Optimal Majoranas in Mesoscopic Kitaev Chains

TL;DR

This paper presents a comprehensive microscopic analysis of mesoscopic Kitaev chains, revealing how hybrid segment states influence Majorana zero modes and identifying optimal conditions for their localization and stability.

Contribution

It introduces a full microscopic treatment of hybrid regions in Kitaev chains, linking microscopic parameters to Majorana mode optimization and experimental regimes.

Findings

Derived analytical expressions for couplings and sweet-spot conditions.

Identified regimes where MZMs are well localized with large energy gaps.

Linked parity-crossings of Andreev bound states to optimal Majorana operation windows.

Abstract

Kitaev chains realized in quantum dots coupled via superconducting segments provide a controllable platform for engineering Majorana zero modes (MZMs). In these systems, subgap states in the hybrid region mediate the effective coupling between quantum dots and determine the emergence of sweet-spots where MZMs are strongly localized. However, existing minimal treatments often oversimplify the mesoscopic hybrid region. We perform a full microscopic treatment of this hybrid segment, capturing the quasiparticle continuum and spin-split Andreev bound states (ABSs), and show that it fundamentally alters the minimal picture. We derive analytical expressions for the renormalized couplings and sweet-spot conditions, establishing a direct link between microscopic chain parameters and Majorana optimization and identifying experimentally relevant regimes for improved device performance. Critically, we find that parity-crossings of the ABS, marking the onset of an odd-parity spin-polarized regime in the segment, identify the optimal operating windows where MZMs are simultaneously well localized with a large gap to excited states.