Tuning odd triplet superconductivity by spin pumping

We study proximity effect in diffusive ferromagnet/normal-metal/superconductor junction with precessing magnetization of the ferromagnet. We find that the odd-frequency pairing induced in the normal metal is modified by spin pumping from the ferromagnet and hence can be tuned by changing the precessional frequency. At the frequency corresponding to twice the superconducting gap, the odd-frequency pairing is strongly enhanced. We find that the odd-frequency pairing can be dominant over the even-frequency pairing in the normal metal by tuning the precessional frequency. This gives a clearcut signature of the odd-frequency superconductivity observable by scanning-tunneling microscopy. According to the pairing symmetries in the normal metal, we find a crossover from the gap to the peak structure in the tunneling conductance between the normal metal and a scanning-tunneling microscope tip.

Figure 1

(Color online) Schematic of the model for a F/N/S junction with precessing magnetization of the F layer. A fictitious exchange field is dynamically induced in the N layer, which interplays with the superconductivity induced by the proximity effect. The electronic structure in the N layer can be studied by STM.

Figure 2

(Color online) Anomalous Green’s functions as a function of $\Omega /E_{\text{Th}}$ at the N/S interface $\left(x=L\right)$ with (a) ${\gamma }_{\varphi }=100$ and (b) ${\gamma }_{\varphi }=10$ and at the F/N interface $\left(x=0\right)$ with (c) ${\gamma }_{\varphi }=100$ and (d) ${\gamma }_{\varphi }=10$. Here, we set $\epsilon =0$. $f_1$ and $f_3$ are the odd-frequency and $f_s$ is the even-frequency pairing amplitudes.

Figure 3

(Color online) The density of states normalized by its normal-state value as a function of $\epsilon /E_{\text{Th}}$ with ${\gamma }_{\varphi }=100$ at (a) $x=L$ and (b) $x=0$.

Figure 4

(Color online) The normalized tunneling conductance as a function of $eV/E_{\text{Th}}$ with ${\gamma }_{\varphi }=100$ at (a) $x=L$ and (b) $x=0$.