We study the physics of a mobile impurity immersed in a
1d topological superconductor. We discuss the system's phase diagram obtained with exact diagonalization. We argue that the character of the transition from a weak to strong coupling regime depends on the phase of the host superconductor. A smooth crossover between a weakly coupled polaron and a molecular state is observed in the topological phase. In contrast, the impurity undergoes a sharp phase transition in a topologically trivial background.
We study a mobile impurity coupled to a Kitaev chain with chemical-potential disorder and ask whether the impurity behavior distinguishes different regimes of the host system. Exact diagonalization calculations for small periodic chains shows that in the deep topological regime the impurity localizes only partially, with a smooth increase of
IPRd, whereas in the deep trivial regime it undergoes a much sharp transition to nearly single-site localization. For open chains at strong interaction, DMRG shows edge-localized impurity density near the Kitaev sweet spot. With increasing chemical potential, the impurity weight spreads into the bulk and eventually becomes almost uniform. We explain the edge preference analytically from the Majorana-dimer structure: a bulk impurity rearranges two neighboring dimers, while an edge impurity affects only one. Disorder competes with this clean edge bias and can pin the impurity in the bulk. Thus, the impurity is sensitive to the regime of the host system, although we do not find a strict one-to-one correspondence between the impurity localization pattern and the host topology. Instead, the disorder-averaged behavior suggests only an indirect correlation between impurity localization and the underlying phase of the chain.
Abstract A scheme to investigate the topological properties in a two‐leg Kitaev ladder system composed of two Kitaev chains is proposed. In the case of two identical Kitaev chains, it is found that the interchain hopping amplitude plays a significant role in the separation of the energy spectrum and in inducing a topologically nontrivial phase, while the interchain pairing strength only affects the size of the energy gap. Moreover, another situation that the system consists of two non‐identical Kitaev chains is also investigated and the corresponding phase diagram is calculated. It is found that two pairs of degenerate nonzero edge modes will, respectively, appear in the upper and lower energy gaps when the interchain hopping amplitude or the interchain pairing strength is large enough. Furthermore, it is pointed out that the winding number is quantitatively equivalent to half of the number of zero energy edge modes in our system.