Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
  • Editors' Suggestion

Signatures of topological Josephson junctions

Yang Peng, Falko Pientka, Erez Berg, Yuval Oreg, and Felix von Oppen
Phys. Rev. B 94, 085409 – Published 11 August 2016
PDFHTMLExport Citation
Abstract
Authors
Article Text
  • INTRODUCTION
  • BASIC CONSIDERATIONS
  • SWITCHING PROBABILITY OF TOPOLOGICAL…
  • MICROWAVE ABSORPTION
  • TOPOLOGICAL VS NONTOPOLOGICAL JUNCTIONS…
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Quasiparticle poisoning and diabatic transitions may significantly narrow the window for the experimental observation of the 4π-periodic dc Josephson effect predicted for topological Josephson junctions. Here, we show that switching-current measurements provide accessible and robust signatures for topological superconductivity which persist in the presence of quasiparticle poisoning processes. Such measurements provide access to the phase-dependent subgap spectrum and Josephson currents of the topological junction when incorporating it into an asymmetric SQUID together with a conventional Josephson junction with large critical current. We also argue that pump-probe experiments with multiple current pulses can be used to measure the quasiparticle poisoning rates of the topological junction. The proposed signatures are particularly robust, even in the presence of Zeeman fields and spin-orbit coupling, when focusing on short Josephson junctions. Finally, we also consider microwave excitations of short topological Josephson junctions which may complement switching-current measurements.

    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    6 More
    • Received 3 May 2016
    • Revised 22 July 2016

    DOI:https://doi.org/10.1103/PhysRevB.94.085409

    ©2016 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Josephson effectTopological phases of matter
    1. Techniques
    SQUID
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Yang Peng1, Falko Pientka1,2, Erez Berg3, Yuval Oreg3, and Felix von Oppen1

    • 1Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
    • 2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
    • 3Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel

    Article Text (Subscription Required)

    Click to Expand

    References (Subscription Required)

    Click to Expand
    Issue

    Vol. 94, Iss. 8 — 15 August 2016

    Reuse & Permissions
    Access Options
    CHORUS

    Article Available via CHORUS

    Download Accepted Manuscript
    Author publication services for translation and copyediting assistance advertisement

    Authorization Required

    Log In
    Other Options
    ×

    Images

    • Figure 1
      Figure 1

      Basic setup of the asymmetric SQUID, involving a weak conventional/topological Josephson junction (blue triangles) and a strong auxiliary Josephson junction (red checked box) with critical current I0. The phase δ across the weak junction is linked to the phase γ across the auxiliary junction and the phase drop ϕ=2eφ/ℏ induced by the magnetic flux φ threading the SQUID loop, δ=ϕ+γ. The applied voltage Vb drives a current I through the resistance Rb and the SQUID.

      Reuse & Permissions
    • Figure 2
      Figure 2

      Upper panels: single-particle energies of the subgap state as a function of the phase difference across the junction for (a) conventional and (a′) topological Josephson junctions. Lower panels: supercurrent as a function of phase difference for the various possible states of (b) conventional and (b′) topological Josephson junctions (G=e2D/π,D=0.95). The blue, black, and red curves in (b) display the currents for the states |0〉,|1,σ〉, and |2〉, respectively. The blue and red curves in (b′) display the currents for the states |0〉 and |1〉.

      Reuse & Permissions
    • Figure 3
      Figure 3

      Upper panels: possible quasiparticle processes numbered by (1)–(4) in (a) conventional and (a′) topological Josephson junctions. The black dashed lines indicate the many-body ground state and the upper blue boxes the quasiparticle continuum above the energy gap Δ. The red lines indicate the bound state at energies EA or EM for conventional and topological junctions, respectively. Lower panels: excitation energies (or energy thresholds) involving the bound state corresponding to the various processes in panels (a) and (a′).

      Reuse & Permissions
    • Figure 4
      Figure 4

      (a) Probability Psw of switching to the resistive state as a function of current for conventional (left) and topological (right) Josephson junctions for δ=0.9π and D=0.95. The dashed lines are the switching probabilities for the junction assuming a fixed occupation state [cf. Eq. (12)]. The black solid curves display the switching probability Psw in the presence of quasiparticle poisoning, and can be obtained from a weighted average over the switching probabilities of the various occupation states [cf. Eq. (13)]. For the conventional Josephson junction, we choose the weight factors c0=0.5,c1,↑=c1,↓=0.23, and c2=0.04. For the topological Josephson junction, we choose the weight factors c0=0.6 and c1=0.4. (b) Width of the plateau ΔI/I0 as a function of δ=γ+ϕ for the case of conventional (red dashed) and topological Josephson junctions (blue solid) (for EJaux/Δ=5.7, where EJaux=ℏI0/2e is the Josephson energy of the auxiliary junction and Δ the gap of the weak junction).

      Reuse & Permissions
    • Figure 5
      Figure 5

      Sketch of the “tilted washboard” potential governing the dynamics of the Josephson junction near one minimum.

      Reuse & Permissions
    • Figure 6
      Figure 6

      Color plot of the switching probability Psw of asymmetric SQUIDs as a function of flux ϕ and height I of the current pulse for (a) a conventional and (b) a topological Josephson junction. The occupation probabilities of the various junction states prior to the current pulse are taken to be thermal, with effective temperature Teff. In (a), parameters are such that the occupation probability of the doubly occupied Andreev state is negligible. The dashed lines indicate the switching currents based on the Josephson currents associated with the various junction states as indicated in the figure, with the phase difference across the weak junction taken as δ=ϕ+π/2. In (a), the purple line corresponds to the ground state, the black line to the singly occupied Andreev state, and the orange one to the doubly occupied state. In (b), the purple and orange lines correspond to the two states of the topological junction. The parameters were chosen as Rs=550Ω,I0=553.7nA,T=100mK,EJaux/Δ=5.7,tp=1μs, and D=0.95, according to the parameters used in Ref. [35]. The effective temperature Teff is chosen as such that EJaux/Teff=10. The gray arrows with labels (i), (ii) indicate values of ϕ for which line cuts are shown in Fig. 7.

      Reuse & Permissions
    • Figure 7
      Figure 7

      Switching probability of a conventional (topological) junction as a function of the applied current for fixed ϕ. The black symbols represent Psw along the fixed-ϕ cuts indicated by gray arrows in Fig. 6 for conventional junctions: (i) switching probability for ϕ=0.4π; (ii) for ϕ=0.6π. (i′) and (ii′) show the corresponding plots along the same ϕ cuts for the topological junction. The dashed curves denote the switching probability when the weak junction is in the fixed occupation state as specified in the figure, similar to those in Fig. 4. Note that for conventional junction, the state with the lower switching current inverts between (i) and (ii). It is this inversion which explains the sudden change in the plateau height for (i) ϕ<π/2 and (ii) ϕ>π/2, as discussed in the text. In contrast, there are no such inversions in the topological case.

      Reuse & Permissions
    • Figure 8
      Figure 8

      Center: parity switching between states |1〉 and |0〉, with rates Γin and Γout. Left: quasiparticle processes that contribute to Γout. The top panel shows the breaking of a Cooper pair, with one electron excited into the subgap state (red line) and the second electron excited to the continuum (blue box). The bottom panel shows the transition of a quasiparticle from the continuum into the subgap state. Right: quasiparticle processes that contribute to Γin. The top panel shows the recombination of quasiparticle excitations from the continuum and the subgap state into a Cooper pair. The bottom panel shows the excitation of an excitation from the subgap state into the quasiparticle continuum.

      Reuse & Permissions
    • Figure 9
      Figure 9

      Various contributions to the real part of the admittance for the Fu-Kane model, based on Eq. (C39), for D=0.95 and phase differences ϕ=π as well as ϕ=π/2. For ϕ=π,EA=0, so that ReY2 and ReY3 coincide. At phase differences ϕ away from π, the two curves differ.

      Reuse & Permissions
    • Figure 10
      Figure 10

      Derivative of the linear absorption rate with respect to the microwave frequency dW/dω [see Eq. (47)]. For optimal visibility of the thresholds, we assume an occupation of n=12 in Eq. (50) independently of flux. While the figure displays the sum of contributions from Y2 and Y3, the bright curves result predominantly from Y2 and Y3 as labeled in the figure.

      Reuse & Permissions
    • Figure 11
      Figure 11

      Subgap energies of a short conventional Josephson junction as a function of the phase difference, in the presence of Zeeman field applied in the junction region. The orange solid curves are the spectra for spin up with Nambu spinor (ψ↑,ψ↓†)T. The blue dashed lines are the corresponding spectra for spin down following from particle-hole symmetry. The panels illustrate the two types of typical behaviors, with parameters chosen as (a) η̃=0.5 and (b) η̃=2.8, with D=0.6 and Rcosγ̃=0.2 in both panels.

      Reuse & Permissions
    • Figure 12
      Figure 12

      Low-energy spectra of Hamiltonian (E1) as a function of phase difference φ, for various Zeeman fields and junction lengths. The results are obtained numerically for finite-length samples, showing all levels which become subgap states at least for some range of phase differences. Energies corresponding to the quasiparticle continuum of infinite wires are shown in gray. We choose a chemical potential μ=0, spin-orbit interaction mα2=Δ, and a total length 60ξ of the system, with ξ=2α/Δ the bulk coherence length of the superconductor when B=0. Results for a short junction with L=0.05ξ are shown in (a)–(c) for increasing Zeeman field: (a) nontopological junction, B=0.2Δ; (b) nontopological junction, B=0.8Δ; (c) topological junction, B=2.0Δ. The subgap spectrum behaves in a qualitatively similar manner in intermediate length junctions with L=0.5ξ. Results for junctions of this length are shown in (d)–(f), with the other parameters equal to those of panels (a)–(c). Additional subgap states emerge only in long junctions, as shown in panels (g) and (h) for L=2ξ, and other parameters again as in (a)–(c). The numerical results are obtained by discretizing the Hamiltonian (E1) with a minimal spacing of 0.025ξ and an eighth-order approximation to the Laplacian.

      Reuse & Permissions
    • Figure 13
      Figure 13

      Low-energy spectra of Hamiltonian (E1) as a function of phase difference φ, for fixed Zeeman fields B=2.0Δ and junction length L=0.5ξ. The results are obtained numerically for finite-length samples, showing all levels which become subgap states at least for some range of phase differences. Energies corresponding to the quasiparticle continuum of infinite wires are shown in gray. We choose a spin-orbit interaction of mα2=Δ and a total length of 60ξ of the system, with ξ=2α/Δ the bulk coherence length of the superconductor when B=0. (a) Nontopological junction with μ=3.0Δ. (b) Topological junction with μ=1.0Δ. Panels (c) and (d) are for parameters as in (a) and (b), respectively, but with an additional potential barrier of height 3Δ in the junction region, which reduces the junction transmission. The numerical results are obtained by discretizing the Hamiltonian (E1) with a minimal spacing of 0.025ξ and an eighth-order approximation to the Laplacian.

      Reuse & Permissions
    ×

    Sign up to receive regular email alerts from Physical Review B

    Log In

    Cancel
    ×

    Search

    Article Lookup

    Paste a citation or DOI
    Enter a citation
    ×