# Z_{4} parafermions in Weakly Interacting Superconducting Constrictions at the Helical Edge of Quantum Spin Hall Insulators.

@article{Fleckenstein2019Z\_4PI, title={Z\_\{4\} parafermions in Weakly Interacting Superconducting Constrictions at the Helical Edge of Quantum Spin Hall Insulators.}, author={Christoph Fleckenstein and Niccol{\`o} Traverso Ziani and Bjorn Trauzettel}, journal={Physical review letters}, year={2019}, volume={122 6}, pages={ 066801 } }

Parafermions are generalizations of Majorana fermions that may appear in interacting topological systems. They are known to be powerful building blocks of topological quantum computers. Existing proposals for realizations of parafermions typically rely on strong electronic correlations which are hard to achieve in the laboratory. We identify a novel physical system in which parafermions generically develop. It is based on a quantum constriction formed by the helical edge states of a quantum…

## 21 Citations

Fractional topological superconductivity and parafermion corner states

- PhysicsPhysical Review Research
- 2019

We consider a system of weakly coupled Rashba nanowires in the strong spin-orbit interaction (SOI) regime. The nanowires are arranged into two tunnel-coupled layers proximitized by a top and bottom…

Quantum dots as parafermion detectors

- PhysicsPhysical Review Research
- 2021

Parafermionic zero modes, Zn-symmetric generalizations of the well-known Z2 Majorana zero modes, can emerge as edge states in topologically nontrivial strongly correlated systems displaying…

Majorana bound states in double nanowires with reduced Zeeman thresholds due to supercurrents

- PhysicsPhysical Review B
- 2019

We study the topological phase diagram of a setup composed of two nanowires with strong Rashba spin-orbit interaction subjected to an external magnetic field and brought into the proximity to a bulk…

Interaction-driven Floquet engineering of topological superconductivity in Rashba nanowires

- Physics
- 2019

We analyze, analytically and numerically, a periodically driven Rashba nanowire proximity coupled to an $s$-wave superconductor using bosonization and renormalization group analysis in the regime of…

Bosonization for fermions and parafermions

- Physics
- 2019

Parafermions are fractional excitations which can be regarded as generalizations of Majorana bound states, but in contrast to the latter they require electron-electron interactions. Compared to…

Edge $\mathbb{Z}_3$ parafermions in fermionic lattices

- Physics
- 2021

Parafermions modes are non-Abelian anyons which were introduced as ZN generalizations of Z2 Majorana states. In particular, Z3 parafermions can be used to produce Fibonacci anyons, laying a path…

Photonic simulation of parafermionic Berry-phase statistics and contextuality

- Physics
- 2020

Quasiparticle poisoning is the main obstacle towards the realization of Majorana-based quantum computation. Parafermions, a natural generalization of Majorana fermions, can encode topological qudits…

Parafermion braiding in fractional quantum Hall edge states with a finite chemical potential

- Physics
- 2019

Parafermions are non-Abelian anyons which generalize Majorana fermions and hold great promise for topological quantum computation. We study the braiding of $\mathbb{Z}_{2n}$ parafermions which have…

Assessing Bound States in a One-Dimensional Topological Superconductor: Majorana versus Tamm

- Computer Science, PhysicsSymmetry
- 2021

It is shown both numerically and analytically that the Tamm state remains partially localized even when the spectrum becomes gapless, and it is demonstrated that the Majorana polarization shows a clear transition between the two regimes.

Parafermions in a multi-legged geometry: Towards a scalable parafermionic network

- Physics
- 2021

Parafermionic zero modes are non-Abelian excitations which have been predicted to emerge at the boundary of topological phases of matter. Contrary to earlier proposals, here we show that such zero…

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