Correlated disorder in one-dimensional topological superconductors

In this study, we investigate the impact of correlated disorder on one-dimensional topological superconductors. Topological phases are known for their robustness against weak, local perturbations due to their spectral gap. However, strong perturbations can disrupt these phases, making it crucial to understand the tolerance levels. We focus on the effects of correlated disorder, where the spatial dependence of system parameters is non-trivial, as opposed to the well-studied uncorrelated disorder. Using numerical simulations and analytical calculations, we demonstrate that while the universality class of the phase transition remains unaffected by correlated disorder, the normal-state localization length is significantly reduced. This reduction leads to a shrinkage of the topological phase the shape of the resulting phase diagram and the disordered topological coherence length differ from compared to the uncorrelated disorder case. Our findings highlight the importance of considering correlated disorder in experimental setups, particularly when the correlation length is comparable to the Fermi wavelength. These insights are vital for the development of robust topological qubits and the advancement of quantum computing technologies.