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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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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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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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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Majorana and parafermion corner states from two coupled sheets of bilayer graphene by Katharina Laubscher, Daniel Loss, Jelena Klinovaja

“…In particular, we find that the system supports a fractional topological insulator phase exhibiting fractionally charged gapless edge states and a fractional second-order topological superconducting phase exhibiting zero-energy Z_{2m} parafermion corner states, where m is an odd integer determined by the position of the chemical potential.…”
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Predicted signatures of topological superconductivity and parafermion zero modes in fractional quantum Hall edges by Noam Schiller, Eyal Cornfeld, Erez Berg, Yuval Oreg

“…Parafermion zero modes are exotic emergent excitations that can be considered as Z_{n} generalizations of Majorana fermions. …”
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Universality of Z_{3} parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atoms by Asmae Benhemou, Toonyawat Angkhanawin, Charles S. Adams, Dan E. Browne, Jiannis K. Pachos

“…Parafermions are Z_{n} generalizations of Majorana quasiparticles, with fractional non-Abelian statistics. …”
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Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes by Avishy Carmi, Yaroslav Herasymenko, Eliahu Cohen, Kyrylo Snizhko

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Measurement-only topological quantum computation without forced measurements by Huaixiu Zheng, Arpit Dua, Liang Jiang

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Cooper-pair splitting in two parallel InAs nanowires by S Baba, C Jünger, S Matsuo, A Baumgartner, Y Sato, H Kamata, K Li, S Jeppesen, L Samuelson, H Q Xu, C Schönenberger, S Tarucha

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Virasoro constraint for Uglov matrix model by Osama Khlaif, Taro Kimura

“…We derive the associated Virasoro constraints on the partition function, and find agreement of the central charge with the expression obtained from the level-rank duality associated with the parafermion CFT.…”
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Dynamically restoring conformal invariance in (integrable) $\sigma$-models by Rigers Aliaj, Konstantinos Sfetsos, Konstantinos Siampos

“…Integrable $\lambda$-deformed $\sigma$-models are characterized by an underlying current algebra/coset model CFT deformed, at the infinitesimal level, by current/parafermion bilinears. We promote the deformation parameters to dynamical functions of time introduced as an extra coordinate. …”
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