Quantum dots as parafermion detectors by Raphael L. R. C. Teixeira, Luis G. G. V. Dias da Silva

“…Parafermionic zero modes, Z_{n}-symmetric generalizations of the well-known Z_{2} Majorana zero modes, can emerge as edge states in topologically nontrivial strongly correlated systems displaying fractionalized excitations. …”
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Dynamics of parafermionic states in transport measurements by Ida Egholm Nielsen, Jens Schulenborg, Reinhold Egger, Michele Burrello

“…Advances in hybrid fractional quantum Hall (FQH)-superconductor platforms pave the way for realisation of parafermionic modes. We analyse signatures of these non-abelian anyons in transport measurements across devices with $\mathbb{Z}_6$ parafermions (PFs) coupled to an external electrode. …”
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Dynamical topological excitations in parafermion chains by Vilja Kaskela, J. L. Lado

“…Parafermions are elusive fractional excitations potentially emerging in fractional quantum Hall-superconductor junctions and represent one of the major milestones in fractional quantum matter. …”
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ℤ N duality and parafermions revisited by Zhihao Duan, Qiang Jia, Sungjay Lee

“…We generalize this story to two-dimensional theories with non-anomalous ℤ N symmetry, focusing on parafermionization. We find the generic operators defining different topological boundary states including orbifolding and parafermionization with ℤ N or subgroups of ℤ N , and discuss their algebraic properties as well as the ℤ N duality web.…”
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A brief history of free parafermions by Murray T. Batchelor, Robert A. Henry, Xilin Lu

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Topological phases with parafermions: theory and blueprints by Alicea, J, Fendley, P

“…We concisely review the recent evolution in the study of parafermions—exotic emergent excitations that generalize Majorana fermions and similarly underpin a host of novel phenomena. …”

Fractional topological superconductivity and parafermion corner states by Katharina Laubscher, Daniel Loss, Jelena Klinovaja

“…We show that in such a system strong electron-electron interactions can stabilize a helical topological superconducting phase hosting Kramers partners of Z_{2m} parafermion edge modes, where m is an odd integer determined by the position of the chemical potential. …”
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Parafermions in hierarchical fractional quantum Hall states by Luiz H. Santos

“…Recent theoretical progress has been achieved in demonstrating the existence of non-Abelian parafermion zero modes in domain walls on interfaces between two-dimensional Abelian topological phases of matter. …”
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Trace functions of the parafermion vertex operator algebras by Dong, Chongying, Kac, Victor, Ren, Li

“…The trace functions for the Parafermion vertex operator algebra associated to any finite dimensional simple Lie algebra g and any positive integer k are studied and an explicit modular transformation formula of the trace functions is obtained.…”
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Discretely holomorphic parafermions and integrable loop models by Ikhlef, Y, Cardy, J

Exotic phases of interacting Majorana fermions and parafermions by O'Brien, E

“…<p>In this thesis exotic phases of models preserving the symmetries of the one-dimensional quantum Ising and three-state Potts chains are considered, the natural habitats of Majorana fermions and parafermions, respectively. Along with numerical techniques, conformal field theory (CFT) is used to study the resulting physics.…”

Discretely holomorphic parafermions and integrable loop models by Ikhlef, Y, Cardy, J

“…We define parafermionic observables in various lattice loop models, including examples where no Kramers-Wannier duality holds. …”

Parafermion excitations in a superfluid of quasi-molecular chains by A M Tsvelik, A B Kuklov

“…For N  = 2,3,4 the corresponding low-energy field theory is the model of Z _N parafermions perturbed by the thermal operator. The results of Monte Carlo simulations are consistent with these predictions. …”
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Overlap of parafermionic zero modes at a finite distance by Raphael L. R. C. Teixeira, Andreas Haller, Roshni Singh, Amal Mathew, Edvin G. Idrisov, Luis G. G. V. Dias da Silva, Thomas L. Schmidt

“…Parafermion bound states (PBSs) are generalizations of Majorana bound states (MBSs) and have been predicted to exist as zero-energy eigenstates in proximitized fractional quantum Hall edge states. …”
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Exceptional points in the Baxter-Fendley free parafermion model by Robert A. Henry, Murray T. Batchelor

“…Certain spin chains, such as the quantum Ising chain, have free fermion spectra which can be expressed as the sum of decoupled two-level fermionic systems. Free parafermions are a generalisation of this idea to $\mathbb{Z}_N$-symmetric clock models. …”
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Holomorphic parafermions in the Potts model and stochastic Loewner evolution by Riva, V, Cardy, J

Discretely holomorphic parafermions in lattice Z(N) models by Rajabpour, M, Cardy, J

Thermopower and thermoelectric power factor of Zk parafermion quantum dots by Lachezar S. Georgiev

“…We give a complete description of the power factor profiles in the Z3 and Z4 parafermion states with arbitrary number of quasiparticles localized in the bulk which could be useful for comparison with the experiments.…”
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A parafermionic hypergeometric function and supersymmetric 6j-symbols by Elena Apresyan, Gor Sarkissian, Vyacheslav P. Spiridonov

“…We study properties of a parafermionic generalization of the hyperbolic hypergeometric function appearing as the most important part in the fusion matrix for Liouville field theory and the Racah-Wigner symbols for the Faddeev modular double. …”
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Energy transport in an integrable parafermionic chain via generalized hydrodynamics by Mazza, L, Viti, J, Carrega, M, Rossini, D, De Luca, A

“…We study energy transport in the integrable $\mathbb Z_3$ parafermionic chain using the partitioning protocol. …”