Emergent pair symmetries in systems with poor man's Majorana modes

Abstract

Few-site Kitaev chains are promising for realizing Majorana zero modes without topological protection but fully nonlocal, which are known as poor man's Majorana modes. While several signatures have already been reported both theoretically and experimentally, it still remains unknown what is the nature of superconducting correlations in the presence of poor man's Majorana modes. In this work, we study few-site Kitaev chains and demonstrate that they host pair correlations with distinct symmetries, entirely determined by the underlying quantum numbers. In particular, we find that a two-site Kitaev chain hosts local (odd-frequency) and nonlocal (odd- and even-frequency) pair correlations, both spin polarized and highly tunable by the system parameters. Interestingly, the odd-frequency pair correlations exhibit a divergent behaviour around zero frequency when the nonlocal $p$-wave pair potential and electron tunneling are of the same order, an effect that can be controlled by the onsite energies. Since a divergent odd-frequency pairing is directly connected to the intrinsic spatial nonlocality of Majorana zero modes in topological superconductors, the divergent odd-frequency pairing here reflects the intrinsic Majorana nonlocality of poor man's Majorana modes but without any relation to topology. Our findings could help understanding the emergent pair correlations in few-site Kitaev chains.

10 pages, 6 figures. Published version

References in corpus (13)

• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Realization of a minimal Kitaev chain in coupled quantum dots
• Parity qubits and poor man's Majorana bound states in double quantum dots
• Majorana Fermions and Odd-frequency Cooper Pairs in a Nano Wire
• Majorana nanowires for topological quantum computation
• A two-site Kitaev chain in a two-dimensional electron gas
• Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism
• Theory of Majorana zero modes in unconventional superconductors
• Unconventional Superconductivity in Double Quantum Dots
• Probing Majorana localization in minimal Kitaev chains through a quantum dot
• Minimal Kitaev-transmon qubit based on double quantum dots
• Controllable odd-frequency Cooper pairs in multi-superconductor Josephson junctions
• Floquet engineering Higgs dynamics in time-periodic superconductors

Cited by in corpus (11)

• Superconducting phenomena in systems with unconventional magnets
• Non-Hermitian multiterminal phase-biased Josephson junctions
• Fate of poor man's Majoranas in the long Kitaev chain limit
• Interplay between Majorana and Shiba states in a minimal Kitaev chain coupled to a superconductor
• Odd-frequency pairing due to Majorana and trivial Andreev bound states
• Nonlocal Josephson diode effect in minimal Kitaev chains
• Properties and prevalence of false poor man's Majoranas in two- and three-site artificial Kitaev chains
• Dynamics of Majorana zero modes across hybrid Kitaev chain
• Revisiting the Poor Man's Majoranas: The Spin-Exchange Induced Spillover Effect
• Entanglement dynamics in minimal Kitaev chains
• Odd-frequency Pairing in Josephson Junctions Coupled by Magnetic Textures