Multichannel Kondo Impurity Dynamics in a Majorana Device

We study the multichannel Kondo impurity dynamics realized in a mesoscopic superconducting island connected to metallic leads. The effective “impurity spin” is nonlocally realized by Majorana bound states and strongly coupled to lead electrons by non-Fermi liquid correlations. We explore the spin dynamics and its observable ramifications near the low-temperature fixed point. The topological protection of the system raises the perspective to observe multichannel Kondo impurity dynamics in experimentally realistic environments.

Figure 1

Schematic setup leading to the topological Kondo effect. A floating superconducting island (center square) with charging energy $E_c$ supports a helical crossed nanowire [10]; alternative realizations using several nanowires are also possible. At the terminal points of the wires, Majorana fermions ${\gamma }_j$ (the circles) are present [11, 12, 13], $M$ of which are coupled to external leads (here $M=3$). Direct tunnel couplings $h_{jk}$ between the Majorana states act like a Zeeman field on this “Majorana impurity spin.” The upper part illustrates the optional coupling to a single-electron box via flux-tunable tunnel amplitudes. This provides a way [14] to read out the effective magnetization $\sim i⟨{\gamma }_j{\gamma }_k⟩$.

Figure 2

Schematic sketch of the temperature ($T$) dependence of the linear conductance coefficient $G_{jj}$, with $j\ne 1$, 2, for $M>4$ and a Zeeman field with $h_{12}\ne 0$. For $T\ll T_h$, the conductance approaches $(2e^2/h)(M-3)/(M-2)$, as appropriate for the $\mathrm{SO}(M-2)$ fixed point. For $T_h\ll T\ll T_K$, on the other hand, it is the $\mathrm{SO}(M)$ fixed point that governs the conductance, with $G_{jj}\simeq \frac{2e^2}{h}\mathbf{(}(M-1)/M-c_1(T_h/T{)}^{4/M}-c_2(T/T_K{)}^{2–4/M}\mathbf{)}$, where $c_{1,2}$ is of order unity.