Even-odd effect on robustness of Majorana edge states in short Kitaev chains
Motohiko Ezawa
Abstract
We construct two-band effective models describing Majorana edge states in a short Kitaev chain. We derive an analytical formula for the effective Hamiltonian as a function of model parameters. Then, we discuss the robustness of Majorana edge states as a function of model parameters. We have found an even-odd effect on the robustness of Majorana states, which is characteristic of short Kitaev chains. It is experimentally observable as a differential conductance in quantum dot systems. We also study effects of coupling to an environment based on non-Hermitian Hamiltonians derived from the Lindblad equation. It is found that the Majorana zero-energy edge states acquire nonzero energy such as $E\ensuremath{\propto}\ifmmode\pm\else\textpm\fi{}{(i\mathrm{\ensuremath{\Gamma}})}^{L}$ for the local dissipation, where $\mathrm{\ensuremath{\Gamma}}$ is the magnitude of the dissipation and $L$ is the length of the chain. The even-odd effect is manifest for small $L$ in this formula. On the other hand, the Majorana zero-energy edge states acquire nonzero energy such as $E\ensuremath{\propto}\ifmmode\pm\else\textpm\fi{}i\mathrm{\ensuremath{\Gamma}}$ for small $\mathrm{\ensuremath{\Gamma}}$ irrespective of the length $L$ for the global dissipation.