Effects of geometric frustration in Kitaev chains

Abstract

We study the topological phase transitions of a Kitaev chain in the presence of geometric frustration caused by the addition of a single long-range hopping. The latter condition defines a legged-ring geometry (Kitaev tie) lacking of translational invariance. In order to study the topological properties of the system, we generalize the transfer matrix approach through which the emergence of Majorana modes is studied. We find that geometric frustration gives rise to a topological phase diagram in which non-trivial phases alternate with trivial ones at varying the range of the extra hopping and the chemical potential. Frustration effects are also studied in a translational invariant model consisting of multiple-ties. In the latter system, the translational invariance permits to use the topological bulk invariant to determine the phase diagram and bulk-edge correspondence is recovered. It has been demonstrated that geometric frustration effects persist even when translational invariance is restored. These findings are relevant in studying the topological phases of looped ballistic conductors.

9 pages, 9 figures

References in corpus (6)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films
• Kitaev chains with long-range pairing
• Sagnac interference in Carbon nanotube loops
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Cited by in corpus (5)

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• Squashed entanglement in one-dimensional quantum matter
• Spin Hall and Edelstein effects in a ballistic quantum dot with Rashba spin-orbit coupling
• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors