Γ K M Multiple Dirac cones and spontaneous QAH state in transition metal trichalcogenides Yusuke Sugita ✓ collaborators Takashi Miyake ( AIST ) Yukitoshi Motome ( U.Tokyo ) 1 2017/10/24 @ NQS 2017
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), MBX 3 - 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 - e ff ects of correlations & SOC: a QAH state with a high Chern number - e ff ects of layer stacking: bulk case Summary & Perspectives 2 2017/10/24 @ NQS 2017
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 e ff ect & Klein tunneling 3 2017/10/24 @ NQS 2017
Post-graphene larger spin-orbit coupling: ✓ candidates of QSH insulators : ✓ spin-valley physics : honeycomb sheets of Si, Ge, Sn,… 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 2017/10/24 @ NQS 2017
Discovery of purely-2D ferromagnets magneto-optic Kerr measurements transition metal trichalcogenides CrGeTe 3 transition metal trihalides CrI 3 C. Gong et al ., Nature (2017) B. Huang et al ., Nature (2017) 5 2017/10/24 @ NQS 2017
Transition metal trichalcogenides (TMTs) MBX 3 ( M =transition metal; B =P , Si, Ge; X =S, Se, Te) honeycomb network of edge-sharing MX 6 octahedra 3-R structure C2/m structure Top view of monolayer MnPS 3 , FePS 3 , NiPS 3 ,etc. B 2 dimer MnPSe 3 , FePSe 3 , CrSiTe 3 , CrGeTe 3 , etc. 6 2017/10/24 @ NQS 2017
Diversity of magnetism in 3 d TMTs FePS 3 NiPS 3 MnPS 3 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.) di ff erence of magnetic anisotropy wide range of band gaps K.-z. Du et al ., ACS Nano (2016) 7 2017/10/24 @ NQS 2017
Motivation Magnetic 3 d TMTs will play an important role in the post-graphene era. 4 d & 5 d TMTs have been less studied theoretically though the synthesis was reported. W. Klingen et al ., Z. Anorg. Allg. Chem. (1973) What happens in 4 d & 5 d transition metal trichalcogenides where the SOC and electron correlations compete? ab initio study of 4 d & 5 d 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 2017/10/24 @ NQS 2017
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 M P X 3 ( M = Ni, Pd , Zn, Cd, Hg) have been synthesized W. Klingen et al ., Z. Anorg. Allg. Chem. (1973) we systematically study group 10 M P X 3 ( 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 2017/10/24 @ NQS 2017
Band structure w/o SOC Y.S., T. Miyake, and Y. Motome, arXiv:1704.00318 PdPS 3 e g orbitals crossing points! crystal field splitting by S 6 octahedra Brillouin zone K t 2g orbitals Γ M 10 2017/10/24 @ NQS 2017
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 2017/10/24 @ NQS 2017
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’ 12 2017/10/24 @ NQS 2017
Origin of multiple Dirac cones Y.S., T. Miyake, and Y. Motome, arXiv:1704.00318 constructed MLWFs transfer integrals unit: meV 3rd neighbor hopping is the most dominant !! e g 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 2017/10/24 @ NQS 2017
Origin of multiple Dirac cones Y.S., T. Miyake, and Y. Motome, arXiv:1704.00318 constructed MLWFs transfer integrals unit: meV 3rd neighbor hopping is the most dominant !! e g orbitals & p -orbital tails Γ K/2 K honeycomb-superstructure hopping paths & “folded” Dirac cones !! 14 2017/10/24 @ NQS 2017
Correlation & SOC effects: mean-field analysis Y.S., T. Miyake, and Y. Motome, arXiv:1704.00318 constructing an e ff ective model 1. multiorbital Hubbard model = （ hoppings within 5th neighbor sites ） + （ an e ff ective SOC for e g orbitals ） + （ Coulomb interaction ） 2. applying Hartree-Fock approx. including 4-sublattice orders ground-state phase diagram half filling: 2 electrons in e g orbitals 3/4 filling: 3 electrons in e g orbitals (case of group 10 TMTs ) (ex. substituting Ag or Cd for Pd) trivial insulator… non-trivial Chern insulator! 15 2017/10/24 @ NQS 2017
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 Berry curvature of the HOMO band ( C =6) C =4 at 3/4 filling Chern number sharp peaks locate at Dirac nodes high Chern number originates in multiple Dirac cones!! 16 2017/10/24 @ NQS 2017
Bulk case Y.S., T. Miyake, and Y. Motome, arXiv:1707.00921 reported bulk structures of PdPS 3 W. Klingen et al ., Z. Anorg. Allg. Chem (1973) monoclinic structure C2/m DFT band structures (PdPS 3 ) k z = 0 k z = π quasi-2D metallic band structures remnant 8 Dirac nodes are hidden near the Fermi level ! 17 2017/10/24 @ NQS 2017
Summary & Perspectives Summary monolayer bulk multiple-Dirac QAH state with quasi-2D metal with semimetal high Chern num. remnant Dirac nodes arXiv:1704.00318 arXiv:1707.00921 Perspectives pursuing novel phenomena due to the multiple Dirac-node (valley) structure - electronic transport - phase transition by electron correlations application to other e g -orbital systems with the honeycomb structure 18 2017/10/24 @ NQS 2017
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