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Transcript of Multiple Dirac cones and spontaneous QAH state in ...nqs2017.ws/Slides/1st/Sugita.pdfMultiple Dirac...
@ NQS 20172017/10/24
KM
Γ
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✓collaborators Takashi Miyake (AIST)
Yukitoshi Motome (U.Tokyo)
Yusuke Sugita
Multiple Dirac cones and spontaneous QAH state in transition metal trichalcogenides
2017/10/24 @ NQS 2017
Outline
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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 - 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
Y.S., T. Miyake, and Y. Motome, arXiv:1704.00318 & 1707.00921
2017/10/24 @ NQS 2017
Graphene
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✓purely-2D honeycomb layer ✓Dirac semimetal
almost ideal Dirac cones: weak electron correlations and weak SOC
anomalous transport, e.g., anomalous QH effect & Klein tunneling
https://www.nobelprize.org/nobel_prizes/physics/laureates/2010/
2017/10/24 @ NQS 2017
Post-graphene
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larger spin-orbit coupling:
larger electron correlations: candidates of purely-2D magnets?
✓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)
transition metal trichalcogenides transition metal trihalides
N. Sivadas et al., PRB (2015) J. Kohler, Ency. of Inorg. and Bio. Chem. (2014)
2017/10/24 @ NQS 2017
Discovery of purely-2D ferromagnets
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transition metal trichalcogenides CrGeTe3
C. Gong et al., Nature (2017)
transition metal trihalides CrI3
B. Huang et al., Nature (2017)
magneto-optic Kerr measurements
2017/10/24 @ NQS 2017
Transition metal trichalcogenides (TMTs)
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MBX3 (M=transition metal; B=P, Si, Ge; X=S, Se, Te)honeycomb network of edge-sharing MX6 octahedra
3-R structure
C2/m structureTop view of monolayer
B2 dimerMnPS3, FePS3, NiPS3,etc.
MnPSe3, FePSe3, CrSiTe3, CrGeTe3, etc.
2017/10/24 @ NQS 2017
Diversity of magnetism in 3d TMTs
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FePS3MnPS3
E. Ressouche et al., PRB (2010) D. Lancon et al., PRB (2016)
NiPS3
A. R. Wildes et al., PRB (2012)
K.-z. Du et al., ACS Nano (2016)
various magnetic ordering (Neel AFM, zigzag AFM, FM, etc.)
wide range ofband gaps
difference ofmagnetic anisotropy
2017/10/24 @ NQS 2017
Motivation
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What happens in 4d & 5d transition metal trichalcogenides where the SOC and electron correlations compete?
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.
ab initio study of 4d & 5d TMTs!
W. Klingen et al., Z. Anorg. Allg. Chem. (1973)
Our DFT predictionsmultiple Dirac cones appear in a family of TMTsinterplay between electron correlations and SOC may turn
the multiple-Dirac semimetal into a QAH state with a high Chern numberinteresting behaviors of Dirac cones depending on the layer stacking
2017/10/24 @ NQS 2017
Setup
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ab initio setup - using OpenMX code - 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
Target materials - group 10 & 12 transition metals can take a divalent oxidation state
- bulk MPX3 (M=Ni, Pd, Zn, Cd, Hg) have been synthesizedW. Klingen et al., Z. Anorg. Allg. Chem. (1973)
N. N. Greenwood and A. Earnshaw, Chemistry of the Elements (1997)
T. Ozaki et al., http://www.openmx-square.org
we systematically study group 10 MPX3 (M=Ni, Pd, Pt & X=S, Se) !!
2017/10/24 @ NQS 2017
Band structure w/o SOC
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crossing points!
Γ M
K
crystal field splitting by S6 octahedra
Brillouin zone
eg orbitals
t2g orbitals
PdPS3
Y.S., T. Miyake, and Y. Motome, arXiv:1704.00318
2017/10/24 @ NQS 2017
Multiple Dirac cones
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multi-species Dirac cones (2 at K, K’, 6 on Γ-K, K’)
Y.S., T. Miyake, and Y. Motome, arXiv:1704.00318
2017/10/24 @ NQS 2017
Multiple Dirac cones
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multi-species Dirac cones (2 at K, K’, 6 on Γ-K, K’)
Y.S., T. Miyake, and Y. Motome, arXiv:1704.00318
cf. graphene: only 2 at K, K’
2017/10/24 @ NQS 2017
Origin of multiple Dirac cones
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transfer integrals
constraint from crystalline and orbital symmetry
all d-p-d hoppings are almost prohibited… some d-p-p-d hoppings are allowed!!
3rd neighbor hopping is the most dominant !!
constructed MLWFsY.S., T. Miyake, and Y. Motome, arXiv:1704.00318
eg orbitals & p-orbital tails
unit: meV
2017/10/24 @ NQS 2017
Origin of multiple Dirac cones
14honeycomb-superstructure hopping paths & “folded” Dirac cones !!
Γ KK/2
Y.S., T. Miyake, and Y. Motome, arXiv:1704.00318
transfer integralsconstructed MLWFs
eg orbitals & p-orbital tails
unit: meV
3rd neighbor hopping is the most dominant !!
2017/10/24 @ NQS 2017
Correlation & SOC effects: mean-field analysis
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Y.S., T. Miyake, and Y. Motome, arXiv:1704.00318
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
constructing an effective model
ground-state phase diagramhalf 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!
2017/10/24 @ NQS 2017
Correlation & SOC effects: QAH state
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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
Berry curvature ofthe HOMO band (C=6)Chern
number
sharp peaks locate at Dirac nodes
high Chern number originates in multiple Dirac cones!!
2017/10/24 @ NQS 2017
Bulk case
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DFT band structures (PdPS3)kz = 0 kz = π
quasi-2D metallic band structuresremnant 8 Dirac nodes are hidden near the Fermi level !
Y.S., T. Miyake, and Y. Motome, arXiv:1707.00921reported bulk structures of PdPS3
monoclinic structureC2/m
W. Klingen et al., Z. Anorg. Allg. Chem (1973)
2017/10/24 @ NQS 2017
Summary & Perspectives
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Summary
Perspectives
monolayer
multiple-Dirac semimetal
QAH state withhigh Chern num.
quasi-2D metal withremnant Dirac nodes
bulk
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
arXiv:1704.00318 arXiv:1707.00921