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The chiral Majorana fermion is an exotic particle that is its ownantiparticle. It can arise in a one-dimensional edge of topological materials,and especially that in a topological superconductor can be exploited innon-Abelian quantum computation. While the chiral Majorana mode (CMM) remainselusive, a promising situation is realized when superconductivity coexists witha topologically non-trivial surface state. Here, we perform fully non-empiricalcalculation for the CMM considering superconductivity and surface relaxation,and show that hexagonal close-packed thallium (Tl) has an ideal electronicstate that harbors the CMM. The $k_z=0$ plane of Tl is a mirror plane,realizing a full-gap band inversion corresponding to a topological crystallineinsulating phase. Its surface and hinge are stable and easy to make variousstructures. Another notable feature is that the surface Dirac point is veryclose to the Fermi level, so that a small Zeeman field can induce a topologicaltransition. Our calculation indicates that Tl will provide a new platform ofthe Majorana fermion.

Topological Band Inversion and Chiral Majorana Mode in Hcp Thallium