15th Annual Congress on Materials Research and TechnologyParis, France

19th February, 2018

Topological)heterostructures)of)layered)telluride)compounds

Yuta%Saito,%Kotaro%Makino,%Paul%Fons,%Alexander%V.%Kolobov,%and%Junji%Tominaga

National)Institute)of)Advanced)Industrial)Science)and)Technology)(AIST)yuta<saito@aist.go.jp

Department)of)Engineering,)University)of)Cambridgeys478@cam.ac.uk

Topological)insulator)(TI)New)matter)arisen)from)topological)insulating)nature

Topological Insulator Materials

Yoichi ANDO!

Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, Japan

(Received April 21, 2013; accepted July 22, 2013; published online September 3, 2013)

Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surfacestates that show up due to a topological character of the bulk wave functions. This review presents a pedagogicalaccount on topological insulator materials with an emphasis on basic theory and materials properties. After presentinga historical perspective and basic theories of topological insulators, it discusses all the topological insulator materialsdiscovered as of May 2013, with some illustrative descriptions of the developments in materials discoveries in whichthe author was involved. A summary is given for possible ways to confirm the topological nature in a candidatematerial. Various synthesis techniques as well as the defect chemistry that are important for realizing bulk-insulatingsamples are discussed. Characteristic properties of topological insulators are discussed with an emphasis on transportproperties. In particular, the Dirac fermion physics and the resulting peculiar quantum oscillation patterns are discussedin detail. It is emphasized that proper analyses of quantum oscillations make it possible to unambiguously identifysurface Dirac fermions through transport measurements. The prospects of topological insulator materials forelucidating novel quantum phenomena that await discovery conclude the review.

KEYWORDS: topological insulator, Dirac fermions, surface state, quantum oscillations

1. Introduction

The progress in condensed matter physics is often drivenby discoveries of novel materials. In this regard, materialspresenting unique quantum-mechanical properties are ofparticular importance. Topological insulators (TIs) are aclass of such materials and they are currently creating asurge of research activities.1–3) Because TIs concern aqualitatively new aspect of quantum mechanics, i.e., thetopology of the Hilbert space, they opened a new window forunderstanding the elaborate workings of nature.

TIs are called ‘‘topological’’ because the wave functionsdescribing their electronic states span a Hilbert space thathas a nontrivial topology. Remember, quantum-mechanicalwave functions are described by linear combinations oforthonormal vectors forming a basis set, and the abstractspace spanned by this orthonormal basis is called Hilbertspace. In crystalline solids, where the wave vector kbecomes a good quantum number, the wave function canbe viewed as a mapping from the k-space to a manifoldin the Hilbert space (or in its projection), and hence thetopology becomes relevant to electronic states in solids.Depending on the way the Hilbert-space topology becomesnontrivial, there can be various different kinds of TIs.4) Animportant consequence of a nontrivial topology associatedwith the wave functions of an insulator is that a gaplessinterface state necessarily shows up when the insulator isphysically terminated and faces an ordinary insulator(including the vacuum). This is because the nontrivialtopology is a discrete characteristic of gapped energy states,and as long as the energy gap remains open, the topologycannot change; hence, in order for the topology to changeacross the interface into a trivial one, the gap must close atthe interface. Therefore, three-dimensional (3D) TIs arealways associated with gapless surface states, and so aretwo-dimensional (2D) TIs with gapless edge states. Thisprinciple for the necessary occurrence of gapless interfacestates is called bulk-boundary correspondence in topologicalphases.

A large part of the unique quantum-mechanical propertiesof TIs come from the peculiar characteristics of the edge/surface states. Currently, the TI research is focused mostlyon time-reversal (TR) invariant systems, where the non-trivial topology is protected by time-reversal symmetry(TRS).1–3) In those systems, the edge/surface states presentDirac dispersions (Fig. 1), and hence the physics ofrelativistic Dirac fermions becomes relevant. Furthermore,spin degeneracy is lifted in the Dirac fermions residing in theedge/surface states of TR-invariant TIs and their spin islocked to the momentum (Fig. 1). Such a spin state is saidto have ‘‘helical spin polarization’’ and it provides anopportunity to realize Majorana fermions5) in the presenceof proximity-induced superconductivity,6) not to mentionits obvious implications for spintronics applications. An

E

ky

kx

Γ

Helical spinpolarization

2D Dirac cone

Surface Brillouin zone

k

Ene

rgy

k = 0

Bulk Conduction Band

Bulk Valence Band

up spindownspin Dirac point

(a)

(b)

(c)

(d)

Vacuum

up spin

down spin

2D Topological Insulator

Fig. 1. (Color online) Edge and surface states of topological insulatorswith Dirac dispersions. (a) Schematic real-space picture of the 1D helicaledge state of a 2D TI. (b) Energy dispersion of the spin non-degenerate edgestate of a 2D TI forming a 1D Dirac cone. (c) Schematic real-space pictureof the 2D helical surface state of a 3D TI. (d) Energy dispersion of the spinnon-degenerate surface state of a 3D TI forming a 2D Dirac cone; due to thehelical spin polarization, back scattering from k to "k is prohibited.

Journal of the Physical Society of Japan 82 (2013) 102001

102001-1

INVITED REVIEW PAPERS

#2013 The Physical Society of Japan

http://dx.doi.org/10.7566/JPSJ.82.102001Topological Insulator Materials

Yoichi ANDO!

Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, Japan

(Received April 21, 2013; accepted July 22, 2013; published online September 3, 2013)

Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surfacestates that show up due to a topological character of the bulk wave functions. This review presents a pedagogicalaccount on topological insulator materials with an emphasis on basic theory and materials properties. After presentinga historical perspective and basic theories of topological insulators, it discusses all the topological insulator materialsdiscovered as of May 2013, with some illustrative descriptions of the developments in materials discoveries in whichthe author was involved. A summary is given for possible ways to confirm the topological nature in a candidatematerial. Various synthesis techniques as well as the defect chemistry that are important for realizing bulk-insulatingsamples are discussed. Characteristic properties of topological insulators are discussed with an emphasis on transportproperties. In particular, the Dirac fermion physics and the resulting peculiar quantum oscillation patterns are discussedin detail. It is emphasized that proper analyses of quantum oscillations make it possible to unambiguously identifysurface Dirac fermions through transport measurements. The prospects of topological insulator materials forelucidating novel quantum phenomena that await discovery conclude the review.

KEYWORDS: topological insulator, Dirac fermions, surface state, quantum oscillations

1. Introduction

The progress in condensed matter physics is often drivenby discoveries of novel materials. In this regard, materialspresenting unique quantum-mechanical properties are ofparticular importance. Topological insulators (TIs) are aclass of such materials and they are currently creating asurge of research activities.1–3) Because TIs concern aqualitatively new aspect of quantum mechanics, i.e., thetopology of the Hilbert space, they opened a new window forunderstanding the elaborate workings of nature.

TIs are called ‘‘topological’’ because the wave functionsdescribing their electronic states span a Hilbert space thathas a nontrivial topology. Remember, quantum-mechanicalwave functions are described by linear combinations oforthonormal vectors forming a basis set, and the abstractspace spanned by this orthonormal basis is called Hilbertspace. In crystalline solids, where the wave vector kbecomes a good quantum number, the wave function canbe viewed as a mapping from the k-space to a manifoldin the Hilbert space (or in its projection), and hence thetopology becomes relevant to electronic states in solids.Depending on the way the Hilbert-space topology becomesnontrivial, there can be various different kinds of TIs.4) Animportant consequence of a nontrivial topology associatedwith the wave functions of an insulator is that a gaplessinterface state necessarily shows up when the insulator isphysically terminated and faces an ordinary insulator(including the vacuum). This is because the nontrivialtopology is a discrete characteristic of gapped energy states,and as long as the energy gap remains open, the topologycannot change; hence, in order for the topology to changeacross the interface into a trivial one, the gap must close atthe interface. Therefore, three-dimensional (3D) TIs arealways associated with gapless surface states, and so aretwo-dimensional (2D) TIs with gapless edge states. Thisprinciple for the necessary occurrence of gapless interfacestates is called bulk-boundary correspondence in topologicalphases.

A large part of the unique quantum-mechanical propertiesof TIs come from the peculiar characteristics of the edge/surface states. Currently, the TI research is focused mostlyon time-reversal (TR) invariant systems, where the non-trivial topology is protected by time-reversal symmetry(TRS).1–3) In those systems, the edge/surface states presentDirac dispersions (Fig. 1), and hence the physics ofrelativistic Dirac fermions becomes relevant. Furthermore,spin degeneracy is lifted in the Dirac fermions residing in theedge/surface states of TR-invariant TIs and their spin islocked to the momentum (Fig. 1). Such a spin state is saidto have ‘‘helical spin polarization’’ and it provides anopportunity to realize Majorana fermions5) in the presenceof proximity-induced superconductivity,6) not to mentionits obvious implications for spintronics applications. An

E

ky

kx

Γ

Helical spinpolarization

2D Dirac cone

Surface Brillouin zone

k

Ene

rgy

k = 0

Bulk Conduction Band

Bulk Valence Band

up spindownspin Dirac point

(a)

(b)

(c)

(d)

Vacuum

up spin

down spin

2D Topological Insulator

Fig. 1. (Color online) Edge and surface states of topological insulatorswith Dirac dispersions. (a) Schematic real-space picture of the 1D helicaledge state of a 2D TI. (b) Energy dispersion of the spin non-degenerate edgestate of a 2D TI forming a 1D Dirac cone. (c) Schematic real-space pictureof the 2D helical surface state of a 3D TI. (d) Energy dispersion of the spinnon-degenerate surface state of a 3D TI forming a 2D Dirac cone; due to thehelical spin polarization, back scattering from k to "k is prohibited.

Journal of the Physical Society of Japan 82 (2013) 102001

102001-1

INVITED REVIEW PAPERS

#2013 The Physical Society of Japan

http://dx.doi.org/10.7566/JPSJ.82.102001

Topological)insulator)materials

Y. Ando, J. Phys. Soc. Jpn. 82 (2013) 102001

CdTe/HgTe/CdTe (2D),)Bi1<xSbx,)Bi2Se3,)Bi2Te3,)Sb2Te3,)Ge1Bi4<xSbxTe7,)Bi2Te2Se,)TlBiSe2,)SnTe etc.

Topological)insulator

Strong)spin<orbit)coupling

Band)inversion)in)bulk

The)band)must)cross)at)the)interface)resulting)in)the)formation)of)Dirac)cone.

InterfaceFeatures

�Dirac)cone)at)the)surface�Helical)spin states

Applications�THz)detector

�Non<dissipative)device�Spintronics

Vacuum

Transition)metal)dichalcogenide)(TMD)MoS2,)MoSe2,)MoTe2,)WS2,)WSe2,)WTe2,…)(MX2)

A. KUC, N. ZIBOUCHE, AND T. HEINE PHYSICAL REVIEW B 83, 245213 (2011)

TABLE I. Calculated and experimental lattice parameters ofhexagonal transition-metal dichalcogenides in the form of T X2 (T =Mo, W, Nb, Re; X = S, Se). Results obtained at the DFT/PBE level.In parentheses, data obtained at the DFT/PBE0 level are given.

TheoryExpt.

(Refs. 1, 2, 6)

Structure a c a c

MoS2 3.173 (3.143) 12.696 (12.583) 3.160 12.295WS2 3.164 (3.139) 12.473 (12.380) 3.154 12.362NbS2 3.332 (3.313) 12.106 (12.074) 3.310 11.890ReS2 3.300 (3.275) 12.724 (12.148) ... ...

hybrid (PBE0) functionals.27 The following Gaussian basissets were used: Mo SC HAYWSC-311(d31)G cora 1997 (forMo atoms), W cora 1996 (for W atoms), Nb SC HAYWSC-31(d31)G dallolio 1996 (for Nb atoms), Re cora 1991 (forRe atoms), and S 86-311G* lichanot 1993 (for S atoms). Thechalcogenide atoms were calculated using full-electron basissets, while for the heavy elements, the effective core potential(ECP) approach was employed. The large-core ECP has beenchosen, what leaves only the valence electrons to be explicitlydescribed on the metal sites: 4d and 5sp for Mo and Nb, 5dand 6sp for W and Re.

In CRYSTAL09 code, the 3D and 2D structures are treatedas crystal and slab structures, respectively, therefore, in thecase of layers there is no need to introduce vacuum.

Optimization of initial experimental structures was per-formed using analytical energy gradients with respect toatomic coordinates and unit cell parameters within a quasi-Newton scheme combined with the BFGS (Broyden-Fletcher-Goldfarb-Shanno) scheme for Hessian updation. The opti-mized lattice parameters for all the studied materials are givenin Table I.

The shrinking factor (commensurate grid of k-points inreciprocal space at which the KS matrix is diagonalized)for bulk and layered structures was set to 8, what resultsin the corresponding number of 50 and 30 k-points in theirreducible Brillouin zone, respectively. The mesh of k-pointswas obtained according to the scheme proposed by Monkhorstand Pack.28 Band structures were calculated along the highsymmetry points using the path !–M–K–!.

III. RESULTS AND DISCUSSION

We have studied electronic properties of T S2 layered struc-tures with respect to the slab thickness of the systems. Bulkstructures as well as mono- and polylayers were considered.DFT is widely used in the field of solid-state physics and itgives excellent structural parameters (see Table I) and chargedistribution; however, typically it does not represent the elec-tronic structure correctly. Therefore, we have introduced twodifferent exchange-correlation functionals (PBE and PBE0) toaddress this problem specifically.

Figures 2 and 3 show band structures of MoS2 and WS2,respectively, calculated using PBE functional and going frombulk to a monolayer. (For band structures results using PBE0functional see supplemental material).29

-0.2

0

0.2

EF

[Har

tree

]

MoS2 bulk MoS2 8-layer

-0.2

0

0.2

MoS2 6-layer

Γ M K Γ

-0.2

0

0.2

MoS2 quadrilayer

Γ M K Γ

MoS2 bilayer

Γ M K Γ

-0.2

0

0.2

MoS2 monolayer

= 1.2 eV∆

∆= 1.9 eV

FIG. 2. (Color online) Band structures of bulk MoS2, its mono-layer, as well as, polylayers calculated at the DFT/PBE level. Thehorizontal dashed lines indicate the Fermi level. The arrows indicatethe fundamental band gap (direct or indirect) for a given system. Thetop of valence band (blue/dark gray) and bottom of conduction band(green/light gray) are highlighted.

The results show that bulk MoS2 and WS2 are indirect-gapsemiconductors. The fundamental band gap originates fromtransition from the top of valence band situated at ! to thebottom of conduction band halfway between ! and K highsymmetry points. The optical direct band gap is situated at Kpoint. As the number of layers decreases, the fundamentalindirect band gap increases and becomes so high in themonolayer that the material changes into a 2D direct bandgap semiconductor. At the same time, the optical direct gap (atthe K point) stays almost unchanged (independent of the slabthickness) and close to the value of the optical direct band gap

-0.2

0

0.2

EF

[Har

tree

]

WS2 bulk WS2 6-layer

Γ M K Γ

-0.2

0

0.2

WS2 quadrilayer

Γ M K Γ

-0.2

0

0.2

WS2 bilayer

Γ M K Γ

-0.2

0

0.2

WS2 monolayer

= 1.3 eV∆

∆= 2.1 eV

FIG. 3. (Color online) Band structures of bulk WS2, its mono-layer, as well as, polylayers calculated at the DFT/PBE level. Thehorizontal dashed lines indicate the Fermi level. The arrows indicatethe fundamental band gap (direct or indirect) for a given system. Thetop of valence band (blue/dark gray) and bottom of conduction band(green/light gray) are highlighted.

245213-2

(from a negligible value) by about 3 orders of magnitude.This dramatic rise corresponds to the onset of opticalabsorption from the direct band edge [28].

In the following simplified treatment of the spectraldependence of the photoconductivity, we neglect both ex-citonic effects and the variation of matrix elements withenergy, factors that should be included in a more compre-hensive theory. The absorbance Að@!Þ at photon energy@! near a direct band edge of energy Eg is then determined

by the joint density of states. For a two-dimensional (2D)material like our atomically thin layers of MoS2, this isdescribed by a step function, !ð@!# EgÞ [1,29]. Afterincluding a phenomenological broadening of 30 meV toaccount for finite temperature and scattering rates, we findthat the photoconductivity spectrum of the monolayersamples can be fit well to this simple model [Fig. 4(b)].This indicates that monolayer MoS2 is indeed a direct-gapmaterial [28]. On the other hand, the photoconductivityspectrum for bilayer MoS2 cannot be described by the

step-function response. We need to include the effect ofan indirect transition. Near an indirect band edge, thecorresponding absorbance can be represented by [1,29]

Að@!Þ / P!½

@!#@"!#E0g

1#expð#@"!=kTÞ þ@!þ@"!#E0

g

expð@"!=kTÞ#1& / @!# E0g.

Here E0g and @"! denote, respectively, the indirect-gap

energy and that of the !th phonon mode, and kT is thethermal energy. By taking this term into account, theexperimental bilayer MoS2 spectrum can be fit well byan indirect transition at 1.6 eV, combined with a directtransition at 1.88 eV [Fig. 4(b)].The indirect-direct-gap crossover as a function of MoS2

thickness N is the result of a significant upshift of E0g

induced by perpendicular quantum confinement. To under-stand this, let us examine the electronic band structure ofbulk MoS2 (Fig. 1). The direct gap of '1:8 eV occursbetween c1 and v1 at the K point of the Brillouin zone(transitions A) [3–5,7,12]. On the other hand, the maximumof v1 and minimum of c1 are located at the # point and

1.4 1.6 1.8 2.0 2.2

0

1

2

3

4

5

6

7

6lay

5lay

4lay

2lay

3lay

I BX 10

X 10

Nor

mal

ized

PL

Photon Energy (eV)Photon Energy (eV)

X 3

A

1lay

1lay 2lay

(b)

1 2 3 4 5 61.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

Lowest EnergyPL Peak

Pea

kE

nerg

ies

(eV

)

Layer Number

Bulk Band gap

(c)(a)

FIG. 3 (color online). (a) PL spectra for mono- and bilayer MoS2 samples in the photon energy range from 1.3 to 2.2 eV. Inset: PLQYof thin layers for N ¼ 1–6. (b) Normalized PL spectra by the intensity of peak A of thin layers ofMoS2 for N ¼ 1–6. Feature I forN ¼ 4–6 is magnified and the spectra are displaced for clarity. (c) Band-gap energy of thin layers ofMoS2, inferred from the energy ofthe PL feature I for N ¼ 2–6 and from the energy of the PL peak A for N ¼ 1. The dashed line represents the (indirect) band-gapenergy of bulk MoS2.

FIG. 4 (color online). (a) Absorption spectra (left axis, normalized by N) and the corresponding PL spectra (right axis, normalized bythe intensity of the peak A). The spectra are displaced along the vertical axis for clarity. (b) Photoconductivity spectra for mono- (reddots) and bilayer (green dots) samples [27]. The data are compared with the 2D model described in the text (blue lines). Eg and E0

g

inferred from the PL measurements, indicated by arrows, are included for comparison.

PRL 105, 136805 (2010) P HY S I CA L R EV I EW LE T T E R Sweek ending

24 SEPTEMBER 2010

136805-3

K. F. Mak et. al., Phys. Rev. Lett. 105, 136805 (2010)

A. Kuc et. al., Phys. Rev. B, 83, 245213 (2011)

PCM

SiO2

TE):Top)electrode

BEor

heater

PCM2(Phase2Change2Material)ChalcogenidesGe<Sb<Te)alloy)(GeTe<Sb2Te3)

H.-S. P. Wong et al., Proceedings of IEEE, 98, 2201 (2010)G. W. Burr et al., IEEE J. Emerg. Selected Topics in Circuit and Systems, 6, 146 (2016)

Phase)change)memory

Tech)Insights,)Flash)Memory)Summit)2017Intel)and)Micron

Chalcogenide)superlattices)for)phase)change)memory

A. V. Kolobov et al., Nat. Mater. 3, 703 (2004)J. Tominaga et al., Jap. J. Appl. Phys. 47, 5463 (2008)R. E. Simpson et al., Nat. Nanotech. 6, 501 (2011)

GeTe/Sb2Te3 superlattice

Reset(High)R)

Set(Low)R)

Sb2Te3 (TI)

Sb2Te3 (TI)

GeTe)(NI)

NI/TI2stackingTI):)Topological)insulatorNI):)Normal)insulator

Unusual)electronic)properties)are)expected.

Motivation• Exploration)of)electronic)structures)of)chalcogenide)heterostructures.

MoTe2/Sb2Te3 (TMDC/TI)GeTe/Sb2Te3 (NI/TI,)phase)change)memory)

Methods• Density)functional)theory)code:)  

• Functional:)GGA<PBE)or)mBJ<LDA    • Spin)orbit)coupling)(soc)• Geometry)relaxation:)DFT<D3)(Grimme)      

  K. Schwarz and P. Blaha. Comp. Mater. Sci. 28, 259 (2003).     F. Tran and P. Blaha. Phys. Rev. Lett. 102, 226401 (2009).       S. Grimme. J. Comput. Chem. 25, 1463 (2004).

Band)structure)of)Sb2Te3

Bulk)Sb2Te3

SbTe

Space)group):)166)(R<3m)a =)4.262)Å,)c =)30.435)Å

W.-S. Kim, J. Alloys and Comp., 252, 166 (1997)

without)soc

with)soc

Van)der)Waals)gap

M Γ K

Typical)topological)insulator

Sb2Te3<6QL<vacuum)(20Å)(QL:)Quintuple)layer)

Vacuum(20)Å)

H. Zhang et al., Nat. Phys., 5, 438 (2009)

J. Zhang et al., Nat. Comm., 2, 574 (2011)

Band)structure)including)vacuum)slab

SbTe

without)soc

with)soc

Dirac)cone)at)the)Γ point

Band)structures)of)MoTe2YSMoTe2-1 atom 0 size 0.20

Γ M K Γ

E F

Ener

gy (e

V)

0.0

1.0

2.0

-1.0

-2.0 YSMoTe2-1_va atom 0 size 0.20

Γ M K Γ

E F

Ener

gy (e

V)

0.0

1.0

2.0

-1.0

-2.0

MoTe

MoTe

Van)der)Waals)gap

Bulk

Monolayer

Indirect)transition

Direct)transition

Transition)at)the)K)point

MoTe2/Sb2Te3 heterostructureYSSLMoTe2-Sb atom 0 size 0.20

Γ M K Γ

E F

Ener

gy (e

V)

0.0

1.0

2.0

-1.0

-2.0

Sb2Te3

MoTe2

Van)der)Waals)gap

Ener

gy /

eV

Dirac)cone)at)the)Γ point

Direct)transition)at)the)K)point

GeTe/Sb2Te3 heterostructure

GeTe

(GeTe)2/(Sb2Te3)1 superlattice

without)soc with)soc

Y. Saito et al., ACS Appl. Mater. Interfaces, 9, 23918 (2017)

GeTe):)Normal)insulator,)Sb2Te3 :)topological)insulator

Sb2Te3

<1.0)GPa <0.7)GPa <0.45)GPa <0.38)GPa <0.3)GPa 0)GPa 1)GPa 3)GPa

Band)gap)tuning

Y. Saito et al., ACS Appl. Mater. Interfaces, 9, 23918 (2017)

Tensile Stress Compressive

Fabrication)of)superlattice)filmsSputter)grown)GeTe/Sb2Te3 superlattice)film

Cross<sectional)TEM)image

XRD)(out<of<plane,)in<plane)

006

009 0015

0018

Si

110

Superlattice)film

Si

Grain)size:)200<300)nm

Applications

THz detector

K. Makino et al., ACS Appl. Mater. Interfaces, 8, 32408 (2016)

R. E. Simpson et al., Nat. Nanotech. 6, 501 (2011)

Phase2change2memorySwitching2device

Y. Saito et al., ACS Appl. Mater. Interfaces, 9, 23918 (2017)

Glassa<Si

Summary

• MoTe2/Sb2Te3 heterostructure)possesses)both)features)of)transition)metal)dichalcogenide)and)topological)insulator.)However,)a)large)difference)of)band)alignment)makes)difficult)to)harness)their)properties.

• GeTe/Sb2Te3 heterostructure)is)promising)not)only)for)phase)change)memory)but)also)for)novel)electronic)devices)that)exploit)topological)insulator)properties.

Thank'you'for'your'attention!

AcknowledgementThis)work)was)supported)by)CREST,)JST)(No.)JPMJCR14F1))and)by)JSPS)KAKENHI)Grant)Nos.)26886015)and)16K04896,)Japan.