Quasiparticle dynamics in ballistic weak links under weak voltage bias: an elementary treatment

Kroemer, H.

doi:10.1006/spmi.1999.0704

Cited by 6 publications

(3 citation statements)

References 25 publications

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“…In order to obtain Zener tunneling, a bias voltage across the junction is required (which is for example the case in Shapiro steps measurements). Due to this bias voltage the quasi-particles in the junction can gain enough kinetic energy so that they can transfer from a lower Andreev bound state to an upper bound state despite the separation by a gap 45,46 . It is noted in Ref.…”

Section: Signatures Of 4π Periodic Abs By Means Of Zener Tunnelingmentioning

confidence: 99%

Andreev bound states and current-phase relations in three-dimensional topological insulators

et al. 2013

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To guide the search for the Majorana fermion, we theoretically study superconductor/topological/superconductor (S/TI/S) junctions in an experimentally relevant regime. We find that the striking features present in these systems, including the doubled periodicity of the Andreev bound states (ABSs) due to tunneling via Majorana states, can still be present at high electron densities. We show that via the inclusion of magnetic layers, this 4π periodic ABS can still be observed in three-dimensional topological insulators, where finite angle incidence usually results in the opening of a gap at zero energy and hence results in a 2π periodic ABS. Furthermore, we study the Josephson junction characteristics and find that the gap size can be controlled and decreased by tuning the magnetization direction and amplitude. These findings pave the way for designing experiments on S/3DTI/S junctions. 74.78.Fk, 74.45.+c, 03.65.Vf with M the magnetization due to the ferromagnet and m = (m x , m y , m z ) the exchange field. σ i are the Pauli

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Section: Signatures Of 4π Periodic Abs By Means Of Zener Tunnelingmentioning

confidence: 99%

Andreev bound states and current-phase relations in three-dimensional topological insulators

et al. 2013

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“…At finite U , the bonding and antibonding even parity modes hybridize via the fully occupied | ↑↓, ↑↓ state and a gap opens, and the odd parity states disperse weakly via CAR into the triply occupied states. The even state is 4π periodic for U = ∞, but by means of Zener tunneling Γ, quasiparticles can tunnel from a lower to a higher Andreev bound state [34,35], and a 4π periodic contribution is expected for a large range of finite U . This FIG.…”

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confidence: 99%

Localized Many-Particle Majorana Modes with Vanishing Time-Reversal Symmetry Breaking in Double Quantum Dots

Wright

Veldhorst

2013

Phys. Rev. Lett.

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We introduce the concept of spinful many-particle Majorana modes with local odd operator products, thereby preserving their local statistics. We consider a superconductor -double quantum dot system where these modes can arise with negligible Zeeman splitting when Coulomb interactions are present. We find a reverse Mottinsulator transition, where the even and odd parity bands become degenerate. Above this transition, Majorana operators move the system between the odd parity ground state, associated with elastic co-tunneling, and the even parity ground state, associated with crossed Andreev reflection. These Majorana modes are described in terms of one, three and five operator products. Parity conservation results in a 4π periodic supercurrent in the even state and no supercurrent in the odd state.The prediction for the existence of Majorana modes [1] has attracted enormous attention in condensed matter physics [2][3][4][5][6][7]. Allured by the possibility of constructing topological qubits for quantum computation [2,4], a plethora of schemes promising the positive identification of Majorana modes has emerged [8][9][10][11][12]. Although superconductors are a natural habitat of chargeless quasiparticles, spin degeneracy in standard s-wave superconductors prevents the appearance of localized Majorana modes. Effective spinless p-wave superconductors can be realized using strong spin-orbit coupling, for example at the interface of a superconductor and a topological insulator [5], or in semiconducting nanowires in the presence of Zeeman and Rashba fields [6,7]. Experimentally, supercurrents [13], Fraunhofer patterns and Shapiro steps [14], SQUIDs [15], and zero bias conductance peaks [16] have been observed in topological insulator systems, which, together with the zero bias conductance peaks in nanowire systems [17], provide prospects for the observation of the Majorana mode, but to date, no conclusive evidence has been observed.Superconductor -quantum dot systems are also proposed to realize Majorana modes [11,18,19], by including spin-orbit coupling [11], or in the presence of anisotropic magnetic fields [19]. Although quantum dots have several advantages, the strong spin-orbit or anisotropic magnetic fields required forms a major hurdle and limits material flexibility. For example, anisotropic magnetic fields only result in spinless localized Majorana modes in fields E Z ≫ ∆ ∼ t, with ∆ the induced superconducting gap and t the inter-site hopping. Here, generalizing the proposal of Ref.[19] to strongly correlated quantum dots, we show that in the presence of small anisotropic magnetic fields, E Z ∼ k B T , a new arena emerges: the concept of spinful many-particle Majorana modes. These Majorana modes are localized in their odd operator products, and thereby preserve the local statistics of spinless proposals [20]. Furthermore, this demonstrates that interactions can greatly relax the constraints of large Zeeman splitting and large spin FIG. 1: (a) Schematic representation of the device. Two superconductors (with p...

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“…Due to this bias voltage, the quasiparticles in the junction can gain enough kinetic energy so that they can transfer from a lower Andreev bound state to an upper bound state despite the separation by a gap [80,81]. It is noted in Ref.…”

Section: Signatures Of 4π Periodic Abs By Means Of Zener Tunnelingmentioning

confidence: 94%

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Quasiparticle dynamics in ballistic weak links under weak voltage bias: an elementary treatment

Cited by 6 publications

References 25 publications

Andreev bound states and current-phase relations in three-dimensional topological insulators

Andreev bound states and current-phase relations in three-dimensional topological insulators

Localized Many-Particle Majorana Modes with Vanishing Time-Reversal Symmetry Breaking in Double Quantum Dots

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