Record High 36 K Transition Temperature to the Superconducting State of Elemental Scandium at a Pressure of 260 GPa

Elemental materials provide clean and fundamental platforms for studying superconductivity. However, the highest superconducting critical temperature ($T_c$) yet observed in elements has not exceeded 30 K. Discovering elemental superconductors with a higher $T_c$ is one of the most fundamental and challenging tasks in condensed matter physics. In this study, by applying high pressure up to approximately 260 GPa, we demonstrate that the superconducting transition temperature of elemental scandium (Sc) can be increased to 36 K from the transport measurement, which is a record-high $T_c$ for superconducting elements. The pressure dependence of $T_c$ implies the occurrence of multiple phase transitions in Sc, which is in agreement with previous x-ray diffraction results. Optimization of $T_c$ is achieved in the Sc-V phase, which can be attributed to the strong coupling between $d$ electrons and moderate-frequency phonons, as suggested by our first-principles calculations. This study provides insights for exploring new high-$T_c$ elemental metals.

Figure 1

(a),(b) Temperature dependence of resistance for samples S1 and S2. (c)–(e) Replot of resistance curves for S1 and S2. All the curves are shifted vertically for clarity. (c) $T_c$ gradually increases with increasing the pressure up to 100 GPa. (d) $T_c$ is slightly suppressed with increasing the pressure up to 130 GPa and then starts to increase again with further increasing the pressure. (e) Superconductivity up to 36 K emerges above approximately 220 GPa.

Figure 2

(a) Temperature dependence of the resistance for samples S2, S3, and S6 with pressures above 230 GPa. The onset of superconductivity at approximately 36 K is indicated by arrows. (b) Superconducting critical transition temperature $T_c$ of elemental scandium (Sc) at high pressure. The dashed areas represent the phase boundaries for compressed Sc with different crystal structures. $T_c$ is determined from the onset of the resistance transition.

Figure 3

Temperature dependence of the resistance of scandium (Sc) at various magnetic fields. The upper critical field ${\mu }_0{H}_{c2}$ for various pressures can be extracted from these curves. $T_c$ is determined from the onset of the resistance transition, as displayed in Fig. S4(a).

Figure 4

Electronic properties of Sc-V at 230 GPa. (a) Reciprocal lattice. The Brillouin zone is surrounded by black lines, with red lines representing high-symmetry-point paths and the blue axis representing the reciprocal vector. (b) Projected band structure and density of states. Red, green, and blue dots or lines represent the contributions of electrons from $s$, $p$, and $d$ orbitals, respectively. The size of the dots in the band dispersion is proportional to the contribution of electrons from related orbitals. The Fermi level is shifted to 0 eV, as labeled by the dash-dotted line. (c) Top view of the Fermi surface, which reveals hexagonal symmetry and complex nesting.

Figure 5

Superconducting properties of Sc-V. (a) Calculated ${\gamma }_{qj}/{\omega }_{qj}$ resolved phonon spectrum, phonon density of states, Eliashberg function ${\alpha }^{2}F(\omega )$, and accumulated electron-phonon coupling strength $\lambda (\omega )$ at 230 GPa. The size of the magenta circles is proportional to the value of the dimensionless parameter ${\gamma }_{qj}/{\omega }_{qj}$, which originates from ${\alpha }^{2}F(\omega )=[\hslash /2\pi N(E_f)](1/N_{\mathit{q}}){\sum }_{qj}[\hslash /2\pi N(E_f)](1/N_{\mathit{q}})({\gamma }_{qj}/{\omega }_{qj})\delta (\omega -{\omega }_{qj})$ and evaluates the coupling in ${\alpha }^{2}F(\omega )$. (b) Superconducting properties at 230, 250, and 270 GPa. The solid red triangles and solid black squares represent the electron-phonon coupling strength $\lambda$ and transition temperature $T_c$, respectively.