Anomalous Josephson effect induced by spin-orbit interaction and Zeeman effect in semiconductor nanowires

Yokoyama, Toshiro; Eto, Mikio; Nazarov, Yuli V.

doi:10.1103/physrevb.89.195407

Cited by 237 publications

(234 citation statements)

References 65 publications

Supporting

Mentioning

219

Contrasting

Order By: Relevance

“…With symmetry broken, the Josephson current is not an odd function of the phase difference. This is called the anomalous Josephson effect [10][11][12][13][14] .…”

Section: Introductionmentioning

confidence: 99%

Singularities in the Andreev spectrum of a multiterminal Josephson junction

Yokoyama

Nazarov

2015

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

The energies of Andreev bound states (ABS) forming in a N-terminal junction are affected by N − 1 independent macroscopic phase differences between superconducting leads and can be regarded as energy bands in N − 1 periodic solid owing to the 2π periodicity in all phases. We investigate the singularities and peculiarities of the resulting ABS spectrum combining phenomenological and analytical methods and illustrating with the numerical results. We pay special attention on spin-orbit (SO) effects. We consider Weyl singularities with a conical spectrum that are situated at zero energy in the absence of SO interaction. We show that the SO interaction splits the spectrum in spin like a Zeeman field would do. The singularity is preserved while departed from zero energy. With SO interaction, points of zero-energy form an N − 2 dimensional manifold in N − 1 dimensional space of phases, while this dimension is N − 3 in the absence of SO interaction. The singularities of other type are situated near the superconducting gap edge. In the absence (presence) of SO interaction, the ABS spectrum at the gap edge is mathematically analogues to that at zero energy in the presence (absence) of SO interaction. We demonstrate that the gap edge touching (GET) points of the spectrum in principle form N − 2 (N − 3) dimensional manifold when the SO interaction is absent (present). Certain symmetry lines in the Brillouin zone of the phases are exceptional from this rule, and GET there should be considered separately. We derive and study the effective Hamiltonians for all the singularities under consideration.

show abstract

“…With symmetry broken, the Josephson current is not an odd function of the phase difference. This is called the anomalous Josephson effect [10][11][12][13][14] .…”

Section: Introductionmentioning

confidence: 99%

Singularities in the Andreev spectrum of a multiterminal Josephson junction

Yokoyama

Nazarov

2015

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

show abstract

“…Our main result is a clear overview that qualitatively links easily observable properties of the supercurrent and the critical current to the structure of the underlying Hamiltonian. In contrast to similar analyses in the literature [14,18], we (i) include disorder and a finite vector potential and (ii) do arXiv:1510.05251v2 [cond-mat.mes-hall] …”

mentioning

confidence: 99%

Effects of spin-orbit coupling and spatial symmetries on the Josephson current in SNS junctions

et al. 2016

View full text Add to dashboard Cite

We present an analysis of the symmetries of the interference pattern of critical currents through a two-dimensional superconductor-semiconductor-superconductor junction, taking into account Rashba and Dresselhaus spin-orbit interaction, an arbitrarily oriented magnetic field, disorder, and structural asymmetries. We relate the symmetries of the pattern to the absence or presence of symmetries in the Hamiltonian, which provides a qualitative connection between easily measurable quantities and the spin-orbit coupling and other symmetries of the junction. We support our analysis with numerical calculations of the Josephson current based on a perturbative expansion up to eighth order in tunnel coupling between the normal region and the superconductors.Semiconductors with strong spin-orbit interaction (SOI) attracted a lot of attention in recent years. The prospect of manipulating electron spin efficiently with electric fields instead of magnetic fields makes SOI an attractive ingredient for spintronic applications [1, 2], as well as spin-based quantum computing [3,4]. Furthermore, several concrete proposals were put forward on how to create topological states of matter in hybrid structures relying on semiconductors with strong SOI: One-or twodimensional semiconductors proximitized by an s-wave superconductor can behave as a p-wave topological superconductor [5][6][7][8]. Two-dimensional semiconductor heterostructures can acquire an "inverted band structure" and enter a (topological) quantum spin Hall state [9,10]. The notion that such topological systems can host nonAbelian quasiparticles and the prospect of using these particles for topologically protected quantum computing [11] sparked an intense activity of research and fueled the interest in semiconductors with strong SOI.In most lower-dimensional semiconductor structures, the electric fields contributing to SOI have two important contributions: (i) a so-called Dresselhaus field resulting from the lack of inversion symmetry of the crystal structure and (ii) a Rashba field due to asymmetries in the applied confining potential. Although the underlying mechanisms are thus well understood, it still remains a challenge to determine the absolute and relative strength of both contributions in a given sample [12,13].Investigating the DC Josephson current through a superconductor-semiconductor-superconductor junction in the presence of an applied magnetic field has been proposed as a way to acquire information about SOI in the semiconductor [14][15][16]. Indeed, SOI can make the current depend anisotropically on the field [16] or produce an anomalous supercurrent (a current at zero phase difference) [14,[17][18][19]. These effects depend on the orientiation and type (Rashba or Dresselhaus) of the SOI and as such could therefore be used to determine or parametrize the SOI in a given sample [20].Previous models produced (semi-)analytic results for the Josephson current as a function of SOI parameters, e.g. for strictly one-dimensional wires [16,17], for quasi-one-dimension...

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Anomalous Josephson effect induced by spin-orbit interaction and Zeeman effect in semiconductor nanowires

Cited by 237 publications

References 65 publications

Singularities in the Andreev spectrum of a multiterminal Josephson junction

Singularities in the Andreev spectrum of a multiterminal Josephson junction

Effects of spin-orbit coupling and spatial symmetries on the Josephson current in SNS junctions

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

Contact Info

Product

Resources

About