Majorana Fermion in Topological Superconducting Element Hcp Thallium

The Majorana fermion is an exotic particle that is its own antiparticle. Chiral Majorana fermion can arise in a one-dimensional edge of topological materials, and especially that in a topological superconductor can be exploited in non-Abelian quantum computation. While the chiral Majorana mode (CMM) remains elusive, a promising situation is realized when superconductivity coexists with a topologically non-trivial surface state. Here, we perform fully non-empirical calculation for the CMM considering superconductivity and surface relaxation, and show that hexagonal close-packed thallium (Tl) has an ideal electronic state that harbors the CMM [1]. The k_z = 0 plane corresponds to the TCI with mirror Chern number |N_M|=2. One of the Dirac points on the (01-10) surface is located almost at the Fermi level. Tl is a textbook-like s-wave superconductor and the gap function has no significant wave-number dependence. Only one of the two Dirac points is relevant for the gap opening due to the superconducting transition, and the CMM appears at the hinge under the Zeeman field. Our calculation indicates that Tl will provide a new platform of the Majorana fermion and quantum computation.
[1] M. Hirayama, T. Nomoto, and R. Arita, submitted.