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Majorana Bound State in Rotating Superfluid He3−A between Parallel Plates

Y. Tsutsumi, T. Kawakami, T. Mizushima, M. Ichioka, and K. Machida
Phys. Rev. Lett. 101, 135302 – Published 23 September 2008
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    Abstract

    A concrete and experimentally feasible example for testing the putative Majorana zero-energy state bound in a vortex is theoretically proposed for a parallel plate geometry of superfluid He3−A phase. We examine the experimental setup in connection with ongoing rotating cryostat experiments. The theoretical analysis is based on the well-established Ginzburg-Landau functional, supplemented by microscopic calculations of the Bogoliubov–de Gennes equation, both of which allow the precise location of the parameter regions of the Majorana state to be found in realistic situations.

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    • Received 21 May 2008

    DOI:https://doi.org/10.1103/PhysRevLett.101.135302

    ©2008 American Physical Society

    Authors & Affiliations

    Y. Tsutsumi, T. Kawakami, T. Mizushima, M. Ichioka, and K. Machida

    • Department of Physics, Okayama University, Okayama 700-8530, Japan

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    Vol. 101, Iss. 13 — 26 September 2008

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    Images

    • Figure 1
      Figure 1
      Spatial structures of the order parameters |A+| (left-hand side) and |A−| (right-hand side) for the (0,2) state. The sense of the phase winding and its number are shown. R=0.8  μm and Ω=100  rad/sec.Reuse & Permissions
    • Figure 2
      Figure 2
      Spatial structures of the order parameters, |A+| (left-hand side) and |A−| (right-hand side) for the (1,3) state. R=0.8  μm and Ω=100  rad/sec.Reuse & Permissions
    • Figure 3
      Figure 3
      Size R dependence of the critical angular velocity Ωc from (0,2) at rest to (1,3) at a higher rotation (T/Tc=0.95). An extrapolated value of Ωc=0.06  rad/sec is found at R=1.5  mm. The inset shows the energy differences (arbitrary scale) between the two states as a function of Ω for R=100  μm.Reuse & Permissions
    • Figure 4
      Figure 4
      Energy spectrum Eq with qz=0 (a) and qθ=1 (b) in the (1,3) vortex under no rotation Ω=0, where Δ≡max|A±(r)|. The branches labeled “Core” and “Edge” in (a) are eigenstates having wave functions tightly bounded at the vortex core and the edge, respectively. The zero-energy state (ZES) appears within |qz|<kF at qθ=1.Reuse & Permissions
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