Extreme high-field superconductivity in thin Re films

We report the high-field superconducting properties of thin, disordered Re films via magnetotransport and tunneling density of states measurements. Films with thicknesses in the range of 9 to 3 nm had normal-state sheet resistances of $\sim 0.2\mathrm{k}\mathrm{\Omega }$ to $\sim 1\mathrm{k}\mathrm{\Omega }$ and corresponding transition temperatures in the range of 6 to 3 K. Tunneling spectra were consistent with those of a moderate coupling BCS superconductor. Notwithstanding these unremarkable superconducting properties, the films exhibited an extraordinarily high upper critical field. We estimate their zero temperature $H_{c2}$ to be more than twice the Pauli limit. Indeed, in 6-nm samples the estimated reduced critical field $H_{c2}/T_c\sim 5.6\mathrm{T}/\mathrm{K}$ is among the highest reported for any elemental superconductor. Although the sheet resistances of the films were well below the quantum resistance $R_Q=h/4e^2$, their $H_{c2}$'s approached the theoretical upper limit of a strongly disordered superconductor for which $k_F\ell \sim 1$.

Figure 1

Scanning electron micrograph of a 10-nm-thick Re film deposited onto fire-polished glass at 84 K.

Figure 2

(a) TEM image, (b) EDS spectrum, (c) SAED pattern, and (d) HRTEM image of a 10-nm-thick Re film.

Figure 3

Sheet resistance as a function of temperature showing superconducting transitions in a 2.5-nm- (diamonds), 3-nm- (triangles), 6-nm- (filled circles), and a 9-nm-thick (squares) Re film. The open circles represent the superconducting transition of the 6-nm film in the presence of a 9-T perpendicular magnetic field.

Figure 4

Normalized tunneling conductance as a function of bias voltage in the superconducting phase of a $d=6\mathrm{nm}$ Re film. The coherence peaks are associated with a gap energy ${\mathrm{\Delta }}_0\sim 1\mathrm{meV}$.

Figure 5

Perpendicular critical field as a function of reduced temperature near $T_c$ for several Re films of varying thickness. For comparison, the inverted triangles represent the critical field $(\times 10)$ of a $d=4\mathrm{nm}$ Al film that was capped with 0.3 nm Au to induce spin-orbit (SO) scattering. The solid lines are linear least-squares fits to the data below 3 T. The values of ${(d{H}_{c2}/dT)}_{T_c}$ are indicated in the panel.

Figure 6

Parallel critical fields of the samples from Fig. 5 as a function of reduced temperature. The solid lines are linear least-squares fits to the data.

Figure 7

Relativistic energy bands of rhenium, including the effects of spin-orbit coupling.

Figure 8

Dots: measured critical temperature $T_c$ vs angle $\theta$ from the film normal in a field of magnitude $H=9\mathrm{T}$. Solid line: best-fit line using $\alpha \left(\theta \right)$ of Eq. (B18) for the pair-breaking strength; dashed line: using $\alpha \left(\theta \right)$ of Eq. (B20) (see text).

Figure 9

Sheet resistance as a function of perpendicular magnetic field at several temperatures near $T_c$ for a 6-nm Re film. The horizontal dashed line represents $R_n/2$ which defines the critical field.

Figure 10

Superconducting transitions of a 3-nm Re film in the presence of a range of applied fields. Upper panel: sheet resistance as a function of temperature with applied perpendicular fields of 0, 2, 3, 5, 7, and 9 T. Lower panel: superconducting transitions in applied parallel fields of 0, 1, 2, 3, 5, 7, and 9 T.