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Electrons in a Dirac semimetals possess linear dispersion in all three spatial dimensions, and form part of a developing platform of novel quantum materials. Bi$_{1-x}$Sb$_x$ supports a three-dimensional Dirac cone at the Sb-induced band inversion point. Nanoscale phase-sensitive junction technology is used to induce superconductivity in this Dirac semimetal. Radio frequency irradiation experiments reveal a significant contribution of 4$pi$-periodic Andreev bound states to the supercurrent in Nb-Bi$_{0.97}$Sb$_{0.03}$-Nb Josephson junctions. The conditions for a substantial $4pi$ contribution to the supercurrent are favourable because of the Dirac cones topological protection against backscattering, providing very broad transmission resonances. The large g-factor of the Zeeman effect from a magnetic field applied in the plane of the junction, allows tuning of the Josephson junctions from 0 to $pi$ regimes.
We propose a scheme to detect the Majorana bound states (MBSs) by a thermodynamically stable D.C. Josephson current with $4pi$-periodicity in the superconducting phase difference, which is distinct from the previous A.C. $4pi$-periodicity found in to
The energy spectrum of cake shape normal - superconducting systems is calculated by solving the Bogoliubov-de Gennes equation. We take into account the mismatch in the effective masses and Fermi energies of the normal and superconducting regions as w
Andreev bound states are an expression of quantum coherence between particles and holes in hybrid structures composed of superconducting and non-superconducting metallic parts. Their spectrum carries important information on the nature of the pairing
We calcuate electronic spin susceptibility and spin-lattice relaxation rate in singlet superconductor near a pairbreaking surface, or in a domain wall of the order parameter. We directly link presence of high-density Andreev bound states in the inhom
The theory of Andreev conductance is formulated for junctions involving normal metals (N) and multiband superconductors (S) and applied to the case of superconductors with nodeless extended $s_{pm}$-wave order parameter symmetry, as possibly realized