Unconventional superconductivity in double quantum dots

The formation of electron pairs is a prerequisite of superconductivity. The fermionic nature of electrons yields four classes of superconducting correlations with definite symmetry in spin, space, and time. Here, we suggest double quantum dots coupled to conventional $s$-wave superconductors in the presence of inhomogeneous magnetic fields as a model system exhibiting unconventional pairing. Due to their small number of degrees of freedom, tunable by gate voltages, quantum-dot systems are ideal to gain fundamental insight into unconventional pairing. We propose two detection schemes for unconventional superconductivity, based on either Josephson or Andreev spectroscopy.

Figure 1

(a) A double quantum dot in an inhomogeneous magnetic field and tunnel coupled to a superconducting lead yields unconventional pair amplitudes. They can be probed via (b) the dc Josephson current through two coupled double quantum dots and (c) the Andreev current from the superconductor into two normal leads. Dashed arrows denote tunnel couplings.

Figure 2

Josephson current in units of $e{\Gamma }_{\mathrm{S}i,a}/\hslash$ for ${\Gamma }_{\mathrm{S}i,a}=U$, ${\varepsilon }_{i,a}=3.5U$, $|{\mathbf{B}}_{i,a}|=10U$, ${\alpha }_a=\alpha$, $k_{\mathrm{B}}T=0$ for (a) spin-insensitive tunneling $t_{\uparrow }=t_{\downarrow }=0.1U$ and (b) fully spin-selective tunneling $t_{\uparrow }=0.1U$, $t_{\downarrow }=0$. The existence of a maximum of the Josephson current for an angle ${\alpha }_{\max }$ with $0<{\alpha }_{\max }<\pi$ (that is for noncollinear magnetic fields) signals the presence of triplet correlations in the system.

Figure 3

Differential Andreev conductance in units of $G_{\mathrm{tunn}}=(e^2/h){\Gamma }_{\mathrm{N}}/\left(2\pi k_{\mathrm{B}}T\right)$ as a function of bias voltage ${\mu }_{\mathrm{N}}$ and (a) detuning $\delta$ for $\alpha =\pi /2$ and (b) $\alpha$ for $\delta =0$. The chosen parameters are ${\Gamma }_{\mathrm{S}}=U/2$, $|{\mathbf{B}}_{\mathrm{L}/\mathrm{R}}|=0.4U$, $t=0.001U$, and $k_{\mathrm{B}}T=0.01U$. The nonmonotonic behavior of the differential conductance on $\alpha$, resulting in a suppression around $\alpha =\pi$, is a signature of triplet correlations.