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-periodic dissipationless ac Josephson effect on a quantum spin Hall edge via a quantum magnetic impurity

Hui, Hoi-Yin; Sau, Jay D.

doi:10.1103/physrevb.95.014505

Cited by 12 publications

(33 citation statements)

References 32 publications

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“…11) cyclically modulates a wire between TRITOPS and trivial phases; provided time-reversal symmetry is maintained at certain points of the cycle, the magnetization at the ends of the system exhibits 8π periodicity. This phenomenon is a cousin of the 8π -periodic Josephson effect that can arise at a quantum-spin-Hall edge [27][28][29][30][31]. The strong version (Fig.…”

Section: Discussionmentioning

confidence: 91%

“…In the latter setting, the anomalous Josephson effect can also be naturally viewed as arising from hybridization of symmetryenriched Majorana modes with a quantum magnetization degree of freedom-similar to Refs. [29][30][31], which analyzed the junction coupled to an impurity spin. Our exact mappings clarify the precise connection between these electronic setups and a system hosting bona fide Z 4 parafermions: The hybridized subgap states mediating the anomalous pumping cycles are in one-to-one correspondence with fusion channels of non-Abelian defects binding Z 4 parafermion zero modes.…”

Section: B Imprint Of Parafermionic Fusion Rules In a 1d Electron Symentioning

confidence: 99%

“…Third, Zhang and Kane [27] and Orth et al [28] showed that proximitized edge states of a two-dimensional quantum-spin-Hall insulator can support zero modes reminiscent of Z 4 parafermions (see also Refs. [29][30][31]). Finally, parafermion chains are related to bosonic clock models (for any Z N ) [15,32]-a relation that we will frequently exploit.…”

Section: Introductionmentioning

confidence: 99%

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Fermionized parafermions and symmetry-enriched Majorana modes

2018

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Parafermion zero modes are generalizations of Majorana modes that underlie comparatively rich non-Abeliananyon properties. We introduce exact mappings that connect parafermion chains, which can emerge in twodimensional fractionalized media, to strictly one-dimensional fermionic systems. In particular, we show that parafermion zero modes in the former setting translate into symmetry-enriched Majorana modes that intertwine with a bulk order parameter-yielding braiding and fusion properties that are impossible in standard Majorana platforms. Fusion characteristics of symmetry-enriched Majorana modes are directly inherited from the associated parafermion setup and can be probed via two kinds of anomalous pumping cycles that we construct. Most notably, our mappings relate Z 4 parafermions to conventional electrons with time-reversal symmetry. In this case, one of our pumping protocols entails fairly minimal experimental requirements: Cycling a weakly correlated wire between a trivial phase and time-reversal-invariant topological superconducting state produces an edge magnetization with quadrupled periodicity. Our work highlights new avenues for exploring beyond-Majorana physics in experimentally relevant one-dimensional electronic platforms, including proximitized ferromagnetic chains.

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Section: Discussionmentioning

confidence: 91%

Section: B Imprint Of Parafermionic Fusion Rules In a 1d Electron Symentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fermionized parafermions and symmetry-enriched Majorana modes

2018

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“…In the presence of a dc voltage bias, three theoretical scenarios have been proposed, with distinct periodicities of the Josephson current on the superconducting phase difference across the junction. [1][2][3][4][5] In the first scenario, concerning non-interacting and TR-symmetric JJs, an ac 2π-periodic Josephson effect takes place, together with a dissipative dc current. 1,2 This is the ordinary Josephson effect for perfectly transparent weak links.…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5] In the first scenario, concerning non-interacting and TR-symmetric JJs, an ac 2π-periodic Josephson effect takes place, together with a dissipative dc current. 1,2 This is the ordinary Josephson effect for perfectly transparent weak links. In the second scenario, involving JJs with broken TR symmetry, the current is dissipationless and its period doubles to 4π.…”

Section: Introductionmentioning

confidence: 99%

Microwave signatures of the Z2 and Z4 fractional Josephson effects

et al. 2019

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We present a many-body exact diagonalization study of the Z2 and Z4 Josephson effects in circuit quantum electrodynamics architectures. Numerical simulations are conducted on Kitaev chain Josephson junctions hosting nearest-neighbor Coulomb interactions. The low-energy effective theory of highly transparent Kitaev chain junctions is shown to be identical to that of junctions created at the edge of a quantum spin-Hall insulator. By capacitively coupling the interacting junction to a microwave resonator, we predict signatures of the fractional Josephson effects on the cavity frequency and on time-resolved reflectivity measurements. arXiv:1809.11133v1 [cond-mat.mes-hall]

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Microwave Studies of the Fractional Josephson Effect in HgTe-Based Josephson Junctions

et al. 2018

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The rise of topological phases of matter is strongly connected to their potential to host Majorana bound states, a powerful ingredient in the search for a robust, topologically protected, quantum information processing. In order to produce such states, a method of choice is to induce superconductivity in topological insulators. The engineering of the interplay between superconductivity and the electronic properties of a topological insulator is a challenging task and it is consequently very important to understand the physics of simple superconducting devices such as Josephson junctions, in which new topological properties are expected to emerge.In this article, we review recent experiments investigating topological superconductivity in topological insulators, using microwave excitation and detection techniques. More precisely, we have fabricated and studied topological Josephson junctions made of HgTe weak links in contact with Al or Nb contacts. In such devices, we have observed two signatures of the fractional Josephson effect, which is expected to emerge from topologically-protected gapless Andreev bound states.We first recall the theoretical background on topological Josephson junctions, then move to the experimental observations. Then, we assess the topological ori-

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8π -periodic dissipationless ac Josephson effect on a quantum spin Hall edge via a quantum magnetic impurity

Cited by 12 publications

References 32 publications

Fermionized parafermions and symmetry-enriched Majorana modes

Fermionized parafermions and symmetry-enriched Majorana modes

Microwave signatures of the Z2 and Z4 fractional Josephson effects

Microwave Studies of the Fractional Josephson Effect in HgTe-Based Josephson Junctions

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