Hybrid superconducting quantum magnetometer

A superconducting quantum magnetometer based on magnetic flux-driven modulation of the density of states of a proximized metallic nanowire is theoretically analyzed. With optimized geometrical and material parameters transfer functions up to a few mV$/{\Phi }_0$ and intrinsic flux noise $\sim {10}^{-9}{\Phi }_0/\sqrt{\text{Hz}}$ below 1 K are achievable. The opportunity to access single-spin detection joined with limited dissipation (of the order of $\sim {10}^{-14}$ W) make this magnetometer interesting for the investigation of the switching dynamics of molecules or individual magnetic nanoparticles.

Figure 1

(a) Scheme of the device. $L$ is the wire length whereas $w$ is the width of the superconducting tunnel junction ($S$${}_2$) coupled to the middle of the $N$ region. $\varphi$ is the macroscopic quantum phase difference in $S$${}_1$, while $\Phi$ is the magnetic flux threading the loop. Furthermore, $R_t$ is the tunnel junction normal-state resistance and $I_{\text{bias}}$ is the current flowing through the structure.

Figure 2

Josephson current vs flux ($I_{\mathrm{eq}}-\Phi$) characteristics calculated for a few values of temperature $T$ assuming ${\Delta }_1^0=0.1E_{\mathrm{Th}}$ and ${\Delta }_1^0=4{\Delta }_2^0$. Thick lines represent the supercurrent calculated using the Ambegaokar-Baratoff formula Eq. (11), whereas the thin lines are the supercurrent calculated for an extended tunnel junction with width $w=L/2$.

Figure 3

Interferometer quasiparticle current vs voltage ($I-V$) characteristics calculated for a few values of $\Phi$ at $T=0.1T_{c2}$. $T_{c2}$ is the critical temperature of $S$${}_2$, $I_{\mathrm{bias}}$ is the current flowing through the device, and $V\left(\Phi \right)$ is the resulting voltage modulation.

Figure 4

(a) $V$ vs $\Phi$ calculated for several bias currents $I_{\mathrm{bias}}$ at $T=0.1T_{c2}$. (b) $\mathcal{F}$ vs $\Phi$ calculated for the same $I_{\mathrm{bias}}$ values and $T$ as in (a).

Figure 5

(a) $V$ vs $\Phi$ calculated for a few temperatures at $I_{\mathrm{bias}}=1.0{\Delta }_2^0/e{R}_t$. (b) $\mathcal{F}$ vs $\Phi$ calculated for the same $T$ values and $I_{\mathrm{bias}}$ as in (a).

Figure 6

(a) ${\Phi }_{ns}$ vs $I_{\mathrm{bias}}$ calculated for different $\Phi$ values at $T=0.3$ K. (b) ${\Phi }_{ns}$ vs $I_{\mathrm{bias}}$ for $\Phi =0.3{\Phi }_0$ calculated at different temperatures. (c) $P$ vs $I_{\mathrm{bias}}$ calculated for different $\Phi$ values at $T=0.3$ K. In all calculations we set ${\Delta }_2^0=200\mu$eV, ${\Delta }_1^0=800\mu$eV, and $R_t=5$ M$\Omega$.