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

TL;DR

This paper investigates the nature of poor man's Majoranas in long Kitaev chains, revealing that not all such states are topologically protected and that distinguishing them via conductance is challenging.

Contribution

It demonstrates that in long Kitaev chains, some poor man's Majoranas become trivial states, challenging their use as topological signatures.

Findings

Some PMMs in long chains are trivial localized states.

No clear conductance signature distinguishes topological from trivial PMMs.

Not all PMMs are connected to the topological phase.

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.