Evolution of band topology by competing band overlap and spin-orbit coupling: Twin Dirac cones in Ba3SnO as a prototype

Abstract

We theoretically demonstrate how competition between band inversion and spin-orbit coupling (SOC) results in nontrivial evolution of band topology, taking antiperovskite Ba3SnO as a prototype material. A key observation is that when the band inversion dominates over SOC, there appear "twin" Dirac cones in the band structure. Due to the twin Dirac cones, the band shows highly peculiar structure in which the upper cone of one of the twin continuously transforms to the lower cone of the other. Interestingly, the relative size of the band inversion and SOC is controlled in this series of antiperovskite A3EO by substitution of A (Ca, Sr, Ba) and/or E (Sn, Pb) atoms. Analysis of an effective model shows that the emergence of twin Dirac cones is general, which makes our argument a promising starting point for finding a singular band structure induced by the competing band inversion and SOC.Singularities in band structures give rise to singular and attracting responses of materials [1][2][3][4][5]. Therefore, significant amount of efforts have been paid on finding what kinds of singularities are possible in principle, and on proposing materials to realize the singularities, both in theory and experiments [6][7][8]. The "standard" singularity is Dirac/Weyl cone [9-13], which is characterized by a linear, or conical dispersion around an isolated gapclosing point in the Brillouin zone. Already a number of materials are confirmed to possess Dirac/Weyl cones, ranging from graphene [14] (two-dimensional) to Cd 3 As 2 [15], Na 3 Bi [16], and TaAs [17] (three-dimensional), and so on. However, the linear dispersion around the isolated gap-closing point is not the only possible band singularity. The gap-closing point can form a line (typically a loop) in the Brillouin zone rather than an isolated point [18][19][20]. Also, a dispersion around a gap-closing point can be quadratic rather than linear [21]. Very recently, singularities involving three bands are also discussed [22,23].Quite often, the three ingredients, i.e., band inversion, spin-orbit coupling (SOC), and symmetry, play key roles in generating a singular band structure. Roughly speaking, the band inversion means an overlap between two bands with different origin, typically originating from different kinds of orbitals, say s-and p-orbitals, or p-and d-orbitals. Naively, the overlapped bands repel with each other (band anticrossing). However the gap opening due to the band repulsion is sometimes prohibited by some symmetry, leading to singular gap closing points. The SOC, on the other hand, determines which kinds of the band repulsion is allowed, in other words, what kinds of gap-closing points can appear. terial Ca 3 PbO is predicted to have three-dimensional Dirac cones exactly at the Fermi energy, and importantly, all of the three ingredients, the band overlap, SOC, and the symmetry, are relevant in the formation of Dirac cones. (Strictly speaking, there is a tiny mass gap. If we make an emphasis on the gapful nature, the system is a topological crystalline insulator ...

Magnetoresistance of a three-dimensional Dirac gas

“…Experimental realizations were found both in two dimensions 13,14 and three dimensions 11,15 . A simple effective model for these materials is the general 4×4 Dirac Hamiltonian with a finite mass term [16][17][18] . The dispersion relation is equivalent to that of relativistic fermions, but with effective values for the mass of the fermion and speed of light.…”

Unusual valence state in the antiperovskites Sr3SnO and Sr3PbO revealed by x-ray photoelectron spectroscopy

“…Around Γ, there is a moderate inversion between the B p-bands and A d-bands. When interorbital hybridization and spin-orbit coupling are taken into account, the six equivalent band crossings at the Fermi energy are only slightly gapped, resulting in the approximate 3D Dirac semimetallic phase [8][9][10], as well as the topological crystalline insulating phase in some cases [6].…”

Negative ionic states of tin in the oxide superconductor Sr3−xSnO revealed by Mössbauer spectroscopy

“…Furthermore, thermoelectric properties of * a.ikeda@scphys.kyoto-u.ac.jp Ca 3 SnO and Ca 3 Pb 1x Bi x O are studied to make use of the multivalley band structure with six equivalent Dirac cones [7]. More recently, it has been proposed that one can tune the size of the band inversion and mass of the Dirac cone via chemical substitution of A and B [10]. Thus, antiperovskite oxides are a good platform to study the Dirac and topological natures.…”