Majorana braiding dynamics in nanowires

Amorim, Cássio Sozinho; Ebihara, Kazuto; Yamakage, Ai; Tanaka, Yukio; Sato, Masatoshi

doi:10.1103/physrevb.91.174305

Cited by 53 publications

(62 citation statements)

References 62 publications

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“…Thus, braiding success and ZBCP are conceptually connected with dissipation playing a central role. While one might argue that braiding experiments differ fundamentally from conductance experiments since the latter depends on Γ L and the former does not, the existing braiding proposals [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65] requires the presence of Majorana fermion tunneling in a key way. The Majorana tunneling enters through the tri-junctions in the Majorana braiding proposals.…”

Section: Braiding and Tunneling Conductancementioning

confidence: 99%

“…Indeed several proposals have been put forth in the literature for probing the non-Abelian braiding properties of MZMs [24,[51][52][53][54][55][56][57][58][59][60][61][62][63][64][65], and experimental efforts are currently underway to carry out MZM braiding to test their non-Abelian properties. An observation of the non-Abelian braiding properties would go a long way in establishing the existence of true MZMs in nanowires.…”

Section: Introductionmentioning

confidence: 99%

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How to infer non-Abelian statistics and topological visibility from tunneling conductance properties of realistic Majorana nanowires

Sarma

Nag

2016

Phys. Rev. B

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We consider a simple conceptual question with respect to Majorana zero modes in semiconductor nanowires: Can the measured non-ideal values of the zero-bias-conductance-peak in the tunneling experiments be used as a characteristic to predict the underlying topological nature of the proximity induced nanowire superconductivity? In particular, we define and calculate the topological visibility, which is a variation of the topological invariant associated with the scattering matrix of the system as well as the zero-bias-conductance-peak heights in the tunneling measurements, in the presence of dissipative broadening, using precisely the same realistic nanowire parameters to connect the topological invariants with the zero bias tunneling conductance values. This dissipative broadening is present in both (the existing) tunneling measurements and also (any future) braiding experiments as an inevitable consequence of a finite braiding time. The connection between the topological visibility and the conductance allows us to obtain the visibility of realistic braiding experiments in nanowires, and to conclude that the current experimentally accessible systems with non-ideal zero bias conductance peaks may indeed manifest (with rather low visibility) non-Abelian statistics for the Majorana zero modes. In general, we find that large (small) superconducting gap (Majorana peak splitting) is essential for the manifestation of the non-Abelian braiding statistics, and in particular, a zero bias conductance value of around half the ideal quantized Majorana value should be sufficient for the manifestation of non-Abelian statistics in experimental nanowires. Our work also establishes that as a matter of principle the topological transition associated with the emergence of Majorana zero modes in finite nanowires is always a crossover (akin to a quantum phase transition at finite temperature) requiring the presence of dissipative broadening (which must be larger than the Majorana energy splitting in the system) in the system. For braiding, this dissipation is supplied by the finite speed of the braiding process itself which must be diabatic in any real experiment for braiding to succeed.

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Section: Braiding and Tunneling Conductancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

How to infer non-Abelian statistics and topological visibility from tunneling conductance properties of realistic Majorana nanowires

Sarma

Nag

2016

Phys. Rev. B

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“…In this case, during the braiding the statistic disorder can in general bring about local rotation on the MKPs, with, however, the rotating angles for γ 1 ,γ 1 and γ 2 ,γ 2 being opposite (details are found in the supplementary material [37]). Thus, a generic The non-Abelian braiding of MKPs is confirmed by that the magnitude η(t) = γ1(0)|γ1(t) |t=2T = −1 after a full braiding at t = 2T (similar for other Majorana modes) [7,39,40]. The adiabatic condition is satisfied in that…”

mentioning

confidence: 91%

Symmetry-protected non-Abelian braiding of Majorana Kramers pairs

Gao

Liu

2016

Phys. Rev. B

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We develop the complete theory for non-Abelian braiding of Majorana Kramers' pairs (MKPs) in time-reversal (TR) invariant topological superconductors. By introducing an effective Hamiltonian approach to describe the braiding of MKPs, we show that the non-Abelian braiding is protected when the effective Hamiltonian exhibits a new TR like anti-unitary symmetry, which is satisfied if the system is free of dynamical noise. Importantly, even the dynamical noise may not cause error in braiding, unless the noise correlation function breaks a dynamical TR symmetry, which generalizes the TR symmetry protection of MKPs to dynamical regime. Moreover, the resulted error by noise is shown to be a higher order effect, compared with the decoherence of Majorana qubits without TR symmetry protection. These results show that the non-Abelian braiding of MKPs is observable and may have versatile applications to future quantum computation technologies.

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“…Recently, there have been some advances in this direction. [243][244][245][246][247][248][249][250][251][252][253] The effects of superconducting fluctuations on Majorana fermion states have also been studied recently. [254][255][256][257] It was revealed that the topological degeneracy associated with Majorana fermions is maintained even for the case of quasi-long-range order with power-law decay of the superconducting correlation, for which the total electron charge is conserved, and the phase of the superconducting gap fluctuates.…”

Section: Discussionmentioning

confidence: 99%

Majorana Fermions and Topology in Superconductors

2016

Self Cite

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type of quantum statistics referred to as non-Abelian statistics, which is distinct from bose and fermi statistics, and can be utilized for application to topological quantum computation. Also, Majorana fermions give rise to various exotic phenomena such as "fractionalization", nonlocal correlation, and "teleportation". A pedagogical review of these subjects is presented.We also discuss interaction effects on topological classification of superconductors, and the basic properties of Weyl superconductors.

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Majorana braiding dynamics in nanowires

Cited by 53 publications

References 62 publications

How to infer non-Abelian statistics and topological visibility from tunneling conductance properties of realistic Majorana nanowires

How to infer non-Abelian statistics and topological visibility from tunneling conductance properties of realistic Majorana nanowires

Symmetry-protected non-Abelian braiding of Majorana Kramers pairs

Majorana Fermions and Topology in Superconductors

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