Quantum transport signatures of chiral edge states in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$

We investigate transport properties of a double quantum dot based a Cooper pair splitter, where the superconducting lead consists of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. The proposed device can be used to explore the symmetry of the superconducting order parameter in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ by testing the presence of gapless chiral edge states, which are predicted to exist if the bulk superconductor is described by a chiral $p$-wave state. The odd orbital symmetry of the bulk order parameter ensures that we can realize a regime where the electrons tunneling into the double-dot system come from the chiral edge states and thereby leave their signature in the conductance. The proposed Cooper pair splitter has the potential to probe the chirality of the order parameters in topological superconductors.

Figure 1

Schematic of the device (not to scale). Two single-walled carbon nanotubes (or one bent nanotube) are used to form a double-dot system tunnel-coupled to a thin platelet of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$.

Figure 2

$I_{\text{CPS}}$ as a function of $\epsilon$ that is tunable by (symmetric) external gate voltages, calculated using Eq. (17) for various values of $|t_{eh}|$. Inset: $|t_{eh}^{\text{II}}\left(k_F\delta r\right)|/|t_{eh}^{\text{II}}\left(0\right)|$ as a function of $k_F\delta r$ for $\epsilon /\Delta =0.01$ calculated using Eq. (15).