Effect Of Random Disorder On Topology And Localization Properties Of A One-dimensional Kitaev Model

Majorana particles,the same as their antiparticles,are a candidate for quantum computing.In condensed matter,superconductors hosting midgap Majorana zero-mode excitations are called topological superconductors,and the Kitaev model as a paradigmatic example is widely discussed.The density of state as an important experimental tool is used to detect Majorana zero modes in the early time.However,the disorder-induced non-topological subgap zero modes mimic most signatures of the topological Majorana zero modes.In this work,we theoretically study a one-dimensional Kitaev model with different disorder effects,including the on-site,the hopping,and the superconducting pairing disorder terms.With the increase of the disorder amplitudes,one can always observe a zero-energy peak appearing in the density of states,which may cast doubts on their topological Majorana origin.We apply the Z₂ topological invariant and the Lyapunov exponent（LE）to characterize the topological phase diagrams for different disorder effects in the Kitaev model.We find that a strong enough disorder always destroys topologically nontrivial Majorana modes except the Kitaev model with the hopping or the superconducting pairing disorder effects atμ₀=0,though the non-vanishing zero-energy peak emerges in the density of states.The nontrivial topological zero modes can also be induced by the on-site,hopping,and full（modulated on-site potentials,hopping terms,and p-wave pairing terms）disorder effects in the topologically trivial regime for a clean case.Finally,by calculating the inverse participation ratio,the fractal dimension,and the standard deviation of the eigenstates,we study the localization properties of the system with the on-site disorder effect as an example.Unlike the one-dimensional Anderson model,the localization transition of the one-dimensional Kitaev model exhibits complex localization behavior.With the increase of the on-site disorder amplitude,the rate of the metal-insulator transition in the low-energy part is much slower than that in the high-energy part.