Thermoelectric effect in the Kondo dot side-coupled to a Majorana fermion

We investigate the linear thermoelectric response of an interacting quantum dot side-coupled by one of two Majorana fermions (MFs) formed at the ends of a topological superconducting wire. We employ the numerical renormalization group technique to obtain the thermoelectrical conductance $L$ as well as the electrical conductance $G$ when the background temperature $T$ and the dot gate are tuned. We distinguish two transport regimes in which $L$ displays different features: the weak- $(Γ_{m} < T_{K})$ and strong-coupling $(Γ_{m} > T_{K})$ regimes, where $Γ_{m}$ and $T_{K}$ are the Majorana-dot coupling and the Kondo temperature, respectively. For an ideal (infinitely long) nanowire where the Majorana end states do not overlap $(ε_{m} = 0)$, the thermoelectrical conductance $L$ in the weak-coupling regime exhibits a peak at $T \sim Γ_{m}$. This peak is ascribed to the anti-Fano resonance between the asymmetric Kondo resonance and the zero-energy MF mode. Interestingly, in the strong-coupling regime, the Kondo-induced peak in $L$ is shifted due to the MF-induced Zeeman splitting in the dot. For finite but small $ε_{m} > 0$, the interference between two MFs restores the Kondo effect in the dot in a smaller energy scale $Γ^{\prime}_{m}$ and gives rise to an additional peak in $L$ at $T \sim Γ^{\prime}_{m}$, whose sign is opposite to that at $T\simΓ_{m}$. In the strong-coupling regime this additional peak can cause a non-monotonic behavior of $L$ with respect to the dot gate. Finally, we examine the case in which an ordinary spin-polarized fermion is coupled to the dot and identify the fingerprint of MFs by comparing two cases.

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