Kondo Correlations and Majorana Bound States in a Metal to Quantum-Dot to Topological-Superconductor Junction

Electron transport through a normal-metal–quantum-dot–topological-superconductor junction is studied and reveals interlacing physics of Kondo correlations with two Majorana fermions bound states residing on the opposite ends of the topological superconductor. When the strength of the Majorana fermion coupling exceeds the temperature $T$, this combination of Kondo-Majorana fermion physics might be amenable for an experimental test: The usual peak of the temperature dependent zero bias conductance $\sigma (V=0,T)$ splits and the conductance has a dip at $T=0$. The heights of the conductance side peaks decrease with magnetic field.

Figure 1

NM-QD-TS junction. An applied magnetic field can induce MBS at the ends of the TS wire. The QD can be gated to adjust the level position in the dot.

Figure 2

Diagrams contributing to the conductance due to the Kondo interaction (2). Upper (lower) panel represents second (third) order contributions. Thick solid line: Majorana GF; thin solid lines: lead fermions GF dashed and dotted lines: impurity spin. Dotted line is the Majorana $F_z$ GF, and dashed line is the Dirac fermion $F_f$ GF. The left vertex in both sets has Keldysh index 1, other vertices have ${\sigma }_z$ Pauli matrix acting in Keldysh space.

Figure 3

The total nonlinear conductance (4) $G=\sigma /\alpha$ versus applied bias. The central high peak and lower plateau correspond to $\nu =0.4\mathrm{T}$, $D=1000\mathrm{T}$ but different values of magnetic field: $B=0$ for the peak and $B=3\mathrm{T}$ for the plateau. The same for the dashed and dotted dashed curves, the only difference is that $\nu =2.4\mathrm{T}$. For all four curves we assume $\Gamma /(2\pi \epsilon )=0.1$.

Figure 4

Zero bias conductance as function of temperature in the region $T_K<T<\Gamma$ at zero magnetic field. $G={\sigma }^{(2)}/(\alpha T/\Gamma )$ is the second order contribution (dashed line), while $G^t$ stands for the total conductance in the same units as $G$ (solid line). We take $\nu =0.4\Gamma$ and use the value $\Gamma /(2\pi \epsilon )=0.1$.

Figure 5

The zero biased conductance as a function of temperature at zero magnetic field in the strong coupling limit ($T<T_K$). The dashed curve corresponds to $\nu =0.5T_K$ and the solid line to $\nu =0.1T_K$.