Sea of Majorana fermions from pseudo-scalar superconducting order in three dimensional Dirac materials

Abstract

We suggest that spin-singlet pseudo-scalar s-wave superconducting pairing creates a two dimensional sea of Majorana fermions on the surface of three dimensional Dirac superconductors (3DDS). This pseudo-scalar superconducting order parameter Δ5, in competition with scalar Dirac mass m, leads to a topological phase transition due to band inversion. We find that a perfect Andreev-Klein reflection is guaranteed by presence of anomalous Andreev reflection along with the conventional one. This effect manifests itself in a resonant peak of the differential conductance. Furthermore, Josephson current of the Δ5|m|Δ5 junction in the presence of anomalous Andreev reflection is fractional with 4π period. Our finding suggests another search area for condensed matter realization of Majorana fermions which are beyond the vortex-core of p-wave superconductors. The required Δ5 pairing can be extrinsically induced by a conventional s-wave superconductor into a three dimensional Dirac material (3DDM).

Chirality blockade of Andreev reflection in a magnetic Weyl semimetal

“…We also discuss the subtle role played by inversion symmetry by contrasting a scalar with a pseudoscalar pair potential [10]. The absence of the chirality blockade for pseudoscalar pairing explains why it did not appear in the many previous studies of Andreev reflection in a Weyl semimetal [11][12][13][14][15][16][17][18][19].…”

“…The corresponding factorization of the hole transfer matrix is 16) as required by the electron-hole symmetry (2.11). For later use, we give the inverse …”

Half-vortices, confinement transition and chiral Josephson effect in superconducting Weyl/Dirac semimetals

“…Therefore in a closed loop geometry of a Josephson junction, the electron has to traverse the loop once again, giving rise to the 4π (two rounds) periodic Josephson effect. The 4π-periodic Josephson effect is a hallmark of topological superconductivity and its associated Majorana modes [6]. This can be the most natural explanation for the observed 4π−periodic Andreev bound states [7].…”

“…Therefore, apart from the U (1) phase e iφ , the most generic form of superconductivity in WSMs can be represented by a number in the complex plane (∆ s , ∆ 5 ). The conventional superconductors are confined to the real axis of this plane, while the pure pseudoscalar superconductors [4,6] are confined to the imaginary axis of this plane. Eq.…”

“…In order to appreciate the importance of the notion of the complex (∆ s , ∆ 5 ) plane, let us consider a purely pseudoscalar superconductor [6], (0, ∆ 5 ). The complex plane structure allows to immediately understand the topologically non-trivial structure of such this superconductors.…”