Screening cloud and non-Fermi-liquid scattering in topological Kondo devices

The topological Kondo effect arises when conduction electrons in metallic leads are coupled to a mesoscopic superconducting island with Majorana fermions. Working with its minimal setup, we study the lead electron local tunneling density of states in its thermally smeared form motivated by scanning tunneling microscopy, focusing on the component $\rho_{2 k_F}$ oscillating at twice the Fermi wavenumber. As a function of temperature $T$ and at zero bias, we find that the amplitude of $\rho_{2 k_F}$ is nonmonotonic, whereby with decreasing $T$ an exponential thermal-length-controlled increase, potentially through an intermediate Kondo logarithm, crosses over to a $T^{1/3}$ decay. The Kondo logarithm is present only for tip-junction distances sufficiently smaller than the Kondo length, thus providing information on the Kondo screening cloud. The low temperature decay indicates non-Fermi-liquid scattering, in particular the complete suppression of single-particle scattering at the topological Kondo fixed point. For temperatures much below the Kondo temperature, we find that the $\rho_{2 k_F}$ amplitude can be described as a universal scaling function indicative of strong correlations. In a more general context, our considerations point towards the utility of $\rho_{2 k_F}$ in studying quantum impurity systems, including extracting information about the single-particle scattering matrix.