Record-High $T_c$ and Dome-Shaped Superconductivity in a Medium-Entropy Alloy TaNbHfZr under Pressure up to 160 GPa

Superconductivity has been one of the focal points in medium and high-entropy alloys (MEAs-HEAs) since the discovery of the body-centered cubic (bcc) HEA superconductor in 2014. Until now, the superconducting transition temperature ($T_c$) of most MEA and HEA superconductors has not exceeded 10 K. Here, we report a TaNbHfZr bulk MEA superconductor crystallized in the BCC structure with a $T_c$ of 15.3 K which set a new record. During compression, $T_c$ follows a dome-shaped curve. It reaches a broad maximum of roughly 15 K at around 70 GPa before decreasing to 9.3 K at 157.2 GPa. First-principles calculations attribute the dome-shaped curve to two competing effects, that is, the enhancement of the logarithmically averaged characteristic phonon frequency ${\omega }_{\log }$ and the simultaneous suppression of the electron-phonon coupling constant $\lambda$. Thus, TaNbHfZr MEA may have a promising future for studying the underlying quantum physics, as well as developing new applications under extreme conditions.

Figure 1

(a) Valence electron count (VEC) dependence of the superconducting transition temperature ($T_c$) for some MEAs and HEAs including TaNbHfZr MEA. The data were taken from Refs. [27, 33, 35, 36, 37, 39]. (The $\alpha$—Mn phase derives from the low-temperature allotrope of manganese and is bcc with a relatively large crystallographic cell that contains more atoms than the simple bcc and CsCl-type structures in MEA and HEA superconductors) (* refers to high-pressure experiment) (b) Crystal structure of TaNbHfZr MEA. (c) XRD patterns of TaNbHfZr at ambient pressure. (d) EDX elemental mappings of TaNbHfZr.

Figure 2

Characterization of the superconductivity of the TaNbHfZr MEA at high pressure. (a) Temperature-dependent resistance of TaNbHfZr MEA from 1.8 to 43.4 GPa. (b) The enlarged view of the temperature-dependent resistance from 1.8 GPa to 43.4 GPa. (Except for data at 1.8 GPa, all other curves in b have been vertically shifted for clarity). The onset $T_c^{\text{onset}}$ was determined as the temperature where resistivity starts to deviate from the extrapolated normal-state behavior. The $T_c^{\mathrm{zero}}$ was determined as the zero-resistivity temperature. (c) Temperature-dependent resistance of TaNbHfZr MEA from 45.8 to 157.2 GPa (enlarged view). (Except for data at 45.8 GPa, all other curves in c have been vertically shifted for clarity) (d) The resistive transition under different magnetic fields at 9.1 GPa. (e) The temperature dependence of the upper critical field ${\mu }_0{H}_{c2}$ with the WHH model fitting and the Ginzburg-Landau function fitting. (f) The pressure dependence of the upper critical field at zero temperature ${\mu }_0{H}_{c2}(0)$ fitted by the Ginzburg-Landau function.

Figure 3

(a) Pressure-dependent superconducting transition temperature of TaNbHfZr MEA (red) and the calculated evolution of superconducting transition temperature $T_c$ (blue). (b) Logarithmically averaged characteristic phonon frequency ${\omega }_{\log }$ (red) and the electron-phonon coupling constant $\lambda$ (blue) under high pressure.

Figure 4

(a)–(c) The phonon dispersion and phDOS at 0, 50, 155 GPa. (d)–(f) The band structure and DOS at 0, 50, 155 GPa.