Erratum: Tuning ferromagnetic BaFe2(PO4)2 through a high Chern number topological phase [Phys. Rev. B 94 , 125134 (2016)]

Abstract

There is strong interest in discovering or designing wide gap Chern insulators. Here we follow a Chern insulator to trivial Mott insulator transition versus interaction strength U in a honeycomb lattice Fe-based transition metal oxide, discovering that a spin-orbit coupling energy scale ξ=40 meV can produce and maintain a topologically entangled Chern insulating state against large band structure changes arising from an interaction strength U up to 60 times as large. Within the Chern phase the minimum gap switches from the zone corner K to the zone center Γ while maintaining the topological structure. At a critical strength Uc, the continuous evolution of the electronic structure encounters a gap closing then reopening, upon which the system reverts to a trivial Mott insulating phase. This Chern insulator phase of honeycomb lattice Fe 2+ BaFe2(PO4)2 corresponds to a large Chern number C = -3 that will provide enhanced anomalous Hall conductivity due to the associated three edge states threading through the bulk gap of 80 meV.

Monolayer of the 5d transition metal trichloride OsCl3 : A playground for two-dimensional magnetism, room-temperature quantum anomalous Hall effect, and topological phase transitions

“…The Chern number C = 1 is obtained for FM z configuration of spins in Fig. 2(c), which also shows how C could increase [29] by tuning E F (such as by gate voltage [47]) into different gaps of the bulk band structure in Fig. 2(c).…”

“…We note that Ref. [37] has proposed a heuristic phase diagram in which QAH insulating phase borders [29] a trivial Mott insulator. Thus, our Fig.…”

“…3 confirm the presence of one chiral state per edge associated with C = −1. While theoretical and computational searches [1,4,18] for QAH insulators have largely been focused on finding materials or heterostructures with nonzero (and as large as possible [29]) C characterizing their bulk band structure, we show that understanding of a variety of possible spin orderings on the honeycomb lattice [27] (see Fig. 4) or spatial and transport properties [23] of chiral edge states (see Sec.…”

Quantum Anomalous Hall Effect in Magnetic Doped Topological Insulators and Ferromagnetic Spin‐Gapless Semiconductors—A Perspective Review

“…Hence, by setting electron spin polarization, say s z = −1, Kane-Mele type SOC [77,78] term effectively reduces to Haldane-like term for NNN tunneling with complex hopping matrix elements. [1] Monolayers of transition-metal trihalides such as MCl 3 (M:V and Os), [41] RuX 3 (X: Br, Cl, I), [41,42] MnBr 3 43 , NiCl 3 , [44] transition-metal oxides V 2 O 3 , [48] Nb 2 O 3 , [49] BaFe 2 (PO 4 ) 2 [50] and transition-metal-organic framework Mn 2 C 18 H 12 , [51] Co(C 21 N 3 H 15 ), [52] TM(C 18 H 12 N 6 ) 2 [53] are typical ferromagnetic semiconducting materials where transition metal ions form honeycomb lattice structure. On the same footing, single layer Cs 2 Mn 3 F 12 of Cs 2 LiMn 3 F 12 [55] and Fe 3 Sn 2 [54] are prototypical examples of ferromagnetic SGS where transition metal ions form kagome lattice structure, as shown in Figure 6.…”

Band crossings in honeycomb-layered transition metal compounds

“…Recently, transition metal (TM) compounds with similar honeycomb-layered structure have gained great interest from the peculiar band topology in their d-orbital manifolds. For instance, the DPNs, QBCs, and topological phases were found in the systems with corner-sharing network of the octahedral ligands, e.g., [111] layers of the perovskite structure [12][13][14][15][16], and with edge-sharing octahedra, e.g., trichalcogenides [17], trihalides [18][19][20][21], corundum [22,23], and rhombohedral materials [24][25][26]. Interestingly, the number and position of the DPNs as well as the shape of the Dirac dispersions strongly depend on the materials.…”