Spin–orbit coupling and anomalous Josephson effect in nanowires

Campagnano, Gabriele; Lucignano, P.; Giuliano, Domenico; Tagliacozzo, A.

doi:10.1088/0953-8984/27/20/205301

Cited by 82 publications

(52 citation statements)

References 53 publications

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“…Further, it was shown that a fractional Josephson effect may be realized at topological insulator edge 16,17 . This prediction has later been extended to different systems [18][19][20][21][22][23][24][25] .…”

Section: Introductionmentioning

confidence: 92%

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Effect of magnetic field and Rashba spin-orbit interaction on the Josephson tunneling between superconducting nanowires

et al. 2017

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We calculate the Josephson current between two one-dimensional (1D) nanowires oriented along x with proximity induced s-wave superconducting pairing and separated by a narrow dielectric barrier in the presence of both Rashba spin-orbit interaction (SOI) characterized by strength α and Zeeman fields (h alongẑ and B in the x − y plane). We formulate a general method for computing the Andreev bound states energy which allows us to obtain analytical expressions for the energy of these states in several asymptotic cases. We find that in the absence of the magnetic fields the energy gap between the Andreev bound states decreases with increasing Rashba SOI constant leading eventually to touching of the levels. In the absence of Rashba SOI, the Andreev bound states depend on the magnetic fields and display oscillatory behavior with orientational angle of B leading to magneto-Josephson effect. We also present analytic expressions for the dc Josephson current charting out their dependence on B, h, and α. We demonstrate the existence of finite spin-Josephson current in these junctions in the presence of external magnetic fields and provide analytic expressions for its dependence on α, B and h. Finally, we study the AC Josephson effect in the presence of the SOI (for |B| = h = 0) and an external radiation and show that the width of the resulting Shapiro steps in such a system can be tuned by varying α. We discuss experiments which can test our theoretical results.

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Section: Introductionmentioning

confidence: 92%

“…with The current-phase relation at magnetic field h = 0.1 calculated by using expressions (24), (25) and (26) is presented in Fig. 6.…”

Section: Equilibrium Josephson Current and Spin Currentmentioning

confidence: 99%

Effect of magnetic field and Rashba spin-orbit interaction on the Josephson tunneling between superconducting nanowires

et al. 2017

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“…This is the so called ϕ 0 -junction, and its interpretation in terms of the inverse magneto-electric effect was reported in 46 . It was actively studied recently in half-metal junctions, noncoplanar ferromagnetic junctions, ferromagnetic Josephson junctions with spin orbit interaction or TI surface states [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] .…”

Section: Introductionmentioning

confidence: 99%

Quasiclassical theory of magnetoelectric effects in superconducting heterostructures in the presence of spin-orbit coupling

Bobkova

Bobkov

2017

Phys. Rev. B

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The quasiclassical theory in terms of equations for the Green's functions (Eilenberger equations) is generalized in order to allow for quantitative description of the magneto-electric effects and proximity-induced triplet correlations in the presence of spin-orbit coupling in hybrid superconducting systems. The formalism is valid under the condition that the spin-orbit coupling is weak with respect to the Fermi energy, but exceeds the superconducting energy scale considerably. On the basis of the derived formalism it is shown that the triplet correlations in the spin-orbit coupled normal metal can be induced by proximity to a singlet superconductor without any exchange or external magnetic field. They contain an odd-frequency even-momentum component, which is stable against disorder. The value of the proximity-induced triplet correlations is of the order of ∆so/εF , that is absent in the framework of the standard quasiclassical approximation, but can be described by our theory. The spin polarization, induced by the Josephson current flowing through the superconductor/Rashba metal/superconductor junction, is also calculated.

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“…This might potentially provide an useful method to also spell out the dynamics of fractionalized excitations in correlated systems [56][57][58] . Moreover, by simply sending to infinity the length of the superconducting part of the ring, our approach provides an exact formula for the Josephson current across an SNS junction, which can be readily applied to cases hard to deal with using alternative techniques, such as in the case of the anomalous Josephson effect in nanowires [59][60][61] . These, and other potentially interesting generalizations of our approach, do actually lie beyond the range of this paper, and we plan to address them as a future development of our work.…”

Section: Discussionmentioning

confidence: 99%

Transfer matrix approach to the persistent current in quantum rings: Application to hybrid normal-superconducting rings

Nava¹,

Giuliano²,

Campagnano³

et al. 2016

Phys. Rev. B

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Using the properties of the transfer matrix of one-dimensional quantum mechanical systems, we derive an exact formula for the persistent current across a quantum mechanical ring pierced by a magnetic flux Φ as a single integral of a known function of the system's parameters. Our approach provides exact results at zero temperature, which can be readily extended to a finite temperature T . We apply our technique to exactly compute the persistent current through p-wave and s-wave superconducting-normal hybrid rings, deriving full plots of the current as a function of the applied flux at various system's scales. Doing so, we recover at once a number of effects such as the crossover in the current periodicity on increasing the size of the ring and the signature of the topological phase transition in the p-wave case. In the limit of a large ring size, resorting to a systematic expansion in inverse powers of the ring length, we derive exact analytic closed-form formulas, applicable to a number of cases of physical interest.

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Spin–orbit coupling and anomalous Josephson effect in nanowires

Cited by 82 publications

References 53 publications

Effect of magnetic field and Rashba spin-orbit interaction on the Josephson tunneling between superconducting nanowires

Effect of magnetic field and Rashba spin-orbit interaction on the Josephson tunneling between superconducting nanowires

Quasiclassical theory of magnetoelectric effects in superconducting heterostructures in the presence of spin-orbit coupling

Transfer matrix approach to the persistent current in quantum rings: Application to hybrid normal-superconducting rings

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