Multiple Dirac cones and spontaneous QAH state in ...nqs2017.ws/Slides/1st/Sugita.pdfMultiple Dirac...

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@ NQS 2017 2017/10/24 K M Γ 1 collaborators Takashi Miyake (AIST) Yukitoshi Motome (U.Tokyo) Yusuke Sugita Multiple Dirac cones and spontaneous QAH state in transition metal trichalcogenides

Transcript of Multiple Dirac cones and spontaneous QAH state in ...nqs2017.ws/Slides/1st/Sugita.pdfMultiple Dirac...

Page 1: Multiple Dirac cones and spontaneous QAH state in ...nqs2017.ws/Slides/1st/Sugita.pdfMultiple Dirac cones and spontaneous QAH state in transition metal trichalcogenides 2017/10/24

@ 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

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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

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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/

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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)

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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

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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.

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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

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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

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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) !!

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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

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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

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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’

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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

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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 !!

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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!

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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!!

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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)

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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