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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 61, Issue 9: 097411(2018) https://doi.org/10.1007/s11433-018-9232-5

Current noises in a topological Josephson junction

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  • ReceivedApr 11, 2018
  • AcceptedApr 25, 2018
  • PublishedMay 24, 2018
PACS numbers

Abstract

We study the transport properties of a superconductor-quantum spin Hall insulator-superconductor Josephson junction both in the absence and in the presence of a DC bias voltage. As the system is predicted to host Majorana fermions at its interfaces, the Andreev bond states are supposed to exhibit a distinct $4\pi$ periodicity in the superconducting phase difference, namely the fractional Josephson effect. Using the non-equilibrium Green's function method, we calculate the current and the related current noise based on a tight-binding Hamiltonian. Our direct results show that the fractional Josephson effect can not be seen in equilibrium junctions. While in non-equilibrium junctions, this effect can be confirmed by the multiple Andreev reflections induced peaks of the non-equilibrium noise, which appear at discrete frequencies $\omega=neV$ with $n$ being an integer number.


Acknowledgment

This work was supported by the National Key Basic Research Program of China (Grant Nos. 2015CB921102, and 2014CB920901), the National Key R and D Program of China (Grant No. 2017YFA0303301), the National Natural Science Foundation of China (Grants Nos. 11574007, 11574245, 11534001, and 11474085), the Natural Science Foundation of Jiangsu Province (Grant No. BK20160007), and the Key Research Program of the Chinese Academy of Sciences (Grant No. XDPB08-4).


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  • Figure 1

    (Color online) (a) Schematic of energy-phase relations with (solid lines) and without (dot lines) energy gap induced by the finite-size effect; (b) calculated Josephson current versus the superconducting phase difference for topological junctions of different transmission probabilities at temperature $T=0$.

  • Figure 2

    (Color online) Zero frequency equilibrium noise as a function of the superconducting phase difference with different Zeeman energies which correspond to different transmission probabilities at three different temperature $T=0$, $T=0.1\Delta$ and $T=0.2\Delta$, respectively.

  • Figure 3

    (Color online) DC current, real part and imaginary part of the first harmonic of the AC current as functions of the applied bias $V$ for different transmission probabilities at zero temperature. The superconducting phases are taken as $\phi_{\text{L}}=\phi_{\text{R}}=0$, while other parameters are the same as in Figure 1.

  • Figure 4

    (Color online) Non-equilibrium noise at a finite frequency for various values of the applied bias voltage for a topological Josephson junction with two different transmission probabilities $D=1$ (a) and $D<1$ (b), respectively. Here, the superconducting phases are $\phi_{\text{L}}=\phi_{\text{R}}=0$, the temperature is $T=0$, and other parameters are the same as Figure 1. The values are vertical displayed for clarity.

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