Γ M K Multiple Dirac cones and spontaneous QAH state in transition metal trichalcogenides Yusuke Sugita collaborators Takashi Miyake (AIST) Yukitoshi Motome (U.Tokyo) 2017/10/24 @ NQS 2017 1
Outline Introduction - van der Waals materials with heavy elements - motivation: towards the realization of topological matters in 2D systems Materials and methods - transition metal trichalcogenides (TMTs), MBX3 - ab initio calculations, Wannier analysis, and Hartree-Fock approx. Results Y.S., T. Miyake, and Y. Motome, arxiv:1704.00318 & 1707.00921 - multiple Dirac cones in monolayer TMTs - effects of correlations & SOC: a QAH state with a high Chern number - effects of layer stacking: bulk case Summary & Perspectives 2
Graphene purely-2d honeycomb layer Dirac semimetal https://www.nobelprize.org/nobel_prizes/physics/laureates/2010/ almost ideal Dirac cones: weak electron correlations and weak SOC anomalous transport, e.g., anomalous QH effect & Klein tunneling 2017/10/24 @ NQS 2017 3
larger spin-orbit coupling: Post-graphene candidates of QSH insulators: honeycomb sheets of Si, Ge, Sn, spin-valley physics: transition metal dichalcogenides C.-C. Liu et al., PRB (2011) D. Xiao et al., PRL (2012) larger electron correlations: candidates of purely-2d magnets? transition metal trichalcogenides transition metal trihalides N. Sivadas et al., PRB (2015) J. Kohler, Ency. of Inorg. and Bio. Chem. (2014) 4
Discovery of purely-2d ferromagnets magneto-optic Kerr measurements transition metal trichalcogenides CrGeTe3 C. Gong et al., Nature (2017) 2017/10/24 transition metal trihalides CrI3 B. Huang et al., Nature (2017) @ NQS 2017 5
Transition metal trichalcogenides (TMTs) MBX3 (M=transition metal; B=P, Si, Ge; X=S, Se, Te) honeycomb network of edge-sharing MX6 octahedra 3-R structure C2/m structure Top view of monolayer MnPS3, FePS3, NiPS3,etc. B2 dimer MnPSe3, FePSe3, CrSiTe3, CrGeTe3, etc. 2017/10/24 @ NQS 2017 6
Diversity of magnetism in 3d TMTs MnPS3 FePS3 NiPS3 E. Ressouche et al., PRB (2010) D. Lancon et al., PRB (2016) A. R. Wildes et al., PRB (2012) various magnetic ordering (Neel AFM, zigzag AFM, FM, etc.) difference of magnetic anisotropy wide range of band gaps K.-z. Du et al., ACS Nano (2016) 7
Motivation Magnetic 3d TMTs will play an important role in the post-graphene era. 4d & 5d TMTs have been less studied theoretically though the synthesis was reported. W. Klingen et al., Z. Anorg. Allg. Chem. (1973) What happens in 4d & 5d transition metal trichalcogenides where the SOC and electron correlations compete? ab initio study of 4d & 5d TMTs! Our DFT predictions multiple Dirac cones appear in a family of TMTs interplay between electron correlations and SOC may turn the multiple-dirac semimetal into a QAH state with a high Chern number interesting behaviors of Dirac cones depending on the layer stacking 8
Setup Target materials - group 10 & 12 transition metals can take a divalent oxidation state N. N. Greenwood and A. Earnshaw, Chemistry of the Elements (1997) - bulk MPX3 (M=Ni, Pd, Zn, Cd, Hg) have been synthesized W. Klingen et al., Z. Anorg. Allg. Chem. (1973) we systematically study group 10 MPX3 (M=Ni, Pd, Pt & X=S, Se)!! ab initio setup - using OpenMX code T. Ozaki et al., http://www.openmx-square.org - in the monolayer case, 10 Ang. vacuum slabs are inserted between monolayers - structures are fully optimized in the calculation without SOC - monolayer case: GGA (XC: PBE) & # of k grids = 30 30 1 - bulk case: LDA (XC: PW) & # of k grids = 8 8 8 9
Band structure w/o SOC Y.S., T. Miyake, and Y. Motome, arxiv:1704.00318 PdPS3 eg orbitals crossing points! crystal field splitting by S6 octahedra Brillouin zone Γ K M t2g orbitals 10
Multiple Dirac cones Y.S., T. Miyake, and Y. Motome, arxiv:1704.00318 multi-species Dirac cones (2 at K, K, 6 on Γ-K, K ) 11
Multiple Dirac cones Y.S., T. Miyake, and Y. Motome, arxiv:1704.00318 multi-species Dirac cones (2 at K, K, 6 on Γ-K, K ) cf. graphene: only 2 at K, K 2017/10/24 @ NQS 2017 12
Origin of multiple Dirac cones constructed MLWFs Y.S., T. Miyake, and Y. Motome, arxiv:1704.00318 transfer integrals unit: mev 3rd neighbor hopping is the most dominant!! eg orbitals & p-orbital tails constraint from crystalline and orbital symmetry all d-p-d hoppings are almost prohibited some d-p-p-d hoppings are allowed!! 13
Origin of multiple Dirac cones constructed MLWFs Y.S., T. Miyake, and Y. Motome, arxiv:1704.00318 transfer integrals unit: mev 3rd neighbor hopping is the most dominant!! eg orbitals & p-orbital tails Γ K/2 K honeycomb-superstructure hopping paths & folded Dirac cones!! 14
Correlation & SOC effects: mean-field analysis constructing an effective model 1. multiorbital Hubbard model = hoppings within 5th neighbor sites + an effective SOC for eg orbitals + Coulomb interaction 2. applying Hartree-Fock approx. including 4-sublattice orders Y.S., T. Miyake, and Y. Motome, arxiv:1704.00318 ground-state phase diagram half filling: 2 electrons in eg orbitals (case of group 10 TMTs) 3/4 filling: 3 electrons in eg orbitals (ex. substituting Ag or Cd for Pd) trivial insulator non-trivial Chern insulator! 15
Correlation & SOC effects: QAH state Y.S., T. Miyake, and Y. Motome, arxiv:1704.00318 band structures & Berry curvature of ferromag. insulator (U=1.5) Chern insulator with C=4 at 3/4 filling Chern number Berry curvature of the HOMO band (C=6) sharp peaks locate at Dirac nodes high Chern number originates in multiple Dirac cones!! 16
Bulk case reported bulk structures of PdPS3 W. Klingen et al., Z. Anorg. Allg. Chem (1973) Y.S., T. Miyake, and Y. Motome, arxiv:1707.00921 monoclinic structure C2/m DFT band structures (PdPS3) kz = 0 kz = π quasi-2d metallic band structures remnant 8 Dirac nodes are hidden near the Fermi level! 17
Summary & Perspectives Summary monolayer bulk multiple-dirac semimetal QAH state with high Chern num. quasi-2d metal with remnant Dirac nodes Perspectives arxiv:1704.00318 arxiv:1707.00921 pursuing novel phenomena due to the multiple Dirac-node (valley) structure - electronic transport - phase transition by electron correlations application to other eg-orbital systems with the honeycomb structure 18