Superconducting Tunneling Spectroscopy of Spin-Orbit Coupling and Orbital Depairing in $\mathrm{Nb}:{\mathrm{SrTiO}}_3$

We have examined the intrinsic spin-orbit coupling and orbital depairing in thin films of Nb-doped ${\mathrm{SrTiO}}_3$ by superconducting tunneling spectroscopy. The orbital depairing is geometrically suppressed in the two-dimensional limit, enabling a quantitative evaluation of the Fermi level spin-orbit scattering using Maki’s theory. The response of the superconducting gap under in-plane magnetic fields demonstrates short spin-orbit scattering times ${\tau }_{\mathrm{so}}\le 1.1\mathrm{ps}$. Analysis of the orbital depairing indicates that the heavy electron band contributes significantly to pairing. These results suggest that the intrinsic spin-orbit scattering time in ${\mathrm{SrTiO}}_3$ is comparable to those associated with Rashba effects in ${\mathrm{SrTiO}}_3$ interfacial conducting layers and can be considered significant in all forms of superconductivity in ${\mathrm{SrTiO}}_3$.

Figure 1

(a) Schematic of the tunneling junction device structure and atomic stacking of the oxide heterostructure. (b) Expected effect of Zeeman splitting on the spin-dependent DOS for two cases: zero spin-orbit coupling ($b=0$) (left panel) and large spin-orbit coupling ($b=6$) (right panel). The dimensionless SOC parameter $b=\hslash /(3{\tau }_{\mathrm{so}}{\mathrm{\Delta }}_0)$ reflects the strength of the SOC relative to the gap energy scale. Dashed blue (dashed gray) and solid red (solid gray) curves represent the spin-up and spin-down DOS, respectively, while the solid black curve gives the total DOS from ${\rho }_{\uparrow }+{\rho }_{\downarrow }$ (shifted upwards by 1 for clarity). The spectra were calculated using Maki’s theory [Eq. (2)] at $T=0\mathrm{K}$, lifetime broadening parameter $\zeta =0.1$, and magnetic field ${\mu }_{B}H/{\mathrm{\Delta }}_0=0.6$.

Figure 2

Tunneling spectroscopy and resistivity in zero field. (a) Tunneling conductance ($di/dv$) of 18 nm thick Nb-doped ${\mathrm{SrTiO}}_3$ thin film measured at the base temperature of the dilution refrigerator. (b) Superconducting gap amplitude ($\mathrm{\Delta }$) (open circles, left axis) compared to the normalized resistance [solid blue (gray) line, right axis]. The superconducting gap closes at $T=315\pm 5\mathrm{mK}$, which is very close to the resistive transition temperature $T_c=330\mathrm{mK}$ defined as 50% of the normal state resistivity at $T=0.6\mathrm{K}$.

Figure 3

Tunneling spectroscopy of the superconducting gap under applied magnetic field. (a) Raw $di/dv$ data for several values of magnetic fields applied out-of plane (${\mu }_0{H}_{\perp }$, left panel) and in-plane (${\mu }_0{H}_{\parallel }$, right panel). (b) Zero-bias conductivity ($\sigma =di/dv$) of the gap minimum normalized to the normal-state conductance (${\sigma }_N$) for both field orientations. The out-of plane ($H_{c2,\perp }$) and in-plane ($H_{c2,\parallel }$) upper critical fields are indicated. The vertical dashed blue line indicates the Pauli paramagnetic limiting field ($H_P$).

Figure 4

Maki analysis of the superconducting gap spectra under in-plane magnetic fields. (a) Total quasiparticle broadening ${\zeta }^{\prime }$ (black dots) determined by fitting the tunneling data in the right panel of Fig. 3 using Eq. (3). The total broadening exhibits a dependence on the square of the applied magnetic field and the solid line represents a fit to ${\zeta }^{\prime }={\alpha }_i+\eta H^2$. (b) Normalized $di/dv$ data (solid black line) measured at ${\mu }_0{H}_{\parallel }=0.5\mathrm{T}$ and theoretical fit [dashed red (gray) line] using Maki’s full theory as expressed in Eq. (2) with $b=6$, ${\alpha }_i=0.056$, ${\alpha }_o=0.11$, and ${\mathrm{\Delta }}_0=47\mu \mathrm{eV}$.