Fate of poor man's Majoranas in the long Kitaev chain limit

Abstract

A minimal Kitaev chain, consisting of two quantum dots connected via a superconductor, can host highly localized near-zero-energy states, known as poor man's Majoranas (PMMs). These states have been proposed as promising candidates to study Majorana bound states (MBSs) in a highly tunable setup. However, it is unclear whether and how PMMs observed in real systems are actually connected to the topological phase of the full Kitaev chain. Here, we study PMMs using a microscopic model and show that, in the long chain limit, not all PMMs are related to topological states. Rather, in long chains, some PMMs evolve into trivial highly localized low-energy states. We provide an explanation for the occurrence of these states and show that there is no clear conductance signature that is able to distinguish PMMs that evolve into true topological states from PMMs that evolve into trivial states.

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• Braiding Majoranas in a linear quantum dot-superconductor array: Mitigating the errors from Coulomb repulsion and residual tunneling
• Spin-Exchange Induced Spillover on Poor Man's Majoranas in Minimal Kitaev Chains
• Nonlocal Josephson diode effect in minimal Kitaev chains
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• Entanglement dynamics in minimal Kitaev chains
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• Analytical classification of Majorana zero-mode spatial profiles in extended Kitaev chains: probability maxima can shift inward