Fig. S12 in Ref. [28]. The corresponding field dependent attenuation change $\Delta \alpha$ is displayed in panel (b) with the same color code and shifted vertically for clarity. The black arrow indicates the same magnetic field value as in (a). The ultrasound frequency is $f= 157$ MHz. Changes in velocity and attenuation are calculated with respect to the zero field value.
• Figure 3: a) Field dependence of $\Delta v/v$ (red, left axis) and $\Delta \alpha$ (blue, right axis), for ascending and descending field, measured in the $c_{11}$ mode at $T=0.49$ K. The dashed line indicates $H_{\rm SC}$ and black arrows indicate increasing or decreasing field. b) Hysteresis of sound attenuation (blue) as a function of field for $T=0.65$ K in the $c_{11}$ mode. The blue curve is obtained by calculating ($\Delta \alpha_{\rm down} - \Delta \alpha_{\rm up})$, see in Fig. S13 in Ref. [28]. The grey line shows the resistivity, $\rho_a$, measured at similar angle and temperature, from Ref. helm_field-induced_2024. c) $\Delta \alpha$ for frequencies ranging from 70 to 388 MHz at a temperature $T\approx1.4$ K, shifted vertically for clarity. $H_{\rm SC}$ measured at 157 MHz is indicated with the dashed line.
• Figure 4: The $c_{11}$ and $c_{66}$ mode relative sound velocity are compared at various ultrasound frequencies and for field orientations along the $b$-axis and for $\theta_{\rm b-c}=30^\circ$ for $T=1.4$ K.
• Figure S1: a) Magnetic filed profile of the dual-coil magnet used for pulsed field measurements up to 80 T. Red curve shows magnetic field versus time, and blue curve shows time-derivative of magnetic field $dB/dt$. Inset shows a zoom on the pulse of the inner coil. b) Zero field specific heat measured through superconducting $T_{\rm c}\approx 2$ K (shown by an arrow) and plotted as $c_p/T(T)$ for the sample where the $c_{11}$ mode was measured.