Properties of multiterminal superconducting nanostructure with double quantum dot

TL;DR

The paper investigates charge and thermoelectric transport in a multiterminal hybrid device comprising two quantum dots in a T-shaped configuration between two normal/ferromagnetic leads and a superconducting lead. By modeling the system with a detailed Hamiltonian and analyzing it in the Δ → ∞ (atomic) limit, the authors show that the interdot coupling t12 controls the emergence of interference (Fano) features at weak coupling and molecular Andreev bound states at strong coupling, which in turn govern both local and nonlocal transport and Seebeck responses. The transport is decomposed into electron transfer (ET), direct Andreev reflection (DAR), crossed Andreev reflection (CAR), and quasiparticle (QP) channels, enabling channel-resolved predictions for zero-bias conductance and thermopower, including signs and divergences that mark crossovers between regimes. The study also extends to spin-polarized (ferromagnetic) leads, revealing spin-resolved spectra and transport that further reveal the competition between ballistic and Andreev channels under polarization. Overall, the work provides a framework to identify proximity-induced Andreev molecular states and offers experimental signatures in conductance and thermopower to distinguish between weak- and strong-coupling regimes in multiterminal superconducting nanostructures.

Abstract

We study the charge transport and thermoelectric properties of the junction, comprising double quantum dot embedded in T-shaped geometry on the interface between two normal/ferromagnetic electrodes and superconducting lead. We show that the interdot coupling plays major role in controlling the local and nonlocal transport properties of this setup. For the weak interdot coupling limit, we obtain the interferometric (Fano-type) lineshapes imprinted in the quasiparticle spectra, conductances and Seebeck coefficients. In contrast, for the strong interdot coupling, we predict that the local and nonlocal transport coefficients are primarily dependent on the molecular Andreev bound states induced by superconducting proximity effect, simultaneously in both quantum dots.

Figures (14)

• Figure 1: Sketch of two quantum dots (QD$_1$ and QD$_2$) on interface of three-terminal junction. QD$_1$ is embedded between two normal/ferromagnetic leads ($L$ and $R$) and is side-attached to QD$_2$, which is coupled to superconductor ($S$).
• Figure 2: Illustration of the charge transport processes in the three-terminal setup contributed by: ballistic electron transfer (ET), direct Andreev reflection (DAR), crossed Andreev reflection (CAR) and quasiparticles tunneling (QP), respectively.
• Figure 3: The spectral function $A_{1\uparrow}(\omega)$ of QD$_1$ as a function of the interdot coupling $t_{12}$ obtained for $\varepsilon_{1}=0$ (a) and $\varepsilon_{1}=0.5$ (b) and using the model parameters $\varepsilon_{2}=0$, $\Gamma_{S}=2$, $\Gamma_{L}=\Gamma_{R}=0.5$, $k_BT=0$ and $p_{0}=0$. White solid-lines display the profile of the spectral function in the weak ($t_{12}=0.1$) and strong coupling ($t_{12}=0.8$) limits, respectively. The quasiparticle energies $\varepsilon_{AD1}^{\pm}$ and $\varepsilon_{AD2}^{\pm}$, given by Eqs. (\ref{['eq_6']},\ref{['eq_7']}), are marked by white-dashed lines.
• Figure 4: The local (panels a and b), and nonlocal (panel c) electron pairing plotted vs the interdot coupling $t_{12}$ for several energy levels $\varepsilon_{1}$, as indicated. Computations are done for the set of model parameters: $\varepsilon_{2}=0$, $\Gamma_{S}=2$, $\Gamma_{L}=\Gamma_{R}=0.5$, $T=0$ and $p_{0}=0$.
• Figure 5: Variation of the local $G_{LL}$ (a) and nonlocal $G_{RL}$ (b) conductance versus the interdot coupling $t_{12}$ for several temperatures, as indicated. Results are obtained for the model parameters $\varepsilon_{1}=\varepsilon_{2}=0$, $\Gamma_{S}=2$, $\Gamma_{L}=\Gamma_{R}=0.5$ and $p_{0}=0$.