Exotic non-Abelian anyons from conventional fractional quantum Hall states

Clarke, David J.; Alicea, Jason; Shtengel, Kirill

doi:10.1038/ncomms2340

Cited by 367 publications

(561 citation statements)

References 63 publications

(109 reference statements)

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confidence: 99%

“…Furthermore, by experimentally introducing a novel concept, the supercurrent spectral density, we determine the supercurrent-phase relation in a tunnelling experiment, thus establishing the connection between Andreev physics at finite energy and the Josephson e ect. This work opens up new avenues for probing exotic topological phases of matter in hybrid superconducting Dirac materials [16][17][18] .When a normal quantum conductor (N) is sandwiched between two superconductors (S), a current can flow in the absence of any voltage, due to the Josephson effect 1 . This macroscopic supercurrent is driven by the difference between the order parameter phases of the two superconductors, ϕ. Microscopically, it corresponds to the coherent flow of Cooper pairs through the conductor, which is made possible by successive Andreev reflections at the N/S interfaces, where electrons (holes) are reflected as oppositespin holes (electrons) (Fig.…”

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confidence: 99%

“…The way ABS form in graphene still remains an open question, especially around the neutrality point, where its unique electronic spectrum should give rise to specular Andreev reflections 27,30 and potentially to exotic ABS. Interest in such a spectroscopy has increased with recent proposals for hosting Majorana modes [16][17][18] within proximitized graphene operated in the quantum Hall regime 29 .To probe Andreev physics in the energy domain, we perform tunnelling spectroscopy of graphene proximitized by superconductors (Fig. 1d).…”

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Tunnelling spectroscopy of Andreev states in graphene

et al. 2017

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A normal conductor placed in good contact with a superconductor can inherit its remarkable electronic properties 1,2 . This proximity e ect microscopically originates from the formation in the conductor of entangled electron-hole states, called Andreev states [3][4][5][6][7][8] . Spectroscopic studies of Andreev states have been performed in just a handful of systems 9-13 . The unique geometry, electronic structure and high mobility of graphene 14,15 make it a novel platform for studying Andreev physics in two dimensions. Here we use a full van der Waals heterostructure to perform tunnelling spectroscopy measurements of the proximity e ect in superconductor-graphenesuperconductor junctions. The measured energy spectra, which depend on the phase di erence between the superconductors, reveal the presence of a continuum of Andreev bound states. Moreover, our device heterostructure geometry and materials enable us to measure the Andreev spectrum as a function of the graphene Fermi energy, showing a transition between di erent mesoscopic regimes. Furthermore, by experimentally introducing a novel concept, the supercurrent spectral density, we determine the supercurrent-phase relation in a tunnelling experiment, thus establishing the connection between Andreev physics at finite energy and the Josephson e ect. This work opens up new avenues for probing exotic topological phases of matter in hybrid superconducting Dirac materials [16][17][18] .When a normal quantum conductor (N) is sandwiched between two superconductors (S), a current can flow in the absence of any voltage, due to the Josephson effect 1 . This macroscopic supercurrent is driven by the difference between the order parameter phases of the two superconductors, ϕ. Microscopically, it corresponds to the coherent flow of Cooper pairs through the conductor, which is made possible by successive Andreev reflections at the N/S interfaces, where electrons (holes) are reflected as oppositespin holes (electrons) (Fig. 1a). Due to this process, resonant electron-hole states form in the central conductor, known as Andreev bound states (ABS) 3-6 . They lie as energy levels inside the superconducting gap [−∆, ∆], only negative-energy states being populated in the ground state (Fig. 1b). Crucially, the Andreev energy E n (ϕ) depends on ϕ, and each populated ABS carries in response a supercurrent (1/φ 0 )(∂E n /∂ϕ), where φ 0 = /2e is the reduced flux quantum, with the reduced Planck constant and e the elementary charge. The overall phase-dependent Andreev spectrum is shown in Fig. 1c and depends on geometric and microscopic parameters 7,8 , such as the conductor dimensions that determine the number of ABS, the scattering processes in the conductor and the contact's transparency. Strong ABS phase dependence, and therefore a prominent proximity effect, is achieved in ballistic systems with transparent N/S interfaces 7,8 .Graphene (G) can exhibit low contact resistance and weak scattering when connected to superconducting electrodes 19,20 . These properties, combined with t...

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Tunnelling spectroscopy of Andreev states in graphene

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“…These models generalise the Kitaev wire model 7 which exhibits localised unpaired Majorana zero-modes at each end. The recent surge of interest is inspired in part by proposals for their physical realisation and their potential application to universal topological quantum computation [8][9][10] , something which is not possible with Majorana zero-modes.…”

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Parafermionic clock models and quantum resonance

et al. 2017

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We explore the ZN parafermionic clock-model generalisations of the p-wave Majorana wire model. In particular we examine whether zero-mode operators analogous to Majorana zero-modes can be found in these models when one introduces chiral parameters to break time reversal symmetry. The existence of such zero-modes implies N -fold degeneracies throughout the energy spectrum. We address the question directly through these degeneracies by characterising the entire energy spectrum using perturbation theory and exact diagonalisation. We find that when N is prime, and the length L of the wire is finite, the spectrum exhibits degeneracies up to a splitting that decays exponentially with system size, for generic values of the chiral parameters. However, at particular parameter values (resonance points), band crossings appear in the unperturbed spectrum that typically result in a splitting of the degeneracy at finite order. We find strong evidence that these preclude the existence of strong zero-modes for generic values of the chiral parameters. In particular we show that in the thermodynamic limit, the resonance points become dense in the chiral parameter space. When N is not prime, the situation is qualitatively different, and degeneracies in the energy spectrum are split at finite order in perturbation theory for generic parameter values, even when the length of the wire L is finite. Exceptions to these general findings can occur at special "anti-resonant" points. Here the evidence points to the existence of strong zero modes and, in the case of the achiral point of the the N = 4 model, we are able to construct these modes exactly. There has recently been growing interest in a class of Z N symmetric one dimensional lattice models known as parafermion chain or quantum clock models 1-6 . These models generalise the Kitaev wire model 7 which exhibits localised unpaired Majorana zero-modes at each end. The recent surge of interest is inspired in part by proposals for their physical realisation and their potential application to universal topological quantum computation 8-10 , something which is not possible with Majorana zero-modes.Clock-like systems of this type have been studied earlier 11,12 , and much is known about the exactly solvable chiral Potts models that occur at special values of the coupling constants (see e.g. Refs 13 and 14). From the perspective of topological quantum computation however, there are a number of interesting open problems surrounding the topological degeneracies and potential zero-modes of the models. In particular, one may ask whether zero-modes exist which result in topological degeneracies throughout the energy spectrum 3,5 . In this context one speaks of strong vs. weak zero-modes (see e.g. Ref. 15) and the question is important because degeneracies that exist at energies above the ground-state potentially allow for topologically fault-tolerant quantum devices at higher temperatures 16 . This area is of course also interesting on a fundamental level, as it addresses if and when decoupled/fr...

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“…These include all the SU(2) k models (such as the Ising and Fibonacci anyons expected to appear in fractional quantum Hall systems), as well as the fractionalized Majorana fermions very recently proposed in Refs. [38,[41][42][43][44][45].…”

Section: B Summarymentioning

confidence: 99%

Braiding of non-Abelian anyons using pairwise interactions

2013

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The common approach to topological quantum computation is to implement quantum gates by adiabatically moving non-Abelian anyons around each other. Here we present an alternative perspective based on the possibility of realizing the exchange (braiding) operators of anyons by adiabatically varying pairwise interactions between them rather than their positions. We analyze a system composed by four anyons whose couplings define a T-junction and we show that the braiding operator of two of them can be obtained through a particular adiabatic cycle in the space of the coupling parameters. We also discuss how to couple this scheme with anyonic chains in order to recover the topological protection.

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Exotic non-Abelian anyons from conventional fractional quantum Hall states

Cited by 367 publications

References 63 publications

Tunnelling spectroscopy of Andreev states in graphene

Tunnelling spectroscopy of Andreev states in graphene

Parafermionic clock models and quantum resonance

Braiding of non-Abelian anyons using pairwise interactions

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