Nontrivial topological valence bands of common diamond and zinc-blende semiconductors

The diamond and zinc-blende semiconductors are well-known and have been widely studied for decades. Yet, their electronic structure still surprises with unexpected topological properties of the valence bands. In this joint theoretical and experimental investigation, we demonstrate for the benchmark compounds InSb and GaAs that the electronic structure features topological surface states below the Fermi energy. Our parity analysis shows that the spin-orbit split-off band near the valence band maximum exhibits a strong topologically nontrivial behavior characterized by the Z(2) invariants (1; 000). The nontrivial character is a consequence of the nonzero spin-orbit coupling and is imposed by the chosen constituents, in contrast to the conventional topological phase transition mechanism which relies on tuning parameters in the system Hamiltonian. Ab initio-based tight-binding calculations resolve topological surface states in the occupied electronic structure of InSb and GaAs, further confirmed experimentally by soft x-ray angle-resolved photoemission from both materials. Our findings are valid for all other materials whose valence bands are adiabatically linked to those of InSb, i.e., many diamond and zinc-blende semiconductors, as well as other related materials, such as half-Heusler compounds.