Spin-orbit-coupled superconductivity

Abstract

Superconductivity and spin-orbit (SO) interaction have been two separate emerging fields until very recently that the correlation between them seemed to be observed. However, previous experiments concerning SO coupling are performed far beyond the superconducting state and thus a direct demonstration of how SO coupling affects superconductivity remains elusive. Here we investigate the SO coupling in the critical region of superconducting transition on Al nanofilms, in which the strength of disorder and spin relaxation by SO coupling are changed by varying the film thickness. At temperatures T sufficiently above the superconducting critical temperature T(c), clear signature of SO coupling reveals itself in showing a magneto-resistivity peak. When T < T(c), the resistivity peak can still be observed; however, its line-shape is now affected by the onset of the quasi two-dimensional superconductivity. By studying such magneto-resistivity peaks under different strength of spin relaxation, we highlight the important effects of SO interaction on superconductivity.

Figure 1

(a) Optical image of the 6-nm-thick Al film. (b) Longitudinal resistivity ρ_xx as a function of T. (c) Longitudinal and Hall resistivities ρ_xx and ρ_xy as a function of B up to 11.7 T at T = 4.4 K. ρ_xx(B) at various T. From top to bottom at B = 2 T: (d) T = 24 K, 22 K, 20 K, 18 K, and 16 K; (e) T = 8 K, 10 K, 12 K, and 14 K; (f) T = 3 K, 4 K, and 6 K. The red curves correspond to the best fits to Eq. (1). The inset of (f) presents the fit considering Maki-Thompson superconducting fluctuations to the data at T = 3 K.

Figure 2. ρ_xx(B) at selected temperatures T for the 6-nm-thick film.

From top to bottom at B = 2 T: (a) T = 3 K, 4 K, and 6 K; (b) T = 0.328 K, 0.914 K, 1.568 K, and 1.980 K. The red curves represent the best fits to Eq. (1) over the limited field range (B_p ≤ B ≤ 2 T) and the blue curves denote the extrapolations of the fits to low B regime using the extracted parameters. The black and blue arrows indicate the experimentally obtained and theoretically predicted peak positions. To emphasize the zero-resistivity superconducting state around B = 0 when T ≤ 1.980 K, the full-scale view at the corresponding T are shown in the inset of (b). (c) ρ_xx(T) at various B around the superconducting transition.

Figure 3

Dephasing length l_ϕ, spin-orbit relaxation length l_SO, and elastic scattering length l₀ as a function of T ranging from (a) 8 K to 24 K and (b) from 0.328 to 6 K. (c) The difference between the measured and theoretically predicted resistivity peak position (ρ_pandat B = B_p and, respectively) as a function of T.

Figure 4

(a) & (b) Magneto-resistivity measurements ρ_xx(B) at different temperatures T for the 3-nm-thick film. The red curves correspond to the best fits to Eq. (1). (c) – (f) Zoom-in of (b) at each separate T. The insets show ρ_xx (B) around B_p indicated by the arrows. The red curves are the best fits to Eq. (1) over the limited field range (B_p ≤ B ≤ 2 T) and the blue curves denote the extrapolations of the fits to low B regime using the extracted parameters.

Figure 5

(a) & (b) Magneto-resistivity measurements ρ_xx(B) on the 12-nm-thick film at different temperatures T. The red curves correspond to the best fits to Eq. (1).