Finite Frequency Noise of a Superconductor-Ferromagnet Quantum Point Contact

We calculate the finite-frequency current noise of a superconductor-ferromagnet quantum point contact ($SF$ QPC). This signal is qualitatively affected by the spin dependence of interfacial phase shifts acquired by electrons upon reflection on the QPC. For a weakly transparent QPC, noise steps appear at frequencies or voltages determined directly by the spin dependence of interfacial phase shifts. These steps can occur at experimentally accessible temperatures and frequencies. Finite-frequency noise is thus a promising tool to characterize the scattering properties of a $SF$ QPC.

Figure 1

Excess noise $S_{\mathrm{ex}}$ versus $\omega$, for $V=1.4\Delta$, $T=0$, and different values of the SDIPS parameter $\Delta \phi$. The symbols correspond to frequencies defined in the above table.

Figure 2

Energy diagram of the $SF$ QPC, for $\Delta \phi \ne 0$, $eV>\Delta$, $\Delta \phi =0$ (a), and $\Delta \phi \ne 0$ (b). The various columns represent the (hole) electron band in $F$, filled (down) up to the energy $(-)eV$, and the density of states in $S$, which presents a gap for $\epsilon \in [-\Delta ,\Delta ]$. The resonance function $D(\epsilon )=|D_{\uparrow }(\epsilon ){|}^{-2}+|D_{\downarrow }(\epsilon ){|}^{-2}$ is shown with red full lines. In (a), the different frequencies $\omega$ at which $S_{\mathrm{ex}}$ is singular are represented with green arrows. In (b), we show with blue and green arrows transfer processes contributing to the ★ and ■ features of Fig. 1.

Figure 3

Excess noise $S_{\mathrm{ex}}$ versus $\omega$. The left and right panels show the effect of an increase of the spin-averaged transmission probability $T_{\mathrm{av}}$ and of the temperature $T$, respectively. The symbols correspond to frequencies defined in Fig. 1.

Figure 4

Excess noise $S_{\mathrm{ex}}$ as a function of the bias voltage $V$, for $\omega =0$ $[\omega \ne 0]$ (dotted [full] lines). We have used no SDIPS on the left panel and a finite SDIPS on the right panel.