Enhanced Shot Noise of Multiple Andreev Reflections in a Carbon Nanotube Quantum Dot in SU(2) and SU(4) Kondo regimes

The sensitivity of shot noise to the interplay between Kondo correlations and superconductivity is investigated in a carbon nanotube quantum dot connected to superconducting electrodes. Depending on the gate voltage, the SU(2) and SU(4) Kondo unitary regimes can be clearly identified. We observe enhancement of the shot noise via the Fano factor in the superconducting state. Its divergence at low bias voltage, which is more pronounced in the SU(4) regime than in the SU(2) one, is larger than what is expected from proliferation of multiple Andreev reflections predicted by the existing theories. Our result suggests that the Kondo effect is responsible for this strong enhancement.

Figure 1

(a),(b) Color plot of $G(V)$ as a function of source-drain voltage ($V$) and gate voltage ($V_g$) in the $N$ state and in the $S$ state for the SU(2) symmetry, respectively. The value, $\mathrm{\Delta }=45\mu \mathrm{eV}$, is extracted from $2\mathrm{\Delta }$ peak of $G(V)$ outside the Kondo region ($n=0$). (c) $V_g$ dependence of $G(0)$ in the $N$ state (solid curve) and $S$ state (dashed curve) for SU(2). Squares represent Kondo temperature $T_K$. $G(0)$ reaches the unitary limit $G=G_Q$ in the $N$ state of SU(2), ensuring a perfect left-right symmetric coupling of the QD. $n$ represents the number of electrons in the last shell of the CNT dot. (d),(e) Color plot of $G(V)$ as a function of $V$ and $V_g$ in the $N$ state and in the $S$ state for the SU(4) symmetry, respectively. (f) $V_g$ dependence of $G(0)$ for the $N$ state (solid curve) and $S$ state (dashed curve) and $T_K$ (square marks) for SU(4). This work focuses on the three states, $\mathrm{SU}(2)n3$, $\mathrm{SU}(4)n3$, and $\mathrm{SU}(4)n2$, whose positions are represented on the top of the figures.

Figure 2

(a) $\mathrm{eV}/k_B{T}_K$ dependence of $G(V)$ at $n=3$ in the $N$ states for $\mathrm{SU}(2)n3$ (solid curve) and $\mathrm{SU}(4)n3$ (dashed curve). The conductance shapes are almost indistinguishable. (b) $\mathrm{eV}/\mathrm{\Delta }$ dependence of $G(V)$ in the $S$ state for $\mathrm{SU}(2)n3$ (solid curve) and $\mathrm{SU}(4)n3$ (dashed curve). For SU(2), a single perfectly transmitting channel allows high order MAR and high $G(0)$, while two channels with low transmission ($T_1=T_2=0.5$) suppress $G(V)$ at low bias for $\mathrm{SU}(4)n3$. (c) $I$ dependence of $S_I$ for $\mathrm{SU}(2)n3$ in the $N$ and $S$ states (solid and dashed curves, respectively). The enhancement around zero bias is due to high order MAR. (d) $I$ dependence of $S_I$ for $\mathrm{SU}(4)n3$ in the $N$ and $S$ states (solid and dashed curves, respectively). The dashed lines correspond to $e^{*}=e$ with $F=1-T=1/2$ and $2e$ with $F=1-T^2=3/4$ (see text and Supplemental Material [35]).

Figure 3

(a) $\mathrm{eV}/\mathrm{\Delta }$ dependence of $G(V)$ in the $S$ state for $\mathrm{SU}(2)n3$ and $\mathrm{SU}(4)n2$, which correspond to the electron-hole symmetry case. Those two states have perfectly transmitting channels leading to high order interfering MAR, which enhances $G(V)$ at low voltage. (b) $\mathrm{eV}/\mathrm{\Delta }$ dependence of $S_I$ in the $S$ state for $\mathrm{SU}(2)n3$ and $\mathrm{SU}(4)n2$. Here, interfering MAR enhances the low bias shot noise.

Figure 4

(a) Fano factor in the $S$ state at half filling. $1/|V|$ dependence of $F=S_I/2e|I|$ in the $S$ state for $\mathrm{SU}(2)n3$ (squares), $\mathrm{SU}(4)n2$ (circles), and numerical calculation result for a QPC (triangles). The points are fitted with Eq. (1). $\alpha$ is the enhancement factor in the Kondo regime compared to an $S$-weak link. (b) $V_g$ dependence of the superconducting noise enhancement $\alpha$ in the SU(4) case. $\alpha$ shows its maximum in the state $\mathrm{SU}(4)n2$ at the electron-hole symmetric point.