Interplay of bound states in the continuum and Fano--Andreev interference in a hybrid triple quantum dot

Abstract

We investigate bound states in the continuum (BICs) in a hybrid normal--superconducting triple quantum dot system, where the central dot is coupled to two normal leads and the lateral dots are proximity-coupled to superconducting electrodes. Local electron--electron interactions are treated within the Hubbard approximation. Finite bias, together with lateral-dot detuning and superconducting proximity, induces interference between elastic electron tunneling (ET) and Andreev reflection (AR) channels, mediated by BIC-related modes and proximity-induced Andreev bound states. As the bias is swept through the subgap resonances, ET exhibits sharp antiresonances that evolve into exact transport zeros, signaling the emergence of (quasi-)BICs. We further find a continuous crossover from a Fano--Andreev BIC-supported regime to a Fano--Andreev quasi-BIC regime as the detuning asymmetry increases. The formation of BICs and quasi-BICs is accompanied by a pronounced change in the occupation of the side quantum dot, providing an internal diagnostic directly correlated with the transport signatures of the bound states.

Figures (3)

• Figure 1: Schematic of the hybrid normal--superconducting triple-quantum-dot device. The central dot $QD_b$ is coupled to the two normal leads $L$ and $R$, while the lateral dots $QD_a$ and $QD_c$ are proximity-coupled to the superconducting electrodes $S_1$ and $S_2$, respectively. The interdot couplings $t_{ab}$ and $t_{cb}$ connect the lateral dots to the central dot, and the lateral-dot levels are detuned as $\varepsilon_{a,c}=\varepsilon_b\pm\eta$.
• Figure 2: Transport and spectral signatures of the interacting hybrid triple-quantum-dot system (Fig. \ref{['Fig1']}) for fixed values of the lateral-dot detuning. Left column: Differential conductance for electron tunneling (ET), $(dI/dV)^{\rm ET}$, and Andreev reflection (AR), $(dI/dV)^{\rm AR}$, versus bias $V$ for fixed value of lateral-dot detuning (a) $\eta=0$, (c) $\eta=0.05$, and (e) $\eta=0.1$. Right column: corresponding local density of states (LDOS) $\rho_i(\omega)$ as a function of energy ($\omega$) at quantum dots $i=a,b,c$, for detuning (b) $\eta=0$, (d) $\eta=0.05$, and (f) $\eta=0.1$, taken at the values of bias corresponding to the electron-tunneling antiresonances near $V=-U/2$. Insets highlight the antiresonance region in the conductance (left column) and the narrow subgap peaks in the LDOS (right column). Other parameters are fixed to the following values: $\Delta_1=\Delta_2=5\Gamma_L$, $U=5$, $T=0$, $\Gamma_L=\Gamma_R=\Gamma_S$, and $\varepsilon_{a,c}=\varepsilon_b\pm\eta$ with $\varepsilon_b=-U/2$. See also Fig. S1 in the Supplementary Material for the additional plots of the occupation number versus bias for the same values of the parameters.
• Figure 3: Contour plots of the differential conductances $(dI/dV)^{\rm ET}$ and $(dI/dV)^{\rm AR}$ versus the lateral-dot detuning $\eta$ and bias $V$, for the interacting hybrid triple-quantum-dot system (Fig. \ref{['Fig1']}). Here, ET and AR denote electron tunneling and Andreev reflection, respectively: (a) $(dI/dV)^{\rm ET}$ and (b) $(dI/dV)^{\rm AR}$. As $\eta$ increases, the ET antiresonances deepen and reach exact zeros near $V\simeq \pm U/2$, while the AR conductance develops corresponding minima. Other parameters are chosen as $\Delta_1=\Delta_2=5\Gamma_L$, $U=5$, $k_B T=0$, $\Gamma_L=\Gamma_R=\Gamma_S$, and $\varepsilon_{a,c}=\varepsilon_b\pm\eta$ with $\varepsilon_b=-U/2$. See Fig. S2 in the Supplementary Material for the corresponding plots in a wider range of $V$.