High-pressure study of the low-$Z$ rich superconductor ${\mathrm{Be}}_{22}\mathrm{Re}$

With $T_c\sim 9.6\mathrm{K}, {\mathrm{Be}}_{22}\mathrm{Re}$ exhibits one of the highest critical temperatures among Be-rich compounds. We have carried out a series of high-pressure electrical resistivity measurements on this compound to 30 GPa. The data show that the critical temperature $T_c$ is suppressed gradually at a rate of $d{T}_c/dP=-0.05\mathrm{K}/\mathrm{GPa}$. Using density functional theory (DFT) calculations of the electronic and phonon density of states (DOS) and the measured critical temperature, we estimate that the rapid increase in lattice stiffening in ${\mathrm{Be}}_{22}\mathrm{Re}$ overwhelms a moderate increase in the electron-ion interaction with pressure, resulting in the decrease in $T_c$. High-pressure x-ray diffraction measurements show that the ambient pressure crystal structure of ${\mathrm{Be}}_{22}\mathrm{Re}$ persists to at least 154 GPa.

Figure 1

X-ray diffraction pattern of ${\mathrm{Be}}_{22}\mathrm{Re}$ at ambient pressure. The blue tick marks indicate the expected locations of the peaks. No additional peaks, indicative of impurity phases, were detected. Inset shows the crystal structure of cubic ${\mathrm{Be}}_{22}\mathrm{Re}$ (8 formula units) with $a_0=11.568\AA , V_0=1547.86{\AA }^3$, and ${\rho }_0=3.299\mathrm{g}/{\mathrm{cm}}^3$ in good agreement with the previous study [21].

Figure 2

Magnetic susceptibility of ${\mathrm{Be}}_{22}\mathrm{Re}$ versus temperature at ambient pressure. The data are consistent with full shielding.

Figure 3

Relative resistivity versus temperature measured while warming at several pressures to 30 GPa. Three arrows represent $T_c$ (onset), $T_c$ (mid), and $T_c$ ($\rho =0$), respectively, as defined in the text. All the data were taken during compression except for those at 9.8 GPa which were measured during decompression. The inset shows the photograph of the ${\mathrm{Be}}_{22}\mathrm{Re}$ sample along with a ruby for pressure calibration, steatite insulation (bright area surrounding the sample at center), a 316 stainless steel metal gasket, and six tungsten leads configuration. Leads 2, 3, 4, and 5 were used for the measurement.

Figure 4

Superconducting transition temperature ($T_c$) of ${\mathrm{Be}}_{22}\mathrm{Re}$ versus pressure. Blue sphere (or open) symbols indicate the midpoint of the transition taken from compression (or decompression). The red solid line refers to the linear fit of $T_c$.

Figure 5

Representative high-pressure XRD patterns of ${\mathrm{Be}}_{22}\mathrm{Re}$ at pressures to 154 GPa. No structural transition was observed throughout the pressure range studied.

Figure 6

PV isotherm of ${\mathrm{Be}}_{22}\mathrm{Re}$ at room temperature. Inset shows the Le Bail fit at 125 GPa with the initial cubic structure. Numbers in the parentheses are the uncertainties on the last digit for $K_0$ and $K_0^{\prime }$.

Figure 7

(a) $\mathrm{\Gamma }$ point phonon frequencies and their respective degeneracies at 0 GPa. (b) Calculated phonon DOS given a smearing factor $\sigma =4.135$ meV (1 THz).

Figure 8

Calculated density of states at the Fermi level $N\left(0\right)$ (red curve: both spins are included), electron-phonon coupling parameter $\lambda$ (blue curve), and $\langle I^2\rangle /M$ (black curve) as a function of pressures.

Figure 9

Experimental and calculated $T_c$, and calculated $\sqrt{\langle {\omega }^2\rangle }$ and ${\omega }_{\text{log}}$ as a function of pressure. The $T_c$ was calculated using Allen-Dynes equation at four values of ${\mu }^{*}$.