Universität zu Köln

Lahtinen, Ville, Ludwig, Andreas W. W. and Trebst, Simon ORCID: 0000-0002-1479-9736 (2014). Perturbed vortex lattices and the stability of nucleated topological phases. Phys. Rev. B, 89 (8). COLLEGE PK: AMER PHYSICAL SOC. ISSN 1550-235X

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Abstract

We study the stability of nucleated topological phases that can emerge when interacting non-Abelian anyons form a regular array. The studies are carried out in the context of Kitaev's honeycomb model, where we consider three distinct types of perturbations in the presence of a lattice of Majorana mode binding vortices-spatial anisotropy of the vortices, dimerization of the vortex lattice, and local random disorder. While all the nucleated phases are stable with respect to weak perturbations of each kind, strong perturbations are found to result in very different behavior. Anisotropy of the vortices stabilizes the strong-pairing-like phases, while dimerization can recover the underlying non-Abelian phase. Local random disorder, on the other hand, can drive all the nucleated phases into a gapless thermal metal state. We show that all these distinct behaviors can be captured by an effective staggered tight-binding model for the Majorana modes. By studying the pairwise interactions between the vortices, i.e., the amplitudes for the Majorana modes to tunnel between vortex cores, the locations of phase transitions and the nature of the resulting states can be predicted. We also find that, due to oscillations in the Majorana tunneling amplitude, lattices of Majorana modes may exhibit a Peierls-like instability, where a dimerized configuration is favored over a uniform lattice. As the nature of the nucleated phases depends only on the Majorana tunneling, our results are expected to apply also to other system supporting localized Majorana mode arrays, such as Abrikosov lattices in p-wave superconductors, Wigner crystals in Moore-Read fractional quantum Hall states, or arrays of topological nanowires.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Lahtinen, Ville UNSPECIFIED UNSPECIFIED UNSPECIFIED Ludwig, Andreas W. W. UNSPECIFIED UNSPECIFIED UNSPECIFIED Trebst, Simon UNSPECIFIED orcid.org/0000-0002-1479-9736 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-445784
DOI:	10.1103/PhysRevB.89.085121
Journal or Publication Title:	Phys. Rev. B
Volume:	89
Number:	8
Date:	2014
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	1550-235X
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MAJORANA FERMIONS; MODEL; SUPERCONDUCTOR; STATES Multiple languages Materials Science, Multidisciplinary; Physics, Applied; Physics, Condensed Matter Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/44578