Superconducting Phase Induced by a Local Structure Transition in Amorphous ${\mathrm{Sb}}_2{\mathrm{Se}}_3$ under High Pressure

Superconductivity and Anderson localization represent two extreme cases of electronic behavior in solids. Surprisingly, these two competing scenarios can occur in the same quantum system, e.g., in an amorphous superconductor. Although the disorder-driven quantum phase transition has attracted much attention, its structural origins remain elusive. Here, we discovered an unambiguous correlation between superconductivity and density in amorphous ${\mathrm{Sb}}_2{\mathrm{Se}}_3$ at high pressure. Superconductivity first emerges in the high-density amorphous (HDA) phase at about 24 GPa, where the density of glass unexpectedly exceeds its crystalline counterpart, and then shows an enhanced critical temperature when pressure induces crystallization at 51 GPa. Ab initio simulations reveal that the bcc-like local geometry motifs form in the HDA phase, arising from distinct “metavalent bonds.” Our results demonstrate that HDA phase is critical for the incipient superconductive behavior.

Figure 1

Electric transport measurements of $a\text{−}{\mathrm{Sb}}_2{\mathrm{Se}}_3$ at high pressure. (a) Resistivity changes under compression and decompression at room temperature. The inset shows the change in the $\sigma \text{−}P$ slope represented by pink, green, and purple colors, respectively. (b) Characterization of the superconducting transition upon compression. (c) Detailed measurements near the superconducting transition temperature. The data at 23.9, 45.4, and 63.3 GPa are from run No. 2. (d) Superconducting upper critical field upon compression (blue) and decompression (orange). Open symbols are from run No. 1, solid symbols are from run No. 2. Magnetic field dependent $R(\mathrm{T})$ of superconducting transition at 51 (e) and 60 GPa (f).

Figure 2

Structure evolution of $a\text{−}{\text{Sb}}_2{\text{Se}}_3$ under high pressure. (a) $S(q)$ and (b) $g(r)$ under compression and decompression. (c),(d) The corresponding principal peak positions shift with pressure, showing a slope change at around 15.7 GPa. (e) Comparison of pressure dependence of $r_1$ for the amorphous $Pnma$ (low-pressure crystalline structure), and bcc phase (high-pressure crystalline structure). Error bar of $r_1$ is smaller than the symbol size. All pressure values are in GPa.

Figure 3

Simulated structural features of $a\text{−}{\mathrm{Sb}}_2{\mathrm{Se}}_3$ upon compression. (a) $g(r)$, the vertical dashed line marks the largest position of the first peak. (b) Angle distribution function, showing the appearance of the 60° bond angle starting at 16 GPa. (c) Simulated partial coordination number around Sb and Se atoms indicates a subtle but definite transition at 16 GPa, which is in accord with experimental CN (gray bars). (d) The statistical distribution of ring length, showing a local structural transition from long to short member rings at 20 GPa. For clarity, the inset shows the distribution of ring length at 0 GPa with a 4-member ring as the main structural unit. The vertical axis value is the relative ratio of various local structure units.

Figure 4

Density dependence of superconductivity at high pressure. (a) Equation of state of $a\text{−}{\mathrm{Sb}}_2{\mathrm{Se}}_3$ that experiences an LDA-HDA-bcc phase transition during compression and an abrupt bcc-LDA transition upon decompression. Volume data of $Pnma$ and bcc ${\mathrm{Sb}}_2{\mathrm{Se}}_3$ are taken from Ref. [38]. (b) Superconducting phase diagram, showing superconductivity starting at 23.9 GPa in HDA and a noticeable $T_c$ upturn at 50 GPa that corresponds to the appearance of the bcc phase. Superconductivity is preserved down to 25 GPa upon decompression when ${\mathrm{Sb}}_2{\mathrm{Se}}_3$ returns to an LDA. The open and solid symbols are for two independent compression runs.

Figure 5

Characterization of PLD (a),(b) depicted by the distribution of long and short bonds and ELF (c),(d) in LDA (0 GPa) and HDA (35 GPa) phase, respectively. The ELF value of 1 represents perfect electronic localization (red), 0.5 represents perfect electronic delocalization (green), and 0 represents void regions (blue).