Linear bands, zero-momentum Weyl semimetal, and topological transition in skutterudite-structure pnictides

TL;DR

This paper investigates the topological electronic structure of skutterudite-structure pnictides, especially CoSb3, revealing a topological transition involving a Dirac-Weyl semimetal phase and its potential to become a topological insulator under strain.

Contribution

It demonstrates the existence of a zero-gap topological semimetal phase in CoSb3 and shows how spin-orbit coupling and strain induce a topological insulator phase, analyzing the origin of linear bands.

Findings

CoSb3 exhibits a topological transition near its ground state.

Spin-orbit coupling and strain convert the semimetal into a topological insulator.

The linear band arises from near-degeneracy and specific orbital characteristics.

Abstract

It was reported earlier [Phys. Rev. Lett. 106, 056401 (2011)] that the skutterudite structure compound CoSb$_3$ displays a unique band structure with a topological transition versus a symmetry-preserving sublattice (Sb) displacement very near the structural ground state. The transition is through a massless Dirac-Weyl semimetal, point Fermi surface phase which is unique in that (1) it appears in a three dimensional crystal, (2) the band critical point occurs at $k$=0, and (3) linear bands are degenerate with conventional (massive) bands at the critical point (before inclusion of spin-orbit coupling). Further interest arises because the critical point separates a conventional (trivial) phase from a topological phase. In the native cubic structure this is a zero-gap topological semimetal; we show how spin-orbit coupling and uniaxial strain converts the system to a topological insulator (TI). We also analyze the origin of the linear band in this class of materials, which is the characteristic that makes them potentially useful in thermoelectric applications or possibly as transparent conductors. We characterize the formal charge as Co$^{+}$ $d^8$, consistent with the gap, with its $\bar{3}$ site symmetry, and with its lack of moment. The Sb states are characterized as $p_x$ (separately, $p_y$) $\sigma$-bonded $Sb_4$ ring states occupied and the corresponding antibonding states empty. The remaining (locally) $p_z$ orbitals form molecular orbitals with definite parity centered on the empty $2a$ site in the skutterudite structure. Eight such orbitals must be occupied; the one giving the linear band is an odd orbital singlet $A_{2u}$ at the zone center. We observe that the provocative linearity of the band within the gap is a consequence of the aforementioned near-degeneracy, which is also responsible for the small band gap.