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Z4 parafermions in one-dimensional fermionic lattices Calzona, Alessio ; ; et al in Physical Review. B, Condensed Matter (2018), 98 Parafermions are emergent excitations which generalize Majorana fermions and are potentially relevant to topological quantum computation. Using the concept of Fock parafermions, we present a mapping ... [more ▼] Parafermions are emergent excitations which generalize Majorana fermions and are potentially relevant to topological quantum computation. Using the concept of Fock parafermions, we present a mapping between lattice Z4-parafermions and lattice spin-1/2 fermions which preserves the locality of operators with Z4 symmetry. Based on this mapping, we construct an exactly solvable, local one-dimensional fermionic Hamiltonian which hosts parafermionic edge states. We numerically show that the parafermionic phase remains stable in a wide range of parameters, and discuss its signatures in the fermionic spectral function. [less ▲] Detailed reference viewed: 89 (1 UL)Missing shapiro steps and the 8PI-periodic Josephson effect in the interacting helical electron systems Pedder, Christopher ; ; et al in Physica B: Condensed Matter (2017) Detailed reference viewed: 44 (2 UL)Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields Pedder, Christopher ; ; et al in Physical Review B (2016), 94(24), 245414 A partially gapped spectrum due to the application of a magnetic field is one of the main probes of Rashba spin-orbit coupling in nanowires. Such a ``helical gap'' manifests itself in the linear ... [more ▼] A partially gapped spectrum due to the application of a magnetic field is one of the main probes of Rashba spin-orbit coupling in nanowires. Such a ``helical gap'' manifests itself in the linear conductance, as well as in dynamic response functions such as the spectral function, the structure factor, or the tunnelling density of states. In this paper, we investigate theoretically the signature of the helical gap in these observables with a particular focus on the interplay between Rashba spin-orbit coupling and electron-electron interactions. We show that in a quasi-one-dimensional wire, interactions can open a helical gap even without magnetic field. We calculate the dynamic response functions using bosonization, a renormalization group analysis, and the exact form factors of the emerging sine-Gordon model. For special interaction strengths, we verify our results by refermionization. We show how the two types of helical gaps, caused by magnetic fields or interactions, can be distinguished in experiments. [less ▲] Detailed reference viewed: 137 (21 UL)Parafermion bound states and the fractional Josephson effect in Rashba spin-orbit coupled nanowires Pedder, Christopher ; ; et al Poster (2015, September) Detailed reference viewed: 56 (0 UL)8pi-periodic Josephson effect in time-reversal invariant interacting Rashba nanowires Pedder, Christopher ; ; et al E-print/Working paper (2015) We investigate narrow quantum wires with strong Rashba spin-orbit coupling and electron-electron interactions. We show that virtual transitions between subbands lead to umklapp scattering which can open a ... [more ▼] We investigate narrow quantum wires with strong Rashba spin-orbit coupling and electron-electron interactions. We show that virtual transitions between subbands lead to umklapp scattering which can open a partial gap in the spectrum even in the presence of time-reversal symmetry. Using the superconducting proximity effect to gap out the remaining modes, we show that the system can host zero-energy states at its edges, which are protected by time-reversal symmetry. We present the parameter regime in which these bound states will emerge. Similarly to Majorana bound states, they will produce a zero-bias peak in the differential conductance. In contrast to the Majorana fermions, however, their fourfold degeneracy leads to an 8π periodicity of the Josephson current due to tunneling of fractionalized excitations with charge e/2. [less ▲] Detailed reference viewed: 133 (4 UL)Non-Abelian parafermions in time-reversal invariant interacting helical systems ; ; et al in Phys. Rev. B (2015), 91 The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical ... [more ▼] The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical potential is at the Dirac point, umklapp scattering can open a gap in the edge state spectrum even if the system is time-reversal invariant. We determine the zero-energy bound states at the interfaces between a section of a helical liquid which is gapped out by the superconducting proximity effect and a section gapped out by umklapp scattering. We show that these interfaces pin charges which are multiples of $e/2$, giving rise to a Josephson current with $8\pi$ periodicity. Moreover, the bound states, which are protected by time-reversal symmetry, are fourfold degenerate and can be described as $Z_4$ parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems. [less ▲] Detailed reference viewed: 117 (4 UL) |
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