Dynamic current susceptibility as a probe of Majorana bound states in nanowire-based Josephson junctions

Trif, Mircea; Dmytruk, Olesia; Bouchiat, H.; Aguado, Ramón; Simon, Pascal

doi:10.1103/physrevb.97.041415

Cited by 36 publications

(25 citation statements)

References 40 publications

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“…Since the supercurrent is a ground state property, transitions between the negative and positive energies are not allowed, because of an energy gap originating from Majorana overlaps. Strategies to detect the presence of MBSs beyond the equilibrium supercurrents described here include the ac Josephson effect, noise measurements, switching-current measurements, microwave spectroscopy and dynamical susceptibility measurements [ 25 – 30 ].…”

Section: Resultsmentioning

confidence: 99%

Andreev spectrum and supercurrents in nanowire-based SNS junctions containing Majorana bound states

Cayao¹,

Black‐Schaffer²,

Prada³

et al. 2018

Beilstein J. Nanotechnol.

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Hybrid superconductor–semiconductor nanowires with Rashba spin–orbit coupling are arguably becoming the leading platform for the search of Majorana bound states (MBSs) in engineered topological superconductors. We perform a systematic numerical study of the low-energy Andreev spectrum and supercurrents in short and long superconductor–normal–superconductor junctions made of nanowires with strong Rashba spin–orbit coupling, where an external Zeeman field is applied perpendicular to the spin–orbit axis. In particular, we investigate the detailed evolution of the Andreev bound states from the trivial into the topological phase and their relation with the emergence of MBSs. Due to the finite length, the system hosts four MBSs, two at the inner part of the junction and two at the outer one. They hybridize and give rise to a finite energy splitting at a superconducting phase difference of π, a well-visible effect that can be traced back to the evolution of the energy spectrum with the Zeeman field: from the trivial phase with Andreev bound states into the topological phase with MBSs. Similarly, we carry out a detailed study of supercurrents for short and long junctions from the trivial to the topological phases. The supercurrent, calculated from the Andreev spectrum, is 2π-periodic in the trivial and topological phases. In the latter it exhibits a clear sawtooth profile at a phase difference of π when the energy splitting is negligible, signalling a strong dependence of current–phase curves on the length of the superconducting regions. Effects of temperature, scalar disorder and reduction of normal transmission on supercurrents are also discussed. Further, we identify the individual contribution of MBSs. In short junctions the MBSs determine the current–phase curves, while in long junctions the spectrum above the gap (quasi-continuum) introduces an important contribution.

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Section: Resultsmentioning

confidence: 99%

Andreev spectrum and supercurrents in nanowire-based SNS junctions containing Majorana bound states

Cayao¹,

Black‐Schaffer²,

Prada³

et al. 2018

Beilstein J. Nanotechnol.

Self Cite

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“…Since Weyl points in crystals require the breaking of

scriptT

or inversion symmetry, in four‐terminal junctions, the Weyl and nodal points may also occur under

scriptT

symmetry. [ 30–32 ] The importance of the Josephson junctions lies in the engineering of Andreev bound states (ABSs) and their control by building topological quantum‐computing architectures based on MBSs, [ 33–37 ] where superconducting phase difference, bias voltage, and magnetic flux play the role of control parameters. [ 38,39 ] To observe MBSs in 1D topological superconductors (TSCs), one of the most suggested models is based on quantum dots (QDs) because they are easily tunnelable objects.…”

Section: Introductionmentioning

confidence: 99%

Josephson and Persistent Currents in a Quantum Ring between Topological Superconductors

et al. 2021

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In this work, the spectra in an Aharonov–Bohm quantum‐ring interferometer forming a Josephson junction between two topological superconductor (TSC) nanowires are investigated. The TSCs host Majorana bound states at their edges, and both the magnetic flux and the superconducting phase difference between the TSCs are used as control parameters. A tight‐binding approach is used to model the quantum ring coupled to both TSCs, described by the Kitaev effective Hamiltonian. The problem is solved by means of exact numerical diagonalization of the Bogoliubov‐de Gennes Hamiltonian and obtain the spectra for two sizes of the quantum ring as a function of the magnetic flux and the phase difference between the TSCs. Depending on the size of the quantum ring and the coupling, the spectra display several patterns. Those are denoted as line, point, and undulated nodes, together with flat bands, which are topologically protected. The first three patterns can be possibly detected by means of persistent and Josephson currents. Hence, the results could be useful to understand the spectra and their relation with the behavior of the current signals.

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“…Since Weyl points in crystals require the breaking of T or inversion symmetry, in fourterminal junctions, the Weyl and nodal points may also occur under T symmetry [30][31][32]. The importance of the Josephson junctions lies in the engineering of Andreev bound states (ABSs) and their control by building topological quantum-computing architectures based on MBSs [33][34][35][36][37], where superconducting phase difference, bias voltage, and magnetic flux play the role of control parameters [38,39]. To observe MBSs in 1D topological superconductors (TSCs), one of the most suggested models is based on quantum dots (QDs) because they are easily tunnelable objects.…”

Section: Introductionmentioning

confidence: 99%

Josephson and persistent currents in a quantum ring between topological superconductors

Medina,

Ramos-Andrade,

Rosales

et al. 2021

Preprint

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In this work, we investigate the spectra in an Aharonov-Bohm quantum-ring interferometer forming a Josephson junction between two topological superconductor (TSC) nanowires. The TSCs host Majorana bound states at their edges, and both the magnetic flux and the superconducting phase difference between the TSCs are used as control parameters. We use a tight-binding approach to model the quantum ring coupled to both TSCs, described by the Kitaev effective Hamiltonian. We solve the problem by means of exact numerical diagonalization of the Bogoliubov-de Gennes (BdG) Hamiltonian and obtain the spectra for two sizes of the quantum ring as a function of the magnetic flux and the phase difference between the TSCs. Depending on the size of the quantum ring and the coupling, the spectra display several patterns. Those are denoted as line, point and undulated nodes, together with flat bands, which are topologically protected. The first three patterns can be possibly detected by means of persistent and Josephson currents. Hence, our results could be useful to understand the spectra and their relation with the behavior of the current signals.

show abstract

Dynamic current susceptibility as a probe of Majorana bound states in nanowire-based Josephson junctions

Cited by 36 publications

References 40 publications

Andreev spectrum and supercurrents in nanowire-based SNS junctions containing Majorana bound states

Andreev spectrum and supercurrents in nanowire-based SNS junctions containing Majorana bound states

Josephson and Persistent Currents in a Quantum Ring between Topological Superconductors

Josephson and persistent currents in a quantum ring between topological superconductors

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