Details

Autor(en) / Beteiligte

• Vaezi, Abolhassan

Titel

Superconducting Analogue of the Parafermion Fractional Quantum Hall States

Ist Teil von

• Physical review. X, 2014-07, Vol.4 (3), p.031009, Article 031009

Ort / Verlag

College Park: American Physical Society

Erscheinungsjahr

2014

Quelle

Free E-Journal (出版社公開部分のみ）

Beschreibungen/Notizen

• Read-Rezayi Zk parafermion wave functions describe ν=2+(k/kM+2) fractional quantum Hall (FQH) states. These states support non-Abelian excitations from which protected quantum gates can be designed. However, there is no experimental evidence for these non-Abelian anyons to date. In this paper, we study the ν=2/k FQH-superconductor heterostructure and find the superconducting analogue of the Zk parafermion FQH state. Our main tool is the mapping of the FQH into coupled one-dimensional chains, each with a pair of counterpropagating modes. We show that by inducing intrachain pairing and charge preserving backscattering with identical couplings, the one-dimensional chains flow into gapless Zk parafermions when k<4 . By studying the effect of interchain coupling, we show that every parafermion mode becomes massive except for the two outermost ones. Thus, we achieve a fractional topological superconductor whose chiral edge state is described by a Zk parafermion conformal field theory. For instance, we find that a ν=2/3 FQH in proximity to a superconductor produces a Z3 parafermion superconducting state. This state is topologically indistinguishable from the non-Abelian part of the ν=12/5 Read-Rezayi state. Both of these systems can host Fibonacci anyons capable of performing universal quantum computation through braiding operations.