We propose a scheme to reveal the possible nematic superconducting order parameter in the doped Bi 2 Se 3 by observing the anisotropic unconventional Josephson effect without an external magnetic field. We find the presence of an intrinsic π-phase in the spin-triplet channel of Andreev reflection. Its competition with the odd-parity superconducting gap phase can lead to unconventional Josephson effect in the Josephson junction, whose normal region is connected to the same side of the superconductor, called the U-shaped junction according to its geometry. For Josephson junctions with the interfaces perpendicular to the nematic direction, the competition will lead to a Josephson π-junctions. In the case where the interface is parallel to the nematic direction, it will lead to a Josephson 0-junction. Thus, this can directly reflect the nematic superconductivity. It is worth noting that Josephson coupling with the 4π period appears only in the normal injected channels. Interestingly, if the Josephson junction adopts a conventional geometry, it always exhibits a normal Josephson 0-junction regardless of the gap function taken by the doped Bi 2 Se 3 and therefore cannot distinguish the pairing symmetry. We thus propose a superconducting quantum interference device containing a U-shaped Josephson junction to detect nematic superconductivity. This proposal not only can be applied to detect nematic superconductivity but also provides a feasible platform for topological quantum computation.
In this work, we systematically study two phases, called Andreev π-phase and orbital-phase, and their influence on the Josephson effect. When the system is time-reversal invariant and centrosymmetric, these two phases only appear in the odd-parity pairings. The Andreev π-phase has nothing to do with the specific form of the odd-parity pairings and means an intrinsic π-phase between the spin-triplet Cooper pairs entering and leaving CTSCs in the Andreev reflections. The orbitalphase corresponds to the phase difference between the spin-triplet Cooper pairs with opposite spin polarization and depends on the specific form of the odd-parity gap functions. When the normal region of the Josephson junction contacts the same side of the CTSCs with some specific odd-parity parings, the competition between the two phases can lead to the Josephson π-junction. Note that this junction is different from that of the conventional Josephson junction (JJ) and is dubbed a U-shaped junction according to its geometry. Meanwhile, in a conventional JJ, the interplay of these two phases causes their impact on the CPR to be completely canceled out. Therefore no matter what kind of pairing symmetries the CTSC has, it will lead to Josephson 0-junction in this case. We obtain our results based on the model of the MxBi2Se3 family where M may be Cu, Sr, or Nb. Therefore, we propose to detect the pairing symmetry of MxBi2Se3 through a superconducting quantum interference device containing a U-shaped Josephson junction.
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