Pressure-Dependent Metallic and Superconducting Phases in a Germanium Artificial Metal

Germanium (Ge) becomes an “artificial metal” and a superconductor ($T_c\sim 5\mathrm{K}$) above the pressure-induced semiconductor-(diamond structure)-to-metal ($\beta$-Sn structure) transition at 10 GPa. We report single crystal resistance studies of the pressure-dependent metallic and metastable phases in the range 2.6 to 23 GPa, and show for a controlled pressure release, Ge is a metastable metal below 3 GPa. We find Ge has a superconducting upper critical field of 300 Oe (at 10.7 GPa and 1.8 K), above which a positive magnetoresistance consistent with that of a compensated closed orbit metal is observed.

Figure 1

Pressure-dependent structural phases of germanium (cell parameters after Qadri et al. [24]). (a) GeI: The semiconducting diamond structure for $P<P_c$ ($P_c\sim 10\mathrm{GPa}$). (b) GeII: The metallic and superconducting $\beta$-Sn structure for $P>P_c$. (c) GeIII: The metastable, low pressure body centered-tetragonal structure for $P<P_c$ after depressurization from GeII (shown herein to be metallic).

Figure 2

The temperature and pressure dependence of the resistance of Ge (sample 2). The sequence of pressures are: 0, ($\sim 1.5\mathrm{GPa}/4–5\mathrm{h}$ up to 8), 9.5, 10.7, 18.7; slow pressure release to 15.0, 14.2, 12.4, 10.7, 10.1, 9.2, 8.1, 6.9, 2.6; slow pressure rise to 4.2, 5.2,10.7, 15.9, 20.9, 23.0; then release to 22.0 (GPa). Inset: Detail of temperature dependent resistance after depressurization at lower pressures.

Figure 3

Pressure-dependent phases of Ge. (a) Resistance vs pressure at room temperature, 100 K, and 10 K (see Fig. 2 caption for pressure sequence). (b) Temperature pressure-phase diagram. For increasing pressure, at 10.1 GPa the resistance becomes metallic, and superconducting. For pressure release below 10 GPa, superconductivity persists in the mixed $\mathrm{GeII}+\mathrm{GeIII}$ phase until 6.9 GPa. At lower pressures, only the metallic GeIII phase remains. (The uncertainly in the pressure determined from the ruby fluorescence, $\sim 0.5\mathrm{GPa}$, is about the size of the symbols.)

Figure 4

The magnetic field dependent resistance of Ge at 10.7 GPa (sample 2). (a) The superconducting transition in resistance vs temperature for different magnetic fields. (b) Superconducting critical field $B_c$ vs temperature based on the magnetoresistive transitions in Fig. 4a: “Onset” indicates the first drop in the resistance from the normal value; “Midpoint” indicates the point where the resistance is 50% of the normal value; “Zero” indicates the point where the resistance reaches the background noise level. The parameters of the empirical fit to $B_c$ for the Onset curve are $B_0=310\mathrm{Oe}$ and $T_c=5\mathrm{K}$. (c) The high field (quadratic) magnetoresistance at various temperatures.