Complex superconductivity in the noncentrosymmetric compound ${\mathrm{Re}}_6\mathrm{Zr}$

We report the electronic structure, synthesis, and measurements of the magnetic, transport, and thermal properties of the polycrystalline noncentrosymmetric compound ${\mathrm{Re}}_6\mathrm{Zr}$. We observed a bulk superconducting transition at temperature $T_c\sim 6.7$ K, and measured the resistivity, heat capacity, thermal conductivity, and the London penetration depth below the transition, as well as performed doping and pressure studies. From these measurements we extracted the critical field and the superconducting parameters of ${\mathrm{Re}}_6\mathrm{Zr}$. Our measurements indicate a relatively weak to moderate contribution from a triplet component to the order parameter, and favor a full superconducting gap, although we cannot exclude the existence of point nodes based on our data.

Figure 1

Powder XRD pattern (open circles) of ${\mathrm{Re}}_6\mathrm{Zr}$ at room temperature. The solid line represents the Rietveld refinement fit calculated for the $\alpha$-Mn cubic-type structure with space group $I\overline{4}3m$. The inset shows a schematic view of the crystal structure of ${\mathrm{Re}}_6\mathrm{Zr}$.

Figure 2

Section of the calculated electronic band structure of ${\mathrm{Re}}_6\mathrm{Zr}$ along high symmetry directions within the range of $\pm 1$ eV around $E_F$. (a) shows bands without SO coupling and (b) shows bands with SO coupling.

Figure 3

Section of the total and individual atom projected DOS (in units of states ${\mathrm{eV}}^{-1}$) of ${\mathrm{Re}}_6\mathrm{Zr}$ within the $\pm 4$ eV energy range around $E_F$. The result here is shown without SO coupling.

Figure 4

Normal-state temperature dependence of the electrical resistivity of ${\mathrm{Re}}_6\mathrm{Zr}$. The solid line is a fit to the data, as discussed in the text. The inset shows the data between 10 and 50 K and the blue solid line indicates a line fit to the data.

Figure 5

Temperature dependence of the electrical resistivity of ${\mathrm{Re}}_6\mathrm{Zr}$ from 2 to 290 K with the inset showing a sharp superconducting transition at 6.7 K.

Figure 6

ZFC and FC susceptibilities for ${\mathrm{Re}}_6\mathrm{Zr}$ at a constant field of 30 Oe. The value of the ZFC volume susceptibility data at low temperatures indicates bulk superconductivity.

Figure 7

Upper critical field of ${\mathrm{Re}}_6\mathrm{Zr}$ as a function of temperature. The transition temperatures were taken from the midpoint of the resistivity drop from the normal state, as seen in (a) and (b). In the left upper panel (a), the behavior of the transition temperature measured in PPMS under applied fields of 0, 0.5, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, and 9 T is shown from right to left, respectively. On the right in (b), the critical fields at different temperatures down to 0.32 K were measured at NHFML. The solid line in (c) is a fit to Eq. (3), as described in the text.

Figure 8

Thermal conductivity of ${\mathrm{Re}}_6\mathrm{Zr}$ above 10 K. The main panel shows the total, phonon, and electronic contributions to the thermal conductivity. The dashed lines are guides to the eye. Inset: Temperature dependence of the reduced Lorenz number.

Figure 9

Low-temperature thermal conductivity of ${\mathrm{Re}}_6\mathrm{Zr}$ in different magnetic fields, showing the enhancement below $T_c$ and the suppression with magnetic field. The vertical dashed line indicates $T_c$ at zero field.

Figure 10

Temperature dependence of thermal conductivity ${\kappa }_{\text{tot}}$ below $T_c$. The dashed line is a linear fit to the data.

Figure 11

Temperature dependence of (a) the London penetration depth and (b) superfluid density. The superconducting transition at $T_c=6.7$ K is shown in the inset of the upper panel. The dotted line in the main body of the upper panel is a BCS fit to the data below $T=T_c/3$, as described in the text. The lower panel shows the corresponding superfluid density, and the solid line is a BCS fit to the data as described in the text.

Figure 12

Temperature dependence of the total and electronic specific heat. (a) shows the superconducting transition and estimation of the phonon and electronic contribution using the fit described in the text (solid lines). The electronic specific heat below $T_c$ is shown in the lower two panels with fits for (b) the BCS and (c) anisotropic gap structures (solid lines).

Figure 13

Change in the superconducting transition temperature as a function of Os doping. The dashed line is a linear fit to the data. Inset: Superconducting transitions in the Os-doped samples observed in the temperature dependence of the electrical resistivity.

Figure 14

Change in the superconducting transition temperature of pure ${\mathrm{Re}}_6\mathrm{Zr}$ due to applied pressure. The solid line is a linear fit to data, which indicates a negative slope.