Seeking out Majorana under the microscope

Lee, Patrick A.

doi:10.1126/science.1260282

Cited by 22 publications

(24 citation statements)

References 9 publications

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“…[4] and [5], respectively for semiconducting nanowire and magnetic adatom systems in the presence of strong spin-orbit and magnetic fields with an s-wave superconducting surface. In the experiments above, it is not clear whether the ZBPs are due to a genuine isolated MQP or associated with disorder introduced by ordinary fermionic states lying within the superconducting gap, crossed Andreev effect, among others [6][7][8] . Furthermore, thermal broadening together with a coherence length much longer than the Kitaev chain size can also lead to the overlap of the MQPs at the chain edges, thus suppressing the ZBP signature 8 .…”

Section: Introductionmentioning

confidence: 99%

Unveiling Majorana quasiparticles by a quantum phase transition: Proposal of a current switch

et al. 2016

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We propose a theoretical approach based on an interferometer composed by two quantum dots asymmetrically coupled to isolated Majorana quasiparticles (MQPs), lying on the edges of two topological Kitaev chains, respectively via couplings (t + ∆) and (∆ − t). This setup enables us to probe MQPs in a quite distinct way from the zero-bias peak feature. Most importantly, the system behaves as a current switch made by two distinct paths: (i) for the upper dot connected to both chains, the device perceives both MQPs as an ordinary fermion and the current crosses solely the lower dot, since current in the upper dot is prevented due to the presence of the superconducting gap; and (ii) by suppressing slightly the hybridization of the upper dot with one chain, the current is abruptly switched to flow through this dot, once a trapped electron as a bound state in the continuum (BIC) [Phys. Rev. B 93, 165116 (2016)] appears in the lower dot. Such a current switch between upper and lower dots characterizes the Quantum Phase Transition (QPT) proposed here, being the ratio t/∆ the control parameter of the transition. This QPT is associated with a change from an ordinary fermionic excitation regime to a MQP in the interferometer, which enables not only the fundamental revealing of MQPs, but also yields a current switch assisted by them.

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Section: Introductionmentioning

confidence: 99%

Unveiling Majorana quasiparticles by a quantum phase transition: Proposal of a current switch

et al. 2016

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“…Despite such a great progress in the observation of (Majorana) edge modes in ferromagnetic atomic chains on a superconducting surface, some loose ends remain to contend with [10]. In fact, it was clear from the estimates [2,11] that Majorana edge fermions in finite-length (of the size L) quantum chains have to hybridize to form a conventional Dirac fermion with the energy proportional to exp( / ), L where is the coherence length of the superconducting chain.…”

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confidence: 99%

“…In this situation, the opposite case L can persist, which means that Majorana edge states strongly hybridize to form a Dirac fermion with essentially nonzeroenergy. The short-distance physics of open superconducting chains with edge Majorana modes is not yet fully understood [10]. Then, the goal of the present study follows: to investigate analytically how the energy of bound edge states in open superconducting chains depends on the length.…”

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confidence: 99%

Majorana bound states in the finite-length chain

Zvyagin

2015

Low Temperature Physics

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Recent experiments investigating edge states in ferromagnetic atomic chains on superconducting substrate are analyzed. In particular, finite size effects are considered. It is shown how the energy of the Majorana bound state depends on the length of the chain, as well as on the parameters of the model. Oscillations of the energy of the bound edge state in the chain as a function of the length of the chain, and as a function of the applied voltage (or the chemical potential) are studied. In particular, it has been shown that oscillations can exist only for some values of the effective potential. PACS: 71.10.Pm Fermions in reduced dimensions;74.20.-z Theories and models of superconducting state.Keywords: Majorana edge states, topological superconductivity.Majorana fermions have attracted a great attention due to their main features, comparing to usual Dirac's fermions. Majorana fermions are particles, identical to their own antiparticles. The combination of a pair of Majorana fermions can form a Dirac fermion. Also, Majorana fermions satisfy a non-Abelian statistics, different from the Fermi-Dirac one. It permitted [1 to point out potential use of Majorana fermions as qubits (elementary cells of quantum computers) in fault-tolerant topological computations. Their another usefulness in quantum computation is caused by the fact that spatially separated pairs of Majorana fermions can encode information as a highly nonlocal qubit, minimizing that way the decoherence of the quantum computer. This is why, the search for Majorana fermions is among the most prominent tasks for physicists.For conventional superconductors with s-wave pairing, superpositions of electrons and holes carrying opposite spin are different from Majorana's construction. Majorana fermions can emerge in special superconductors, in which electrons and holes with the same value of spin can be paired. Kitaev has proposed to use zero-energy Majorana bound states at the opposite edges of a superconducting chain for the construction of a composite nonlocal qubit [2]. He has considered the simplest model of one-dimensional (1D) spinless fermions with pairing. 1D systems are important for the potential use in the quantum computation because: (i) their quantum features are enhanced (comparing to systems of higher dimensionality) due to the 1D peculiarity in the density of states, and (ii) theorists can obtain exact (nonperturbative), often analytic results in 1D. The latter can be used for comparison of experimental data with theoretical predictions, very important for probabilistic quantum computation.For the realization of Kitaev's scenario several 1D superconducting systems were proposed: low-dimensional topological insulators [3], quantum wires with the strong spin-orbit coupling in the external magnetic field in the vicinity of the standard s-wave superconductor [4], and ferromagnetic chains on the surface of such a superconductor [5]. Experimental attempts to implement the semiconductor wire proposal were successful to observe the zerobias peak in the t...

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“…To conclude, it is interesting to note that Nadj-Perge et al reported the observation of Majorana fermions in a chain of Fe atoms, which intrinsically have ferromagnetic nature, on a superconducting Pb substrate [13,14]. It is also noted that the recent developments in the field of cold atoms open a route to the experimental realization of one-dimensional interacting fermion systems [22].…”

Section: Resultsmentioning

confidence: 93%

One-dimensional extended Hubbard model with spin-triplet pairing ground states

Tanaka¹

2016

J. Phys. A: Math. Theor.

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We show that the one-dimensional extended Hubbard model has saturated ferromagnetic ground states with the spin-triplet electron pair condensation in a certain range of parameters. The ground state wave functions with fixed electron numbers are explicitly obtained. We also construct two ground states in which both the spinrotation and the gauge symmetries are broken, and show that these states are transferred from one to the other by applying the edge operators. The edge operators are reduced to the Majorana fermions in a special case. These symmetry breaking ground states are shown to be stabilized by a superconducting mean field Hamiltonian which is related to the Kitaev chain with the charge-charge interaction.

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Seeking out Majorana under the microscope

Abstract: A chain of iron atoms on lead may reveal a signature of the elusive Majorana particle [Also see Research Article by Nadj-Perge et al. ]

Cited by 22 publications

References 9 publications

Unveiling Majorana quasiparticles by a quantum phase transition: Proposal of a current switch

Unveiling Majorana quasiparticles by a quantum phase transition: Proposal of a current switch

Majorana bound states in the finite-length chain

One-dimensional extended Hubbard model with spin-triplet pairing ground states

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