Photoemission Study of Low-Dimensional Systems:...
60
Photoemission Study of Low-Dimensional Systems: V02 and TIGaTe2 Master Thesis Kozo Okazaki Department of Physics, University of Tokyo January, 2000
Transcript of Photoemission Study of Low-Dimensional Systems:...
Photoemission Study of
Low-Dimensional Systems:
V02 and TIGaTe2
Master Thesis
Kozo Okazaki
Department of Physics, University of Tokyo
January, 2000
Contents
1 Introduction 1
2 Photoemission Spectroscopy 5
2.1 Simple Description of Photoemission Spectrum. . . . . . . . . . . . .. 5
2.2 Generalized Formulation of Photoemission Spectrum .. . . . . . . .. 6
2.3 Measurement System . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9
3 Photoemission Study of the Metal-Insulator '1凶nsitionin V02 13
3.1 Introduction................................. 13
3.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18
3.2.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . .. 18
3.2.2 Photoemission measurements
3.3 Results and discussion
3.3.1 Metal-Insulator transition
3.3.2 Temperature dependence in the insulating phase .
nδnδnδa位向
4
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i
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i
n
4
q
d3.4 Conclusion.
4 Photoemission Study of TIGaTe2
4.1 Introduction.
4.2 Experiment
4.3 Results and discussion
4.3.1 Angel-integrated photoemission spectra .
4.3.2 Angel-resolved photoemission spectra . .
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q
d
q
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q
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4.3.3 Band-structure calculation . . . . . . . . . . . . . . . . . . . .. 45
4.3.4 Comparison between UPS spectra and band-structure calculation. 50
4.4 Conclusion.................................. 55
5 Conclusion 59
11
Chapter 1
Introduction
Low-dimensional systems han~ attractcd much intcrcst bぞ('<lllseof their unique physicλi
properties. 1n systems ¥v here elec:trOlトlatticeinteraction is dominantう itis theoretica11y
predicted that one-dimensional systems have a Peierls instability or a Kohn allomaly
and caωe Peierls transi tion [1.1]，叶uleill systellls ¥巾ereelec:tron-electron illterac-
tion is dominant or in so-ca11ed one-dirne'l川 onα11VI ott-Hubbαrd 8y8tern8， it is preclicted
that spin CI川 駅 sepαnLtωn will t北 eplace [l.2]. In tけi附 e10¥¥、刊jin附1肘 nslO凶1syst山e引叩川?汀汎I口III
photoemission spectroscopyう espcciallyう angle-resolvedphotoclllission spectroscopy is a
power-full tool for investiιating the electronic propenies of these systems. vVe hm.e
investigated the fo11O¥γillg two systems ¥yhich han~ olH'-climcnsional c・rystalstructll r< ~s.
孔VO'2un白 rgoes a III陀削eta叫lト-寸引叩II山II削 lato叫rtra剖illsitioll札t 3-10 l¥: [l.3司].1t h凶ω正a泊お a r川 ile st口か山川liれ印u山
i山nthe metallic ph川t礼lseabove :3-10 K心.wh('迅刊守引reヲ¥"OG octah 引 II・a al'e rUllning along the c-axis
with their eclge山il'cdwhil(、礼lc叫 tlぽ [110]山川tion¥¥"ith comer sharecl. TI附 this
structure can be regarclcd as討 礼川n1山II五llit(れ、 olle-di山lllC白、T立1ヨllsiollal('け.haIl山ualoug the c-axiおsき3. The
n附 t同ωaι1-i附
because of the structural instabilitv of the one-clilllCllsional crvstal structure aucl be-
cause this transition is accolllj)孔uicdbyλstructllral tl孔u討itiouallcl dilllerizatioll of V
atoms. On the other 11<孔川u凶う .¥Ioωtt [1.5う 6司lω l日lic何e[1.7う 8針]p川tυ}山 t印Cα吋dout tけh日e山山III叩i
of cl< 、ctれroncor口re叶latioll(い什Bイi任fect.This problclll rernaius rather coutroversial still no¥¥". ¥¥"e
have iuvestigated this trausitioIl by lllcallS of photocmissiou spectroscopy.
TlGaT，匂 hasthe TlSe-type (837) structure alld co凶 istsof Tll+ and Ga Te41 0ω)川11凶c-
din附I削 i路山sio凶 1ch凶凶凶lalll附IS[1.9ヲ 10]. From th山iト行; st山 :tureう 羽we1
electrical properties and investigated its dimellsionality by mca川UlSof angle-resolved
photoernission spectroscopy. To interpret the resultう wehave performecl full-potential
lirw(tl・<ill父lllP11t(刊l-plal1('-¥¥，¥¥"(， (FPーし¥P¥¥")1)，¥Jld-日tructure ('(¥!clll川 1011パlId('Ot1lj川 l刊 l
bot h n市111ts.
Thiメ th(明isis orgλIII川河1as fo!l()¥¥"s. In (‘hapter :2， ¥¥・('1・p，，('¥¥・ th(、pri!l("ipl('sof phot 0-
Prtll出 1011SPC(・troscop'". Th(' photoellli出 iOllstllCh" ()f t h(、ntetal-i11日1I1ator tnmsitioll i11
¥"0白"2 1討 pr('日(，l1t('<Iin Cltaptcl・:3.TII<もけ11只l(、一1111<'gratυda11d a11只l(、1・(情。h"(、dplJOto('llIi出 1011
stlldi(、日孔11<1t h(当 b乱nd叶r1l<寸111・(' ("，dcl1latio!l ()f T1CaT円パ1"(' pl・('S('llt (刊 inChaptel・-1.
(刈haptero is de¥"otec! t () (・otlClllsiO!l
フ
References
[1.1] P. Peierlsう QωntumThc川
[1.2] E. H. Lieb alld F. Y. W仏 Pl肝 Rcy.Lett. 20， 1-1-15 (1968)
[1.:3] J. ~Iorin ぅ Phy臼. Rey. Lett. 3， 3-1 (1959)
[lA] ~く. Tsu肌吋lC吋da丸う K. ~a泊釧S剖u う A. Fu吋IリJllll山llOω)凡1"1，うa削I吋 K. Sir、Y司川atoriう Elec仇ゴ
(Shokaboう Tokyo，1993)
[1.5] N. F. Mott， Metal-In8ulαtor Tn川 ition
[1.6] A. Zylebersztejll and ~. F. ~Iott ， Phys. Rey. B 11， 4383 (1975).
[1.7] J.P.POl伊tぅ H.Lal山 Jis，T. ~I. Rice， P. Dernicr， A. Gωardう G.Villellcuve， and
P. Hagenmullerぅ Phys.Rcy B 10ぅ 1801(1974)
[1.8] T. ;¥1. Riceぅ H.Launωぅ alld
[1.9判]E. 孔MoωOωsera 凶 \\~\. B. PC側削t孔川u附 l凡1，う .J. El('代川、刊ctroωI山l
[l.10] A. Kashida， unpublishecl
3
Chapter 2
Photoemission Spectroscopy
1n this chapterぅ ¥vewill desc山 ethe principles of phOtOClllis
2.1 Simple Description of Photoemission Spectrum
1n this sectionヲwewill describe the principles of the photoemission spectroscopy in thc
simplest reprcsentation.
'vVhen an electron in the solid absorbs a photon of energy hνう itis emitted as a pho-
toelectron. From the energy cOllservatiun， the kinetic cnergy Ekin of the photoelectron
1S wntten as
Ekin = luノ-rt-EBぅ (2.1 )
¥¥" here Ekirt is III犯e閃aωS引印ur削 1f仕.旨rOlllthe γ刊礼C引叩U川1
S柿加a削m叫npleぞeう<l.剖t汀I吋 Eβisthc b山 li略目以下rgy. 1n realほ perilllclltsthe killctie ellergy (Ekin)
measurecl from the Fcrmi le¥"cl (E F) is clirectly observed rather than Ek川・ Tl日 ll.
Ekin二 luノ - EI3' (2.2)
1n thc one-electron approximation， the binding energy is円lualto the 1H、gative
Hartree-Foek orbital energyう
ElJ二九・ (2.3)
This relatioll is callcd K oopman8' theoTem [2 A‘5]. This assumption is valicl wlwn the
W品 'efUllctions of both the initial ancl final states can be cxpressed by singlc Slater
cletermi
F d
れl河川
!(ん)x 2二バ(1二11十(1..):::x: ~V( ← EI3 ) (2. -1 )
T!l1l討. ¥yh(，ll the りII('-(' leけrOll(¥ pprox illlil t iOll is valid， t he photo(，lIli出 1011叶)('(・tl・11mIS
ProI川 rtio/lλ[t () t [1(' d(，llSi t ¥. ()f s1川円.¥"( f:')( Fi只:2.1.)
E I 5ample
E" 1 (ore Level B
EF
NIE I
Ekin Spectrum
Valence B口nd
下山
N(E)
hω
l均1¥刊 2.1:SCI!('1川 1icpict1¥1¥‘ ()f 1 I!(、 pl!()to('llli同 ]0/1討l川 trosco]lv[2.1].
2.2 Generalized Formulation of Photoemission Spec-
trum
1n thiト sectiollぅ 日・れ ¥¥・iII forlllula t (主 t 11(、 p!JotoPlIlis討iOIlspectrum in the g('!l('l孔liχ(吋 dc-
町 1・iption b('¥'OlH! tl!e one-p]('c(roll applけXllll孔1io 11.
1ll the dipole approxilllatioll.け1(、 transitiOllprobability仁川1be Wl廿tellaメ follO¥¥"s，
1141<IfillU11(EfL-lw)? (2.5 )
6
¥¥'h<'1"(、 I('i >λ川 I~γ> are t
(2.17) P(c0') = L Iくけ/.1'ぃ 1，.loi.A > I人1(/'-. ;.，.: )
。11('ohtλII1S
EIf (Eq. (2.:2)). H('r('. A(k. c0') is t h(' (k-l州 )lyrd).'ipf'C
tm.l fUlIdioll. ¥¥"hich 討 λ111m;問111λJ"¥"川rt()f singlト partic](‘(1川 λr<l('<¥) Creen・sjunctiοη
G(九ω).
仁討111只th(、D刊()11 (可111川 iO!l.C 1"('('11‘S fllll(・ti(lll is ¥¥Tit t (、11川
Eklfl - '"ノ¥¥" h('rr ~'二
(2.18)
(2.19)
G(k， ~，)ニ Go ( ょう ω) ナ(，' 11 (1，・~，)ど (k. ，"-')G(k， "，.:).
G(~ 山 )-1二 (J()(L u) l-E(ょう"，))，
wherr GO(/，、?ω)alld ~(k. ，"-，) i日 th('Greい11‘Sf¥ll1ct i(川 ()ft!te 山口ー111仲間・ti時 systemand
the ，';f'lf-en灯 qy，1叫)代 tiwl¥".:'¥on-int('l(¥("t il明 Gr仰 n":-;fU!lction Go(k¥ωIS rrpresぞ川刊i
(2.20) Go(J，¥ム)二 1~'-fk- If
as
G(k， ;.，.:)二一一一」~' - fl; - ~(k ， ω)
Therでfonもう
、、，，t/
1li
qノ-
q4
，J'f1
・、、i
¥nH'11 'E.(k.ω)阿川11-/('1'0.¥.('‘ th(、ドl代 trOll CO!T(' la t iOIl effect 討 llot11('ιligible， tl刊
討j)ectra1 fllIl(・tiOll iぉ¥¥・nttド11as
(2.22) Illl~ (1，う中旬)
A(k ぅ ω) 二 ~G(k. 中)二六介 (w'-(1. - n江 (k.~'))2 + (Im~(九 ω
This仁川1lw diUd(叶 int U t ¥¥'0 PλI・ts.討()(λ11円!tll(' (γJI! ('{'('1I1 po.r.t孔n<lt h(' illr:oheTellt pll7L
，¥ ear t 11(' f('rmi !(、¥"('1. e¥ S i Il只lぃ一l川 rticl(、(':¥:('itatiull ・λ111)(， rドpn引いllt刊!a討 il IJUIL川-pαrtir:le.
If 011('バドalldsthc s('lf河川lkrλl川Ildt ll(、Felilli[('¥ド[(ぷ二 0.1，二 kF)， ()川()btains
Ù~ I ()~ ~(k. ~.)竺 ~(k ， ρ) 十ヨ二しO.h 二AI J 一五-1"，二()トニAl (l h)+1IIIlE(kyJ) (2.:2.3)
Th('r('for(' .
さ/， 1 III竺(/.'F.w') .-1(k. ~，) ':::'ー
lπ [トω← ご礼1;(や(/. 十竺(μk，..()川)斗 古Iw. -I).hドM二斗/;/(付k-1，ん川lけ))日r+トhJ山IIll~
(2.2-1)
(2.25)
8
。2Ù~，
wherc
which也therenormalization fiαctor. A(k，w) in Eq. (2.24) has a peak at
/ θEI 、EZ = Zdik + E(kF，O) + :: 1__，，，__，- (k -kF)}. 1θklω=O，k=kF ，_. -.'-'1 (2.26)
Ek is the quαs~-pαrticle energy. The coherent part of the spectral function is located
atω = Ek with the spectral weight Zk・ Theremaining spectral weight is transferred
to the incoherent part away from the Fermi level with the spectral weight 1 -Zk.
Hence， from the ratio of the spectral weight of the coherent part to the incoherent part，
zk/(l - Zk) = [-~:Iω=O，k=kF l- l， one can estimate the significance of the correlation
effect， if the momentum dependence of the selιenergy can be neglected， i.e.， the long-
range interaction おcompletelyscreened.
2.3 Measurement System
vacuum chambcr
hcmisphcrical /伽位。nanalyzer
Figure 2.2: Sketch of the photoemission measurement system.
Photoemission measurements are carried out using a VSW hemispherical analyzer
and a VG helium discharge lamp. Figure 2.2 shows the sketch of出ephotoemission
9
mea.surement system. In the ultra-high vacuum chamber， electrons in the solid sample
are excited by the incident photons. The emitted photoelectrons enter the electron lens
and are focused by electrostatic fields. The photoelectrons is decelerated by a retarding
potential VR before they enter the electron analyzer， where only photoelectrons which have a given energy (pa.ss energy Ep) can p剖 sthrough. The relation betweenもhe
retarding potential '"イRand the pass energy E p is
Ep = Ekin + l匂-4JA・ (2.27)
Here， Ep is measured from the vacuum level of the electron analyzer and the photcト
electron kinetic energy Ekin is mea.sured from the Fermi level of the sample.(Fig. 2.3)
photoelectron ..一一 一一一一一一-l砂c0一-.-一一-一一vacuumlevel
仇
h V'¥f¥f¥f1t E:.ci> デ E，
…~TrT-'E
一
JVEti--111111
・・L
d
一EB
sample
analyzer
Figure 2.3: The relation between Ep， and VR・
One can sweep Ekin by sweeping Ep or "包.The energy resolution of the electron
analyzerムEis expressed as
ムE=Ep(ーと+三)2Ro ' 4"
(2.28)
whereωis the slit width (We have selected 6 mm.)， Ro is a mean radius of the hemi-
spheres (150 mm for a VSW hemispherical analyzer)， and α也theacceptance angle at
the entrance slit. Because of the above relation， generally Ep is fixed and VR is swept，
so thatムEis constant independent of Ekin-
10
References
[2.1] S. Hufn町、 PI川
[2.2] ;¥1. Ca吋 0凶 andL. Leyぅ PII，otocm川'，(
[2.3] K. Kobayashiぅ thcsis(仁lllV 叶 Toky仏 1999)
[ロ2.4]P. F山 le札う Elたe白ωctroη Coro
附γ陀εclaαtμω1ωO川川凡Mο川l行目閃正Cω!
1991)
[2.5] T. A. Koopmansう Physica1， 104 (1933).
11
Chapter 3
Photoemission Study of the
Metal-Insulator Transition in V02
3.1 Introduction
V02 undergoes a rnetal-insulator trallsition (MIT) at Tt = 340 K [3.1]. In the higlト
temperature phase， ¥;アO2is a pararnagnctic metalぅ whilein the low-tcmperature phase，
it is a nonmagnetic insulator. Thc .¥IIT in V02 has attracted much interest for se¥二
eral decades. The crystal structure ill tl凹 high-temperaturephase is the rutile type
(Fig. 3.1ぅ spacegro叩 P42/rnn札 ¥"0.13G).Belo¥¥" the transitioll tcmperature， V atollls
dimerize and twist， and thc str町 turebccomes distorted to n削凶clil山c(sp胤 egro飢∞)汎川u
P21/μCう N尚0.1川4叫).The resistivity and the Scebeck codficient a刊は川11in Fig. 3.2 [:3.2]
Thc resistivity in the high-tcIllperatm・ephase is about 10-1 n (・mand the temperatllre
dependence is meta11ic. At the trallsition temperatmで itjurnps by fi¥"e orders of mag-
nitude to 10 n cm in the illsulatillg phase and the temperature dependence becomes
semiconducting. The acti¥"atiull energy of the conducti¥"ity is 0.34 e V. Because the See-
beck coe血cientis negati¥"C in both phases， V02 in the luw-t('mperature phase is a ル type
semicond町 tur.The sωωptibility ano the ¥' K川ghtshiftλlいshuwnin Fig. 3.2 [3.2]. III
the high-tell1perature phaseウ ¥'02is paramagneticう ¥V・hileill the low-temperature phasο う
it is ω川
for口mlocal singlets in the low-ぺtemper、aturephase.
Since the discovery of the .¥IIT ill ¥'02 [3.1]ぅ the町 havebeen a lot of disc山 SlO凶 about
its mecl則 IS瓜 Goodenough[3.3]ほ plainedthe fvlIT ill V02 based on a simplified band
rnodel (Fig. 3.3). In the me引taι孔a11
13
C-8XIS ¥し../"
ι •
• • Oxygen
Vanadium •
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コ10)
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400
T(K)
-400
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104}"' .. =."......AO ..__. _s_ 一ー「二-...----l ー 伝記キ4
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T1 (IO)K-1j
Figurr 3.2: L('ft palle] : I1('討i川i¥'it¥.alld S('('!)('ck coefiicient. Ri巴htp礼ncl: Sll討ceptibi]it~"
14
and ¥-1山 i巴htshift [:3.2]
by the tNra以011λlc:r・y討talfield. Theπ* balldお礼reh~'bl・ idized wi t h thC' 0 '2 fJ7了 bandsand
are Pllshcd towarcl higher ellergies. The dll balld 討礼 nOllbondingstλte and has the
lowest (， llng~・川1l01lg the V 3d bands. These two bands overlap bccau問。fthe large
band widths and are partially filled. In the insulating phasc人theπ* ballds is shifted
up¥¥"ard alld the dll balld is split illtO t¥¥"o b孔lldsby the crystal distortioll. As a resultう
the π* b孔nclsbい(・Ollleempty alld the 10れで1・banclof the ¥" 3 dll bancls is completely白lled.
( a) (b)
v
Figure 3.3: Balld structure of ¥102 ・ (a) High-ternperature phase. (仏刷b川)Low-ぺt忙ernp戸仰e白I削 ur
pl胤 e[3.4].
The clrivillg force for the l¥IIT is the lllost cOlltroversial problern in ¥"02・ Thereare
sevel凶a叫1r叫e吋p肌Oωr山.
from b凶凶M泊川and-str肌 ture a 凶 phonon吋 ISpμ凶e引r口rSl百E
of ele任伐附ct北tronト-pho∞nωOllinteractioll frOlll experirnental results [3.7， 8]. On the other hand う
there are削 I
10叫]. Cr-cloped V02 or pure V02 uncler uniaxial stress in the [110]R direction shows two intermediate phases !vh and T (the insulating phase of pure VO仇2b快凶el臼em時1
Mr p凶ha剖S問e吋)[3.11-14引]. From x-ray di百ractio凡 intheル12 phase half of the V atorn
15
The V a10lIlS ill t l!(、
p礼i1'sfo1'm locλ1 sin広1(寸討パIldλ1・(' !lOI¥IIl孔只1¥('1ic. On t.l!(‘ othe1' handう theχiε-zag("l!λIII討
。f¥.λtom討礼1'(' interpr<、t('da討 aoll('-dilll(，llsional Hei討i'nlw1'g(・hainsfrom NI¥IR and
fOllll P孔irsalld t!J(' ot l!('r l!a!f fOrJllχl広川氏ぐhains(Fi月・ 3.-1)
EPR measurelllr山[:3リ1:3].POII只刊行fal. [3.9] reported the importance of the illtra-
at OI11ic COII!omb (・orrel川 iOIl il¥l(l COl¥clud(刊!lhM¥.().) お礼 :¥Iott-Hubbardins1¥!ator.
Z 戸7汁ル.!(い山3
III日l山hバh，礼川tr噌1叶CIil川l川trcλt-礼川tOllll(白 c刊'()り川)凡lTl'川、，1じJλ川l川1iO川山!口1¥¥"マJλlSlI川l日川lリ]lort，孔川t汀I川11.. ¥ t t!te 討出a口山lll(' tiIIlr、1う tけh(υ~y po汁山illt 代 ! ou t
t l!e scrpell i Ilg eH'pct ()f t I!(、 πネ h川 lds011 1 I!(、 rll! ('!円 troll討 illt he lllet allic、pha問.
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V
+
t
+
+
Fi!!(刊lJ![ ph川(-'-討υ 、‘
B (
l
(
I
.l
〆-I
1
3
(
} 1
1j
〆
t
、Cl戸'stal川r11ct1Ir<、叶 ¥'I-，Crr()L[:3.12]
Clrc・1('月 jihphase.
Figlll・e:3.-1:
¥¥'hether・¥'02is孔 ballcl(Peiドr!討)illS1¥l川 01・ora :¥Iot t-H ubh札口1insu!ator is tlH、1110叫
II叩川tantp川 )lemand !川Soft(，ll !>l'pn di討("1¥川d.¥¥・P山 ω¥'1什 hetαl. [3.15] couclud引 l
that the ins山ttl時 ph出 eof・V02 日礼IIC山 li凶r.vIJaw! (Peinls) insu!ator 011 thr ba
sis of local-density 叩 proximation(LDλ) bandーは1"1川11reωlcl山 tions.Rice et al. [3.16]
objected this conc・lu討ionbeca1¥se the ¥' chain討 inthl' .¥h phase孔re.¥Iott-Hubbard insula-
16
tOl・討 awl a contillllOllS J12 → -'11 t 1 λ llsi t iりtl t hrυllgh th(、11山nt♂内.，cr円町rmθ代吋dia川孔川tれ(】 i山IlS刊ulatit時l培gtricl仁clin山lC
Tp山 1問 i 討 ob州討刈Pr¥'でcd.Th(叩(、y 孔川rg引II以(刊川、刊dt山h川K孔川ltピλ川dlいthい(、11山II凶l凶削削S剖u山l
T)川 l討叫tbい)(、 oft 1山 制111('tYI川 andshould 1)(、(・l川 sifiedas Mott-H山 bardinslllators and
llot balld illsulatυrs.
S 何 e 川 lド山hc山 X斤川川、'11山l11S泊m山S幻山l(山川川o川仙}川川11S叫山山tl印11山
w引v吋アt廿叫i比川th('01 山 11川 1011 叶 ult1口tλ川肝川1¥'吋iわ01('付、t 1山
Sh山山11山neけt“al. [3.10] h川t礼l¥"eprlυ川山)八川1吋ide代吋dfru山itfuι1 i口山II凶iはd凶1'1五f()り山(り)
bauc川d~δ日づ-itru以(ぐ川.tれ\l川l口rでes as ShO¥¥"ll ill Fig. 3.5. They ha¥'e cOllcluded that the importance of the
itillerantπホ dcctronsfor・thc 討cl収、llln広of・thrdll electron in the metallic phase was
recogllizecl. HO¥¥'e¥"e1・ヲ they repOl・tedt hat it ¥¥"as a problern ¥¥・hythe UPS intensity of
theπ* ballcl is strollger than that of t h(' dll bancl in the metallic phase.
(a) (b)
V~I 1-
" V02 -・・・
V3d I ...輯，1.1
a ‘-• ‘・'〉、-ε ω .，
hV・ω@V M l I e T.tragona'
Metal ，。 5 o 以ndingenergy (eV)
Figure 3.5: Pl川 oemissiollspectra叶 ¥'0:2 by Shin et al. [3.10] (a) GPS spectra of
V02. Thc solid c:urve shows the spぞ仁trumin the insulating phase measured at 298 K.
The dashed curn shows thοspectrum in t 1日 metallicphase 1肘 asuredat 375 K. (b)
Sc:hematic energ~' diagrarn of the :3d band日 aroundthe Ferrni level.
17
3.2 Experiment
3.2.1 Sample preparation
， SillglC' crystalお()f V02 ¥WJ'(' sl1ppli(刊11 η， Prof・ ¥I. OIlO(川d，礼dけ[11ト討itit山tl日11い('ofPhひ戸刊守有叶SlC討札， Cniれnでeもf刊叶討i t守y
of Ts引叩1日lkll1刈 円仙III培吋glC'、 ("川川'1ηI円戸刊's叶川宍山tれJ汁山1
T('、Cl1孔川討 all礼1広仰(当nt 111，孔川1け1れ(ド川川、可T叶f叶'ial. ¥'2()l j>mY(!(、fS "'(' J'(、 白1・日1prf'J 川 n、d1Jv hratin只¥'20:; (¥1
973 K for 24 hours， :'¥('xt， POhTl下叶allin(' smll p 1 ('s m、!"e民ro¥¥"n1)¥， Iwatin只λlllixtUf(，
()f V20:l and V20弓川 1173K for・2-1hours 11I1c!Cf tl日、Ililro只('11atlllosphf'r(" !lesultallt
])01."口下アstallinesam ple討 andT(、Cl1，actin日a日孔 tnm討por(a印、Ilt.¥¥"('r('同 al('dinλ Cjllλrls
tllbeう。fwhich th(' higlwr telllperatlll・(、 paflw九日 1323I¥: ，¥lld t IIP ](nw'l・tPlllprraturrpart
was 11 73 K. The rpsu 1 t of thc、allal."おお むJrOX."保守1('()ntf'llt '"川 2，002土 0，0002， The
lattic(' ('onstant討川 町 川11telllprr<ttllre a]'(、(f 二 3，764(.1)λ ん二1.339(1)λ，(二，).393(4)λ
andβ= 122，61(5)0.
3.2.2 Photoemission measurelnents
ul川Jltravic臼o舟tph山
va叶乱川1('円3可I1C何e-b泊and1日1討幻叩inga ¥'S¥口Yh廿1('円叩11山11山llS討plH以(ο川川、'r川n山'1台H'a叶孔刈1(礼川i!l，礼川1叶ln判χ刀{ド、r盲 and a ¥'C hdilllll di以・h川町、 lamj)
( 111ノニ 21.2eV). Calibratic山川1(1estim川 iOIl01' th(' instl'¥lIllPlltal r附 )111t川 ¥W1'(， c!olle h."
ll1easuring the Fermi ('dge ()1'λ11 (、vapOl・ated011 t l!f' salllple sl1d孔('('討 TII(' total ('ncr只Y
r<~sol l1 tion was about 30 ll1P¥'. Clp 礼II 討mf・孔('(‘討 ¥¥，('r(' obt aill(、dh." scraping UI， .sit71 ¥¥'ith a
diamOlld fil(当 llnc!eft he 111 t fa-h igl! ¥'('ICI111111 (Jf 10-! () TOl'r. TIH' lIleλSlll・('111川 11telllj)υratuf(，
was T二 100， 150‘ 200. 25()‘:300川 Id3ろ()K (7~二 :WlIく). Th(' temp('rRtlllド()1't l!(、
討礼IIIpl(' was ltle礼、II1'('<1 !J¥' ein 九11-F(' dll・()Il!い1tlJ('l'Itlo("(Juple. FOl・ t.he 11]('(¥日 Irelllents川
high telllp('ratures， "'(' calihrated t 11(' thC'flll()(・ollple，)Is() ahm'い 30()K.
3.3 Results and discussion
3.3.1 Metal-Insulator transition
Fig.3.6討ho¥V討 a仁PSspe(・trum of ¥ 'O:! and t he secolldal下 el円 'tronb孔ckgrolllldc!(、ter-
Illll 町 1bv th(' II肘 tけho山川)川川d01' Li ar川 H 巳円enrich[:3.2η叫2司lλ川I1t 11(' 、i日仏川(り川Jll(仇)九¥¥'叩.
!い)(甲nrHο)川I口'maliχ川(い、dto th(】l刊)(、孔kh(以('川'1叫巴広一:ht孔川t江rひ川o例)川UlIμ川dEn 二 :) ('首ヘ¥¥' λ1't('1' t h(‘ 附 condλr¥' e!(】けrOll
l胤 :kgrou凶 ¥¥'as suhtl・出 t.ed. Fi広urC' :3.7 (λ) 討hO¥刊 CPS 討p付 train the C'lltire valen('C'-
18
(ωtcコ.0」何
)kC一ωcgc
lV021
hv = 21.2 eV
10 8 6 4 2 Binding Energy (eV)
Figure 3.6: UPS spcctrum of V02 ancl the scc:ondar.v electron backgrouncl detcrmined
by the methocl of Li and Henrich [3.22].
19
b孔nd I'q~iOll ()f ¥'0:.> at tf'lllpcrat lIr<'Sけhoy!'alld 1)('10¥¥・ th(' lI}('t al-iJlS1Il川01'trall討it i 011 .
The叶1'1I("t1ll"CS frolll E l3 = :3 t () 1 () (、¥' (iJ"(、 ("()lltl・ihlltiollsmaillh' frolll t JJ(、 o21) hand. ()ll
th(' OtlJ('1・hanclづ t)1<'regiotl f・romEu二 Lいヘマ t() E"， iぉaぐontrihlltiolllllainh' hom t h(、V
3d band. :¥lthollgh the c!eanlill('ss of th(、討礼lllpleslIrCλ("PS ¥n¥s c!J('("k('<! hv t h(-'λbS!'llc(，
。fλ 叶ruct1¥l、f'arolllld Eu二 9C¥' dmill只t!1('llH'a511l"f'Il}('llt凡 the 1川~i() Jl from En二 G(' ¥'
to 10 e¥' of tlle おpectI"ll1l1at :rJ() K s!Jo¥¥'s a f('atm・('illdi(・川 1¥1月th(' 川 Illp!(、C!e広lλ(IatiOIl.
¥yhiけ1¥¥'(' ("ollJd not avoid ("OlllpJ川 el戸¥
Figur(' 3.7 (h)日hm刊 theおp代 traill th(、¥'3d l'('giOll t akf当nλhυ¥'('礼11(1hpl(町 the
transi tiOll tem pera tm・e. One ("(tll附(' c1ear differCll("(-，巧 1)('t¥¥・eellt!1(' t¥¥'O spect ra. Thc
Sp付 tI"ll1ll !w!ow Tt shm刊 a!)('ak川 ER 二 l.1eV， ('0凶 日tellt¥¥'ith Shill f:t (}l. [3.19]，
where t!w measurelllent was perforllH刊1¥yi t h t he photOll encr幻T of 111/ 二 60cV. T!j('¥・
rcported that the peak of t he ¥' .3d b孔ndwas lo("atec! at EB = 0.9 e¥'. Thi日 di百er<'ll(，('
may bp exp!ailled by the clifferellt ionizatioll cro出 scctionsf01" hν二 21.2eV and GO
eV. For h1ノニ 21.2eV， tllP ('ontrilllltion ()f thc tail of 0 2p band 日 larger，討othat the
peak is apparentl~' located atλhi日hel・hiwlin広PIlprE7・Thespectrlll11 above Tt sho¥¥'s a
dear Fermi eclge and thc peak at Eu二l.3e¥¥This spectrulll h川 λrathel"important
di百erCllcefrom Shin etαl.. which l"eport('d tll川 the l TS intellぉi竹 oftlwπ* band ¥¥'a自
stronger than thλtof tllP「1111〕ttIl(l.TlMBVMλt<刊1that this is孔 problemthat co111<1 llot
be cxplai!lf'd wit hill hiぉIllodel. Om 討p刊寸1"11Illfor t l!e met allic・pl!孔討eSI!OiYSλstroll只
inteIlsity around the 1.3 e¥' pいのk.孔1t h01!巴11，，'e mllst ('011自id('r代('(り)!日ltri日1J川Iltionfr唱Ol1ltけ11<'、
S飢刊u町l
The ('け'h孔旧nge何S1山nthe 同I>('('tra t hrOllgh t 11(' t I'allsi t ion m出ア 1)(' ('勺x壬勺叩p1a札出t札山II凶n刊e引T刊K叶di II t¥れ1γ'(υ)¥れ1γ.孔小i"吋 孔川討
fo削削O叶"011日10¥羽¥'札'
th( 、vア 3d ba旧1汀!lC吋d討叶叫4刊刊truc寸叱引t1lre札司ヒ. 111 the 当 nu'什‘吋t(λil日!icpha 同 • thc dl 礼nd π * hand 白 0¥"er1 礼P IH' 乱r t!H 、
Fermi !en>l. H('IlCC， t1l(' rcgion礼1"0
20
excitatioll or a rCllOnllaliχcd d-l川 ndstatc. On the othcr halld. the b孔nd討 al'Ol111dtlH、
1.3 e V pcak correspollcl (0 t h('“illcoherellt pλrtう¥whi(・his a hn孔1state with a rdati\"(~ly
localized hole. Frolll thc ratio ()f the spectral weight ()f thい coherentpart to th(、l!lCυ-
herent part， wc call estimatc the illlportallce of the con'dation effect. One can sec that
the incoherent partぅ孔 1でltlll<lllt of the 10¥¥'C1・ H11 b bard ball(しisrathcr large. HC!l(:e， ¥¥'e
can say that the COl・1でlationcffect in the llletallic phaおい IS llllpm・tant.III thc insulλIIll広
phaseう tooう thcCOI・relatiolldfect ¥vollld ¥)c importallL ¥)(、caus(' t he Y 3d band in tll<、 11ト
sulating phase call essclltially be n、gardedas the lower Hubbard balld frorn COlllp孔1・i討Oll
with spectra of othcr :¥Iott-Hllbbard insulators.
Comparison with band-structure calculation
Figure 3.8 shows comparison of the UPS spectra 'with band-structure calculations. The
upper and 10¥¥明， panels sho¥¥' the spectra ancl the calculated DOS above and b叶owthe
transition temperatureヲ respectively. Both calculations are broaclenecl by an energy-
dependent Lorentzian and a Gaussian for the instrumental resolution. The calculation
for the metallic phase is based on the full-potentiallinear augmented-plane-wave method
(FP-LAP¥iV) [3.28]. The other 0町 forthe illsulating phase is based on the LDA + U
method (parameter Uニ 4.0eV) [3.29]. ¥Ve call state tl削 neithercalculation a仰
、wi比ththe expe白rμ'imentalspectr乱a.Frolll this factう tooヲ ¥¥'ccan cOllc¥ude that the corrclatioll
e百'ectin ¥102 is important.
21
C
コム」何
四 一一 350K------300K
、、---
〉、+-'
ωco一=」
12 10 8 6 4 2 O
E Binding Energy (eV)
一一 350K・ 300K
C
コ.2」の、、-
〉、+-'
ωCDHC
2.5 2.0 1.5 1.0 0.5 O
Binding Energy (eV)
Fi色川e3.7: CPS討p町 tratakell パbo¥'('λIldbe!ow Tt = 340 K. (孔)th(' C'Jltire ，"a!cllce-balld 作広iOIl. (b) the V 3d band regIoIl.
うつ
四10
a
u
λ
『
nJ』
(=00〉
@¥ω25ω)ω00
6
2 1 0 Binding Energy (eV)
0 3
四20
否15〉Q) 、、‘ω ~ 10 <<s 喝・4
ω
ω 0 0
5
Figure 3.8: Comparison of the UPS spectra in the V 3d band region with band-structure
calculations [3.28， 29].
23
2 1 0 Binding Energy (eV)
0 3
3.3.2 Temperature dependence in the insulating phase
We have measured UPS spectra of V02 at various temperatures in the insulating phase.
Figures 3.9 and 3.10 show the results of the meωurements. Figure 3.9 shows spectra
in the entire valence-band region and Fig. 3.10 shows spectra inもheV 3d band region.
On these energy scales， one cannot recognize the difIerence between these spectra. The
peaks of the 0 2p and the V 3d bands does not shift when the temperature changes.
Figures 3.11 and 3.12 are enlarged plots of the above spectra. Figure 3.11 shows the 0
2p region. Dashed lines show the leading-edge midpoint of each spectrum. From these
results we consider that the width of the 0 2p band becomes wider as the temperature
increases， although the higher binding-energy side of the 0 2p band is very sensitive
to the surface degradation and has a poor reproducibility. Figure 3.12 shows spectra
near the Fermi level. We have fitted the leading edge of the V 3d band by a straight
line and estimated the change in the band gap below the Fermi level. The fitted region
is between the points where the spectral intensity is 3/4 and 1/4 of the V 3d peak
height. We can see that the band gap becomes smaller剖 thetemperature increases.
This means that the width of the V 3d band becomes wider because the peak position
does not change with temperature.
We have plotted the relative shifts of the spectral features as function of temperature
in Fig. 3.13. In the figure we also compare the results with the infrared absorption
measurement [3却].The temperature dependence of the absorption edge shows the
variation of the energy gap between the top of the valence band and the bottom of the
conduction band. Remarkably， the shift of the leading edge accords with the variation
of the absorption edge. Since photoemission measures binding energies relative to the
Fermi level， the temperature dependence of the photoemission spectra reflect variation
below the Fermi level. On the other hand， the absorption measurements reflect variation
both above and below the Fermi level. Therefore we conclude that the bottom of the
conduction band does not shift with respect to the Fermi level as the temperature is
varied.
24
|V02
(ωtcコ V 3d
300 K
250 K
200 K
150 K
100 K O
Figure 3.9: CPS spectra iu the cntire valence-baud region in the insulating phase at
vanous temperatures .
• 2」何
)kC一ωCOVC
10 8 6 4 2
Binding Energy (eV)
25
-、21 、~ ¥ 、斗 1300 K C コ4コL申
~I ー叫----- ¥ 、寸 1250 K _6<0ペMι
〉、4・d
(/)
c (J)
崎田d
¥ 、吋 1200 K c -~
150 K
100 K 2.5 2.0 1.5 1.0 0.5 O
Binding Energy (eV)
Figure :3.10: CPS spectra ill tll<' ¥" :3r1 !Jalld n、giOllill the ill討1l1atill巳ph礼討P 礼t¥'λ1・IOllS
U'III ]wra t 11 res.
26
l V021
(ωtcコ.0」何
)kC一ωcsc
4.5 nU 3w
e
vy
nuu
VEE
5
m
quFヒ
門
uvnH
aG nH
nuRU
A『
Figure 3.11: Enlarged spectra in the 0 2p band region.
27
300 K
250 K
200 K
150 K
100 K 」2.5
lV02
、句、仏 1300 K 〆-、(/) 4・d
c コ 吋~ ¥1一一門事川畑附，1250K . 工L-2 cu 、、-〆
〉、
Z |可恥c
¥Y柏戸一斗…vV蹴四ffi1200 K ω 4・d
c 一同恥 へ市町、時』←
~~150
一一由ノ1100K
0.8 0.6 0.4 0.2 O ー0.2
Binding Energy (eV)
Fi月UI・e3.12・Elllal又刊lトipい(・tl・孔 11<'(11・thい Felmile¥で1.
28
5ト固
> ~ 0 〉、
亡刃~
ω c
t-005 〉-4-'
回
ω cr:四0.10
-0.15 O
一・-V3d leading edge 一口ー 02pleading edge midpoint --0-V3d Peak 一色ー 02pPeak
-absorptiQn edge
100 200
Temperature (K)
穴=340K
r
Figure 3.13: Temperature dependence of the energies of several spectral features. The
ellergy of the absorption edge has been taken from Ref.[3.30].
29
From the facts that V02 in the insulatin広pha，seis a n-type semiconductor and that
the activatioIl energy of the conductivity is礼bout0.34 eV， we can know that the energy
separation betw何 nEF and the bottom of the conduction band is 0.34 eV. Frorn the
above analysis for the leading edge of the V 3d bandう wehave estimated the energy
separation betv刊 enE F and the top of tl日 vale町 eband is 0.22 eV (300 K) to 0.32 eV
(100 K). Therefo民 theenergy gap bet問 enthe top of the vale町 eband and the bottorn
of the condl 川 ion band is 0.56 eV (300 K) to 0.66 eV (100 K). The i山nf仕ra紅re引吋dab苅別S叩orp戸凶〉式川ti白onl
rneas叩urer
K). This is a little larger tl
re日ectsthe direct gap守 sothat it is larger than the indirect gap estirnated frorn the
activation energy and UPS results. These results mean that the Ferrni level is located
a little below the middle of the band gap. This might seem to be inconsistent with the
fact that V02 in the insulating ph邸 eis a n-type semiconductor. Hov¥引 'er，this may be
explained by consideration of the correlation effect. The aけ.ivationenergy of 0.34 eV is
the energy to excite an electron froln the impurity level to the conduction band. The
energy to excite a hole from the impurity level to the valence band is probably larger
than 0.34 e V due to the correlation effect.
According to R.ef. [3.31]， the energy gaps of typical semiconductors Si and Ge are
1.12 eV (300 K) to 1.17 eV (0 K) and 0.67 eV (300 K) to 0.75 eV (0 K)， respectively
Those values at 100 K are a little smaller than those values at 0 K because at lov"
temperatures the energy gap of typical semiconductors becomes srnall quadraticly as
the temperature increases. Thereforeう thetemperature dependence of the energy gap
of 0.56 eV (300 K) to 0.66 eV (100 K) for V02 is somewhat larger than those of typical
semiconductors.
Figure 3.14 shows a schematic diagrarn of the energy bands in V02 and their changes
with temperature. In the insulating phaseぅ剖 thetemperature increases， the width of
the 0 2p band and the occupiθd part ofthe V 3d band become wider. Ho¥¥'everぅthepeak
position of these bands do not shiftうl.e.ウ theFermi level does not shift with temperature
with respect to those peaks. In going from the insulating pha.'3e to the metallic phaseう
spectral weight of the V 3d band is shifted frorn the incoherent part (the peak at ("V 1.1
e V) to the coherent part and the Fermi edge emerges. At the sarne time， the peak of
the incoherent part is s
30
Metallic phase
02p
/¥4 / ¥ ァ十月/
/¥J ¥タInsulating phase
仁!?件-¥/¥
f 、/L- dJ叫dl/リ/ dιiし/μ，耳fX
/¥ /¥/1¥'t//J/T
ど乙一一一一一一一一一一一一一+一一←←-一一 一 一一一一一一一一一-一-こ￥L一一一〈←←一一-一一」一一-
h 、、、
02p /~I~\
/¥
/¥ffj:iM /\/\ f:~て
ー乙一一一一一 一一ーとL)~_..__._-_._~'\_-.Lビ2--i-
/ / 〆
叶OB唱
2・白骨-HO
EF
Figure 3.14: Schematic energy band diagram of V02・
31
3.4 Conclusion
¥Ve h爪 'emい孔討u1'edhi巳h-1'esυ1111iUIl tャ P月sp代 'tl代 0[¥'02λt¥'λrJ()l1計れ'Illperatllr何ー Al・ru出
the phase transitiunヲ ¥yeob附1'n'(1(・leλ1・chanp;科iin t h(> specl.!・λ， 111 the metallic・pha附.
the ratio of the cuherent sp代寸ral¥yeip;ht to t11いilll'oherel1t()Ile "，:1討 rathersma!1. 111 tlw
IIIト孔ilatingpha同， the spectr孔1fllllctioll ()f the ¥' 3d hλnd l・λ11bいrep;ardいCIas the lcm'円、
Hubb孔rdbancl， Band討t1'uぐ1¥Ilド(，l!(・lllatiollSdid not an'onl ¥¥'ilh the CP日付pectrain th('
V 3d band region， These I 刊1I1tS impl~・ thatlhel・o !Te!atiυ11 い汀円・ is important in ¥'02
both in the metallic ancl in討111λtlll宮 phaト，es， FOl・ thい me孔sllI'emいnt討 oft he tem pe1'a t 1¥I'e
depぞndenぐeof the CPS討pel'tlλinthe in日d孔tingph出 t¥thep川 l品川・ the0 2j) band
and the V 3d bancl did not shift ancl t heir leading edges討hift刊 1upward， Thf当討hiftsυf
the leacling eclges aぞぐo1'cl¥¥・iththat of the ab同 rptioned巳('in thいinfraredmeasu1'emぞnt ，
These results imply that the ¥¥'idth兄 oftlH' 0 2j)孔ndOl'l'U pied states of ¥' 3d b孔nd
become wider as the temperature increas円 anclthat the bot 10m of the concluction
band c10es not shift with 1'e討pec寸 tot he Fermi lew 1.
32
References
[3.1] J. Morinぅ Phys.Rev. Lett. 3ぅ 34(1959).
[3.2] ¥1. Onoda， unpublished.
[3.3] J. B. Goodeno時hヲ Phys.Rev. 117， 1442 (1971).
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FujimoriヲY.Ueda， and K. Kosuge， Phys. Reb. B 43， 7263 (1991).
[3.5] M. G叩 ta，A. J. Freeman and D. E. Ellis， Phys. Rev. B 16， 3338 (1977).
[3.6] F. Gervais and W. K町民 Phys.Rev. B 31ぅ4809(1985).
[3.7] R. Srivastava and L. L. Chase， Phys. Rev. Lett.27ヲ 727(1971).
[3.8] D. B. McWhan， M. ~Iarezioぅ J. P. Remeikaぅ andP. D. Dernier， Pl肝 Rev.B 10う
490 (1974).
[3.9] J. P. POl伊 tぅH.Launois， T. M. Rice， P. Dernier， A. Go制 rdヲ G.Villeneuveヲ and
P. Hagenmullerう Phys.Rev B 10ぅ 1801(1974).
[3.10] A. Zylebersztejn and :¥. F. Mott， Phys. Rev. B 11， 4383 (1975).
[3.11] G. Villeneuveう A.Bordetぅ A.Ca砧 lotぅ andP. Hagenmullerヲ ;¥Iat.Res. B凶 .6う
119 (1971).
[3.12] M. Marezio， D. B. J¥仕日アhanヲ J.P. Remeika， and P. D. Dernicrう Phys.Rev. B 5う
2541 (1972)
[伊3.13司]J. P. Poug伊酬e叫tう H. LaunoiおSう J. P. D ヲ官Ha舵制e白I附
Rev. Lett. 35ぅ873(1975)
[3.14] J. P. D'Haenens， D. Kaplan， and P. Me町 nda，J. Phys. C 8， 2267 (1975).
33
[戸3.15]R. :¥1. W('¥ト('¥ド円孟斗1¥川¥t χ ( '0川肝川'"叶"if(什川(ぐ什.hし、 ¥Y. ¥Y.守¥. S(けhいh日川川1日dχ tλ川川1汀叩n川I
(1994)
[3.16] T. :¥1. Ri("(¥1-1. La ¥lIloisぅ礼nd.J. P. PC川
[ロ3.17可]C. sla山川川t孔川川川11川1¥川lれ¥¥".r. Le伴州ぞ円I山 01山可 F ¥'c孔川川tr山nd心山lいle¥円r¥¥"(川川(ο川)川川1日1<1い(οB¥司 孔川I吋 G. A. Sawat口zkyう J. Ph川;
459 (1979)
[3.18] G. A 品川ltχk~' and D. Post. Pl山.H('¥.. s 20ぅ 1546(1979)
[ロ3.19司]S. Sh山山11山n凡1うS.S白1¥唱gλλう.¥1. Tc代削削l日川I日l日i巳伊U('けf什hi吋i，~L F1¥吋1.リ.]1問 m ウ H.Ka削I凹孔kiうλ. Fu山j
Y. 仁じC('刊刈泊叱daλ，K.Kωυω州臼削叩¥l広停(、¥う 孔川仙制n山川1dS. K山礼訂川fけ('hiうPh川 • Re引肝帆V.アヘ. B 41， 4993 (1990).
l伊3.20叫1V. i¥r. Be円rmude何凡又九う R.T.WミVマi日llia山a川叩III杭 .1. P. Lo略ウ R. K. Re伺ぞd.崎 and P. H. Klcい('1叩m‘4七lI1ヲ Phys. s.
Rc¥'. B 45ぅ 9266(1992)
lロ3.21]E. Go肘附ぞ引円凶r吋nn
de円enBoe肝rう九削I吋 S. HornうPh~.s. n円.s 55う4225 (1997)
[3.22] X. Li and ¥'. E. Henri('h， J. Elcctron. Spectr側~. Relat. Phenom. 63う 253(1993)
[3.23] GGK. :¥Iaiti. P. ;¥Iah乱心vanぅ and D. D. Sar・山
[3.24] C. SOIllIlW¥日λndS. Do山l('h司 SolidStatc C01IllI1Un. 28司 133(1978)
[3.25] A. Fujimoriう 1. HaseうH. ="amatanHヘY. F吋i担shima礼う an飢吋dY.Tokur瓜 P斗h阿;
L
[3.26] 1. H. lno肘‘ 1. Hasc， i". Ai旧 λ A.Fゆmonヲ Y. Haru町町lりFうya羽a出ma礼う T. ¥Ia紅加n川uザy司刊a出I山I
:¥!isト討4心hi日l削 a ‘ P円h肝 • R('門門V.Le吋tt.74 う 2539 (1995)
[3.27] K. :¥lorikawaうT. Mizoka¥¥ア九 K. Kobayashiヲ and A. FujimoriうPhys. Rev. s 52う
13711 (1995)
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1614 (1992)
[.3.29] X. H凶 nι¥V.YangぅandC. Eckern， cOlld-lllat/9808137.
[3.30] L. Ladd and ¥¥¥Paul， Solid State Comrr
[3.31] N. ¥V. As日山h恥lC忙m川c口げ叩:rofta加n凶d=". D. ¥le肝側r口I山I
Phi日la凱ad山州lおlel叶lp治hia，1976)
34
Chapter 4
Photoemission Study of TIGaTe2
4.1 Introduction
A series of compounds TLVleX2 (;Vle=G人 In; x=sう Se， Te) have highlぅ・ anisotropic crys-
tal structures. TIGaS2， TlInS2， and TIGaSe'2 have qll川 it，，'o-dimensionallayered struc-
tures and exhibit incommensurate ferroclectric pl川町 transitions. TIGaTe2ぅ TlInSe2ぅ
and TlInTe2 have TlSe-type (B37) quasi ollc-dimensio川 1chain structures [4.1](Fig. 4.1)
and exhibit ω凶肘arelectlω1 p川河rtics[4.2ぅ 3]. ¥¥・(‘おtudythe electronic structure
of TIGaTe2 by ultraviolet photoelectroll叩 ectroscopy(じPS)motivated by the sugges-
tion that the electrical conductivity in t hiおs(仁:ompou山Il(川diおsgO¥"er口nedby the Tl 6δone-
di1口附I削
i山nthe e叶lectronicstr冒uctur問'e0叶fTIGaTe匂2う¥¥'hile ¥¥で ¥youldlike to discuss other intercst-
ing propertic~き of this compound as ¥yell as of uthcrぐりlllpoundswith the same crystal
structures.
As for the properties of the TlSe-type compo¥llldおう tけh日ef，おo辻llowin培gs剖tu山lCiie伺shave oeen re-
po 巾 d. TlSe u山山nd巾伽e引I昭>csap附 S 山 eト目叩.寸引III凶l
un肌吋【d仇le1'ambi蛇e白叩n川ltcωon凶d心it札10凶 the res 凶 1V凶V吋'1比tie出sparallel (孔川仙u山lld
a剖仙n凶1dρ ム) of TlSe are 400 and 208 OClll. respectin'ly. s υ th ρ 11 alld ρ J.. decrease C011-
tilluuusly with pr伺 surealld reach lllctallic resistiviti(市川 preSSUl'eawund 2.7 GPa.
U lldcr ambie叫 co川 itiUllSヲ the川 iu(Jli/PJ.. is l.92. HO¥刊vel・， there is a report that
ρ11 <ρ上山derambient co凶 itions[4.6]. Cnder high 1川制urc，the ratio becomes unity
at abuut 0.6 GPa， decreases continuuuslyう andbeCOlll(うs0.016 at 5.0 GPa. According
to NMR studies [4.7ヲ 8]， it is suggested that the indirect nuclear spin-spin inte1'actioIl
of Tl isotopes between chaills is bigge1' than that along the chain. The oand-structure
35
J
マ
~ー一、
，-、d 、
、，円¥、---'
「一?
;kcalJ J:(:;
Figure cl. 1: CI下叶
!FJh
，、丸、，、
Jてl士、、戸'
どbn
"
TI
，1ぞ少y
Ga
トキ弘、;九¥
Te
ωlculations using a pseudopot(，lltiλI Ilwthod [-1.0. 10]ぉhow乱 di討p('rsionalo叫 th('ι
r('ction pe印円l山・1山 rto tlH' chaillλc('or仙 l日toth(' x-ra¥' diffracti(川 H.ll]， TIG汀円
has an incomnwllsurate ph川(' ¥¥・itha rpc!llctioll ()f the lattic(' (・OllSt孔nta. Frolll th(刊 3
factsう itis suggested that TI-¥[(' int('raction is illlport<mt for・I1IHI <'rS t a nd in広th(、ドl代 .t1・ical
prope1'ties and tl日 phaset IけIlsitio川 inTI¥[(';¥:2 [-1.12]
Because a¥'a日t巾leexpnillH'lltλ1 dat a ()Il TIGλT円 IS ¥'('η-メ{・孔n・e.¥n' h川'('llO knmd-
円 1geabout thr当乱IllS0tl・0]れ.()f t I!(、 resisti¥'it¥，りfTIGaT円 it州、11'.Hcm・('¥'('1'.i f t h (' ('1代・tricコu
I'esistivi ti(、討 ofTISp-t¥'p<， C()Ill!l()l1llds IlelW t I!(、引)lIllllOllf('a t 11 nも ¥¥'ithTIS(¥th(、alllsotropプ
of the I'f'sistivit:v of TIGaT(':2 Illight 1)(' oppo日itpto thれt('XI)(、ct('dfroJll t I!(' (・l凶 inst1'1l(・ー
tu1'eぅ andone-dilllrn討ionalit，vIllightわい r('aliχ刊 1onl，v I1wl('!・hi月hp1'essl1n¥To unclerstalld
e!('ct1'ic・λ!properties ofTIGaT(':2・ it只1¥'('S 11日(イ111infol'lllat iOll to illWSti即日('Ih(' e!(、('t1'O1l i(・
日1・11cturebv UPS.
4.2 Experiment
Single crystals of T!G孔Te:2 ¥¥'('1'(' suppli代1h，v Or E. J(erimova and Prof ~. :¥larnedO¥・
(Institute of Phy町 s，Bakll) Th('~' wprp grown by a modi白いdB1'idgeman methoc! in
evacuated quartz tubes. AIl日l('-integratedand ang!トI'eso!v刊 1photoelllission sp円・tra
36
竺4 5
if /'(I'.l":，-;，)
Figure 4.2: Elcctrical resistiyity of TlSc [4.5]
(AIPES a 凶 ARPES) we白町r陀~e rnca紛州S別別l旧千
He diおscha剖rgelarnp. AIPES spectra ¥vere measured USillg thc Hc I alld He II resonance
lines (hv = 21.2 and 40.8 e¥"， reぉpectiyely)alld ARPESト，pcctra附叩 mcasuredusing
the He I resonance line. Calibratioll and estimatioll of thc instrulllental resolution were
done using Au (了、¥"aporated011 thc sarnplc、 m<111ipulatorby lllcasurillg t he Fcrmi edge.
Clean (110)れぱaceswere obtaillCcl by c:leavi時川 8山. ¥Ve took Laue photographs
of the crystals to con五rrnthc directioll of the crystal axis and that they were single
crystals. The cnergy resolution for AIPES was about 30 meV for the He I and about
90 rne V for the He I1. The accept anc:e angle of the electron analyzcr for AIPES was
about 土80 • The allgular and cllergy n古川lutiollfor ARPES was about 土10 and 90 rneV，
respectively. The rneasurcrnents ¥¥"8re lllade at 22 K a1ld 1・001lltemperature. The base
pressurc of the analyzer chamber was ¥)(、low1 X 10-10 Torr.
37
and discussion Results 4.3
Angel-integrated phOtOeIllission spectra 4.3.1
Figure 4.3 shO¥¥討入IPESsp円.tra()f TIGaTe:.! 11H'aSllI刊1¥SI11広 H(，1 (111ノ二 21.:2ド¥')and
He 11 (1uノニ-Hl.8υ¥')川 30{)K. B刊孔川(' t!l<' plt(山
ぃ!('ctronrelati¥'(、to T! G.'; ('!(け1・り11IS (、stullat刊!t 0 1川、 rv 110 at 11.，/ = 21.2 ドVλ11<1 rv 4.:3
allcl EF3 = [) ('V. ¥¥・hich¥)(町Ollt(‘¥¥刊1k('r川 1)，1/ 二 40.8バ[4.J:3L引nwt1¥1何 b州 ¥¥'('llr'， 21.2パ， to hu二10.8ド¥'.are lllainl~r <11¥(' to Tc 5jJ川川(、日孔ndin going from 1/1ノ二
structlll・P討 atEH二 3-8('¥'λre III礼i Il l~ア<1 11いい Tl G.可stat円. Thi討仕出ignl1lf'1lt討 COll自l1W 刊l
by referring to PES sp州 I礼 。fTlInS勺 [-1.11]ウ which h凶孔討 th('‘ S制削a旧I日問I
as TIG礼Tc匂B刀2う andcυlllj)λrlll月 this AIPES r(，s1¥l村 ¥¥'ithour FP-LAP'" h孔l¥(トぉtruc・tur('
cal仁川ation(Spc. 4..3.3)
pse引叩u山吋lC【clopc川o附)
bancls are ぐontれr吋川‘t廿i日butれ(通刊吋df什'rOlllTl 68 ~引叫4孔孔ta吋tいJイ('トs.Tlw寸戸¥' 白p(，円m to hav ぞ r ぞacけ'hedthis討 iclぞa 1口山n凶5叶lド)Irれ(可l
This c・ondI¥siOIl is in(・on日ist('ntwith that ()f Gashimza山、k
by the work by ~Io川('1・孔凶 PrarsoIl [1.15]， λ凶川t1州代lωobta山
I Te 5p
「Angle Integrated
300 K
hv=21.2eV
(日で
CコD」何)KAV
一日
COF「』一
hv = 40.8 eV
O 2 4 6 8 10
Binding Energy (eV)
Fi民広広印'U日lre4.3: λ IPES 吋叶叩p('('引('叶.叱tれrλ ()f TIG 礼T(内可勺'2 IrHい~a削1桁討1川l日r刊 11¥討叩II山Il広 He 1 (リ1/1γ/ 二 21.2 E♂4へ¥')孔川川Ilμ川{什1He 司I日I
38
(1/'//二 40.8cV) at 300 K
4.3.2 Angel-resolved photoemission spectra
λ 時 lc-附 01 もve代吋d1 山 )to例州Clll山l
i山llgthe elcいectronicba剖ll(川dお引i花t1'u山lctureof s以ωolids討4仁. ¥口¥'e、d( 川刊("1'甘11出beI>asic p1'ill比Cl江plいes0汁fλ RPES
below [4.16]
In the direct trλnsitioll regimcう Olle01>日('1・¥"(、sa trλnsitioll b引weCllthe initial state
Ei and the fillal st礼teEJ. ¥yhel・eboth ell(、1'gH、S<11'(' measured ¥¥'ith respect to the Fe1'mi
lc、vel.The mcasur刊 quantityis the kinetic ('llC1'幻.Ek川 ofphotoelectrolls cletected at
a take-off anglc () relati¥で tothe samplc sm・facellonnal. Knowing the wo1'k fUllctionゅう
one obtains the final and illitial state cncrgies as (Ei二 -EB)
EJ = Ei十 tL叫
EJ = Ek川十 0・
Ekin二五ωーの -EB.
The component parallel to the surface of the wa¥'e vector of an electron of the Bloch
state in the crystal kll is cOllserved when this electron is photoexcited ancl escapes from
the surface， so that
PII/tL = KII竺 kll+G1卜
Here P is the mornentulll of the photoelectroll in the ¥'aCUUIllう K is the wave vecto1' of
the photoexcitecl electron and G is a recipr・ocal¥vave vector. Thereforeぅ onehas
K l l 二 | PIII/n， = j(ρ2わ仇川1υ川I川νiげ/hf的‘2つ之つ)E川川i山II
=v山山(ρ2川 hが的内2つ引)(1iんWωJ- (t) 一 Eιβ川)川司山n
Detcrmination of thc perpenclicular rnomellt Ulll Kム islllore complicated because thc、
perpendicular component is not conserved through the sllrface. In the free-electron
final-state model， the dispe1'sion rclatioll of tl日 白 川1statc (a photoexcited state in the
crystal) is assur凶 clto be that of a free dectwn:
EJ = (n，2/2rn*)K2 -IEolぅ
where m* is the effective massう forwhich the f1'伺-electron-massm is usually employecl.
Thereforeう
Kょ=再亡ki= V(2叫が)(Ekin+ゆ+IEol一 Eω1Il山I
=v山山(ρ2m/nが的2つ)(Eki川ぽB+Vo川)
39
i日1(い1('¥門州、守引J'(刊(い、¥， 1町()バ(二 IEιoバ|十 φ ¥s 討 th( 、i山11川11山11山1('ド'r1ド)()tれ仲川p門】11川lけ山山t¥川¥e礼刈1吐1. Th肘r川川p円円叩B可rれ唱'(、礼川[('、 討川川ド門門¥¥'1"<
HO¥¥"(，刊B刈¥'('川川、可マr、¥， fo仇)r、0Il(' 冶 or tW(トdi !tlPIlSiOllal S¥'st PIll日， ¥H' c!o Ilot haw' to c!eれも1・mIlw it， 1)('cλuおい
tlJ(' balld disp(~rsion Ei(k) d川討lIotc1<'JH'lld (川 Kょ
TIGa Te2 has a TISト t.¥l><'O!H'-dilll('J[siollλ1 str1¥ctur<¥()f ¥y!tich t如、 el円'tronic日truc・-
tUl・('¥¥・oulclal日o]w expect(刊11.0 ])(' Ollいーdi¥ll('Jlsiollal.¥¥・e¥l [('孔自I!r('c!.:¥n PES speぐtraaloll只
k 三 k!1 + k 上、when、kl: ¥¥'1討 takell eit hf'r 1 川 I 孔11 ドl 川 l刊)川r川{い川川‘守叶叩l川印Iい)附)('¥円刊〉斗IldiClれ.叱1山 rto t h(附C(ト-a削X引抗 (円1口W山¥'(、
(eλ川dlt什!t('川(い、市刊刊w行Sfド一λ、a削川n礼川l附主引刊III山11('川('可II川ltS討 "k:. 11 (〆'0う a川川Il川d ..~川11 上 {通Jぺ?
(川)汁fTIG孔汀T匂 凶 tけ山山lw、 (11 0) 引l山(，<'， kll ¥yhiCh is pal孔lle1 t () t 11<' c-axis 人11 11 c) is lllapp刊 l
()¥山) thr r -，¥-HドMωthpX-l不 P-H三Xline ill th(、srillo1¥inZO肘 (sZ)for the bc州(
(刊川p円n山u、'¥附1 t ('什t叫 O 川 1 (bct) la州tけtice、 ()lItけ]1('(υ)此川油tけ山her]1<::凶削<1¥日nd，ki丸i，¥¥巾ich is 討 p斤則e引rp('川(ド川川川、可川I日肌¥(仙:1¥日l山r 1，0 the
bA v W
ctk-ii X
σ/ ど¥-?;;Y
Figu刊 4.4:Brillouill zo肘 fortlH' ]州
Figurc 4.5討how日 AnPESSj)(、，tra ill t Iw CIl tire ¥.孔leIlC('-band regioll a t 22 K PλIlf' ls
(λ) alld (b) are 1l18aSUfed川0開 kll 11 c a川 kll上 r:， resp代 tively. ¥¥'モ canc:lcarl.v spド
clisp町出iH:featur何 for both anλ11 ge 1lI('I!竹. ¥礼Vアebλyマ(υ) obta孔IIH、刊叶dth('、('xl)('円nme叶nta]ba剖¥H川d l
S叶tn町 tu川 frOJ
(れdり)Oll t he日開ysω!e. ¥¥'Cぐansee fonr banc!s at t!J(' ZOlleぐれnteraround E B 二 1， 2う 4
ancl 6 eV. These h孔ndsλresymmetri， with re自pectto the 7:one ceIltel¥mぞaningthat
the dispersions correspond to the intrinsic・bandstrudnre of TIGaTe2・
40
0
4EB
4EE
0
41
4E'
210
00
2
kll 11 c 22 K
--‘、CI"J
司炉-
c コ.0
_100旬、ー〆〉
同炉・d
CI"J r-
. 1100 2 r-
200
300
00
。8 6 4 2
Binding Energy (eV)
(ω=zコ.2』C)〉一一切戸」む吉
2
BindinC) EnerC)y (eV)
o 1 Mornenturn " Jt
刈斗
(〉
ω)kFa』む乙川出。
c一32一白
2 o 1 Momentum/π
4
(〉
ω)』河口』
ω己出。
c一百三回
8
Figure 4.5: Angle-resolved photoemission spectra in the entire valence-band region of
41
TIGaTe2・
figlll・(、 -1.Gs!to¥¥'Sヘnrcs叶)(け lパ!!(川l't J 1<、 l了(，rtlliJ('¥'('1. ¥¥'p， IlWaS¥ln刊It hesrお1)(、(・t!，¥
礼Jon巴kll[[ C 礼Ildkl ..l (パr22 I¥:パnd300 T¥:， For hoth arrangelllellts， ¥刊川l刷、
討!tiftsof thc bλ!Hいl川、t¥¥'(中11SP(、ct!，¥tak(，lI at diH'(、1'('11t (C'lllperat.me， The ¥乱lE'I1C巳 bands
れ!'(、l'igicllyshift.代It，o Jo¥V円|〉llkilllxiTIPI-21円¥¥'h(、11t Jl(、temperatureis decreased， This
rλ11 be explain('d hv礼 dO¥¥'I1¥¥'ardsJ!ift of t.h(、Fl'rtnilevel. Sincfふ TIGaTe2isλ ρ-t.ype
日('111icond ¥1ぐtOI'，川 th(、10¥¥'¥(、!1I1)(、l川 I!['(、theF(，l'lui I(、円、1is pillllrcl I!('ar the accept<、1・J(、¥'(']
¥¥，11 ich is u日tallyloc・川edb(、1m¥'thr Illidcll(、()f t!t(、 band g孔p，At high temperatun¥川 t h(、
Fel'mi levt~ \ is shifted towal・d計七h('ll1iddl(、01't ¥1<' band gap， Snrprisingly， w町eob討p円r崎、吋¥'rdl
(けl怜ぞ伺arba川a出nddi凶sp斤川川p円円rSl唱
obs舵ser引TVccld お叫p冗erslO凶 al日(、rv O，G e凶Van町nd"へrv 0，5 eV for kll [1 c and kll l.. c， resp 州 ivpl 戸
Fl川 hermore，the top of t he valen何 bandbecornes nearest to EF not. for kll [[ C but fOl
kll上仁 Frornthese facts， th(' one-dirnrllsionality of TIGaTe2 turns out to be doubt.fu1.
Rather， perpendiculれ1・ clirectionmight he more concluctive as in TlSe， The chemic;:t¥
bond model proposecl hv :¥IooserれndPearson [4，15]lead to the 0肘 べ
TIGaTe句2because th(' 、top of ¥'司叫ale刊11('('、b，礼川1口Il(川d¥V孔柿sas日surne何dtωo be largely cont廿n出bχ川u川1此tedf仕ro】III ]日l
T16sヲstates，although actually the top of ¥'alellce band is contributed from Te 5]) sta(何.
This will be discussecl in more detail ill t he next. s('ction，
42
RTI k// i c IRT
一.... 向~
... 崎、、
+U・~c
コ コD 4コ
~ ~
C1J C1J )
)
〉、・4ー・4CJ) c 4。-d
c
|TIGaTe21
2.0 1.0 0 Binding Energy (eV)
(
喝U・2c コ
4コ 正コ~ ~ C1J fぢ
) )
4〉-d、4〉幽・4、CJ) c 4ω ・dC
2.0 1.0 0 Binding Energy (eV)
、‘‘，，，
vv
nuou
，，s，‘‘、
vy
nuu
vi
Dm
イ
l
E」門
uunH
nUAU
2n
RU
2.0 1.0 0 Binding Energy (eV)
Figure 4.6: Angle-resolved photoemissioll spectra near the Fermi level.
4:3
|TIGaTe21
0.0
〉
~0.5 〉、
ol
~ 1.0 μJ
ol
長1.5c
∞ 2.0
2.5
0.0
〉
旦0.5〉、
ol
~ 1.0 μ」
ol
毛1.5C
∞ 2.0
2.5
O
Momentum /7r
2
(ー1，-1) (0，0) (1，1) (2，2)
Momentum /7r
〉
旦0.5〉、
ol
~ 1.0 は」
ol
告1.5C
∞ 2.0
2.5 。 2
Momentum /π
1-1，-1) (0，0) (1，1) (2，2)
Momentum /π
Figure 4.7: Expcrirnclltal band stnlctllrp of T1GaTE'2 Ilear the Fermi levcl.
-l4
4.3.3 Band-structure calculation
III ordc1' to intcl'pret thc UPS rcslIltsプ¥¥'(、Itawpい1'fol'lllcc!balld-st1'uctur巳 calculation
for TIGaTe2' This calいculati山onh;:孔川l防汚 bc ぞ白11 Ciλ川川l日げlTI忙ed0¥川l刊till thc、locaιl卜-べ寸dl'引、'll凶印S幻It句yapprox泊i山ma仕-
tiOll (LOA) u凶山S臼l叫I
au喝g附 ntecl-plane-wave(LAPW)則、thod [U8]. Thc LλP¥¥' basis illdlldes 1山 newaves
with a 8-11)' ω to 百(rv 80 LAPW's/ atolll) iλ川仙II川ll(川d只叫叩lいμ)汁hc川(ο、'1口IC仁Uω:i¥孔ιl
i山n凶凶S釘idethe mllf而f自in-tinsphe引re白s.The C l'~ 叶 allillt、charge clCllsity ancl potelltial have been
expanded llsillg rv 5700 pla肘 waves(35 11y c川 off)in the in tersti t凶1'egionand lattice
harmonics ¥山hlmux = 8 insidc the mu任in-tinsphe1'es (RT1 rv 3.14 a.u.， RGa rv 2.36 a.u.，
RTe rv 2.66 a.ll.). Brillouin-zone (BZ) integl'atio凶 lω'e山 lizecla 12 puint k sample
in the 1/16 ir川1'e任吋CI山l
the Wi氾gner凶n川t加e白r叩'p卯凶O叫la瓜山ti山onformula [4.19判].The a剖叫t正O訓oω)江ml
and Te (5s2 5p4) states were treated as vale町 eelectrons in this study whereas the more
tightly bound levels were included via a f1'uzen-co1'e app1'oximation.
The results are shown in Figs. 4.8ラ 4.9and 4.10. Figure 4.8 shows band dispersions
in the entire valence-band region. The bands at -16 e V are mainly cuntributed from Ga
3d electrons， the bands at -11 eV from Tl5d and Te 5δelectrons， the bands from -7 e V
to -4 e V from Tl 68 and Ga 48 electrun爪削ldthe bands f1'om -4 eV to +2 eV from Te
5p electrons. Figure 4.9 shows band dispe1'sions nea1' the Fermi level. The four (Tl，Ga)
8 bands and the ten Te 5p bancls a1'e occupied. The bancl gap seems to uccur within
the Te 5p bandsう whichis 1'ather inte1'esting. This wiU b巳 clearer¥¥'hen one sees the
calculatecl DOS shown in Fig. 4.10. This rneans that the ionic picture Tl+Ga3+(Te2-h is not valid ancl that the1'e is signi白cantcO¥'alency between the Tl ancl Ga atomsう as
inferred from the crystal structure.λs for the sellliconclucting propertiesう however，one
can see an electron pucket in the W symmetry line， ancl therefore an indirect gap is not
observed， probably due to inherent deficiency of the LOA. The tup of the valence bancl
is observecl at the M symmetry puillt (2π/αヲ0，0). This state is co山 ibuteclby about
50% Te 5px，y and by about 20% Tl 6s. Consiclering these facts， the overlap or hopping
integ1'als between the Te 5p and Tl G8 orbitals seem rather large in the tight-binding
scheme， an
45
a日¥¥"(、 rnellt iOlled a hm'(、(弘、(・-1.:3.1).Illlcgrλt in日th(、Illldfill-tillpro.i(、ctf一、dDOS frO¥Il -8
eV to E，:， 仁けhe円肝刊ヲr作7
t什11<‘ II山llte引肝rstitiaJ r口'(、glO川I日1. r¥lthougb cOlltrihlltioll frolll th(、interstitia! tで巴ionis !arge， tll(‘
¥'1.lrllce of Ga sr.eltlS to be ¥)(、[0¥¥'Gλ糾 furt!l<'r! 110n" h円九u伊 tlwb孔ttdgap SC('1l1S 10
OCC¥lt' ¥¥'ithin t}H‘T(， :3p stM('sぅ th(、va]c!tc・('of T(、州、('111日(・}OS(，1"to T("-rcuhe1" th九IlT戸一.
46
|TIGaTe21
(〉の)kAO』
ωC凶
-10卜|…ー……1........ ・e・....1...山 … |
iiiiii 漁j i j i l --j : i i d i r i l l i i i i i i i i l i i i i i i i i i ! 1 ! i ! ' iH川d恥!II::いい恥11:いい似11川m引1111型!T!;U. j山日出ωj日問W料ii:所凶““!ド戸ぷ凶凶川"話山““両ぷ“l円ぷ出ぷι". 一….1... ・・ | ・ー ー.'・;.:二 ..1.............・・ '1Te 5s
-15tヒt"，川川"川…"
M Y X A F 八M エr A X -20
pW
Figure 4.8: FP-LAPW band structure of TIGaTe2 in the entire valence-band regioll.
47
•
-
e
•
••
•
.
・
0
.•
•
•
•
•
•
•
••
2
・
••• ・
2
. .
. .
Te 5p
O
-2
-4
(〉ω)kAO」ωC凶
TI 65 +
Ga 45 -6
.・
•
M Y X 6 「八M エr 6 X W ー8P
Figure 4.9: FP-LAP¥Y b礼ndstructul'<、 ufT1GaTe2 arolllld the Fc~rmi level.
--18
|TIGaTe21
Total
10
8
2
4
6
O 4
2
。2
ご石O
〉
ω¥ω2何日ω)ω00
O
4
2
O -8 6 4 2 O
Energy (eV)
-2 -4 ー6
Figure 4.10: Total and mu侃n-tinprojected DOS of TIGaTe2'
49
4.3.4 Conlparison between UPS spectra and band-structure
calculation.
:¥o¥¥' WC COIll]】孔r('th(、r<'討ItltSof the pxperilll(，llt.al UPS spectl礼 alldthe calclllated band
strllctme. figmes 4.11λnd -!.12日howc・omparisoll ]wtm'(，ll t he ARPES spectrλand
t h(、 calc・1l1atcdbれIldト什rllctlll・(、 Dpcれ11お(、 of t.he Illlcprtainty ill k.l.. ・ ¥¥で have plotted
(礼 I(・Illat収 In~ slll ts h川 h 川0 11民 x-~ -r-.¥-H-V-M 川 lclM-Y-X-W-P-W-.¥. Bcc<l.IIsP llO¥¥'
¥¥"(-' kno¥V t hat ¥¥"(' callnot ne日l('ctthe k上 depぞnclc、nceof the ('ll('rgy bancls of TIGaTe2ぅ
¥¥'P must ('討timatedominant k.l.. ¥'alucs ill the ARPES spれctra. In orcler to c¥o thおう
¥H' have 去しちsumedthr val1H、 of the inner potential to be 14 e ¥.'， which is 九norclinarv
¥'alue [4.16]. Then tl開 sampleclk poi川sin the BZ are sh(川 1in Fig. 4.13 accordingω
the free-electroll final-statp moclel (SeC'. 4.3.2). Near the Fermi level， samplecl k points
are almost along the X-W-P-W-X ancl X-Y-Mlines， so that the experimental dispersion
curve agrees welいviththe C礼lculateddispersion along this line. On the other handう at
high binding energies， sampled k points become near the r -A-H-V-l¥イandr-ムーXlinesう
so that t.he experiment.al dispersioll curves rather agree with the clispersions along these
lines. 1n fact， t.he kょsel町 tionrulc is only approximate and the ARPES spectra have
been integrated with r('spect to /，;.l.. arollncl the "sampled k points" to some extent，
and thereforぞ k'salong high symmetry lines contribute to the ARPES spectra most
slgm白cantly
50
2 .-‘、
〉ω 、、--
〉、
0L-3 。c 斗J
0> 4 C
てコC
∞
O
6
8XM
A Y
A H V M w x
F X W P
Figure 4.11: Comparison of the ARPES spectra with the result of band-structure cal-
culation in the entire valence-band region.
51
0・511TIGaTe2
〉Q)
〉可。、M
0.0
0.5
El-O m C
Bけ
てづ己「寸
国
1.5
2.0
2.5 X
M
d
Y
r x W
A H V M
P w x
Figllre 4.12: Comparison of the A.RPES叶)刊:tra¥YIt.h the res1l1t of band-strllcture cal-
culation near the Ferllli levpl
52
21 M 晴寸 」話、 o M| ト.....-J~→ ~4卜.....-Jf-*ィ叫2
0
~・“・ I--*-i ‘¥
民 トタ十寸
o 卜う十イ
R ・4 トす←→o ト→←→
ト→←→x I.~ ト十 口
) 山 市占片阜」どとと ~ 卜t4 J -460
同 町ト骨→時-AO
H判明~同 ← → : 時+.0f--*--jト-t--l~ 。irI J〔l lA|||ふ.pU rI 2
Eヨ
4 5 6 3 4 5 6 7
k1-(x(π3π30))Ka (X(π， 0， 0) )
• EB = 0.0 eV • EB = 2.5 eV
企 EB= 5.0 eV x EB=10.0 eV
Figure 4.13: Sampled k points in the Brillouin ZOllC according to the free-electron
final-state model.
53
Fi広111¥' ，1. 1-1討hc)¥¥'日(・Oll1Pれnsoll 川、t¥¥'円、111 11< ~ 人TPES討p円.t1'11111 illld 111(、(λ1<-111川(可l
DOS hro孔c!el¥(可[hy九IlFlipIKY(l{、¥)(、Ild川 ltL()I'(、IItχiパ11alld il C<ll1出 lλJlf()f' t 11<、i11strlll1 1<'11-
t.al reおりIlltioll.¥¥'8 call sce自"('叫1・lldll]，('s(lalH'lr、d;¥s λ-E) ill 11](、λIPE円spectlillJl. ¥Ve
con日iderthat these strllctlll・esill t h ('λIPr:月刊p(刊、tl'11tncorrcspolld to str¥lctnrいお illtll('
The str¥l('t 111・円 D 川 IdE， ¥¥'hiけlれ['(、c:al(・11latedDOS川 indi('atcd¥)¥' t!J(、r!ilS!t(可II ilH明
maillly C()llt rihut8d from TI G匂 alldCi¥ -1巧 st川 ('S.;¥日re('¥¥'(，11 ¥)(寸¥¥，('('11t 11<' eXj)(、rillleJltal
l'e日ultsλlIdthe calι・ltlatedn市111t日.¥¥・llil(、1I ¥(、rcパ¥'('sorrw d iS(T(、l川1I('J(、計 1)('1¥¥'(、ド1I the ex-
pnimental result丹市ldth(、(・λI(・nlれれマ[]'(明Illtsill t!Je regioll of叶 1'11<・tlllTSλ:s and C，
which九rellIainly ('olttribut刊[fl'Orn Te ')11 st川何
|TIGaTe21
AIPES
(的一二口口
~C
iD
パUe
-----E'・0
・削.，.as
ひ
O
恥
unυ
-(七市)hua円一山口一Uμじ円
O 2 4
Binding Energy (eV)
6 8
Figun、4.14:COlllp九riSOllof thれ λIPESsp円 :tmITlwith t.he calcltlat(可[DOS.
54
4.4 Conclusion
We have studiccl the electronic stl'uctun、。l'TICaTc2 llsing angle-intcgl'arcd and angle-
resolved photoemission spectrosc:opy a11(1 the 1'ull-potcntial LAP¥ V bancl-stl'ucture c:al-
culation. The top 01' the valcnce band is ObSCl・¥"cd川 th(、M point ill the BZ ancl l1lainly
contributed from Te 5p states. Fl'om both stlldics.. thc、olle-climensiollality of Tl Ga TC2
becomes questionablc. COllversel.v， thc dil'刊一tiollpcrpcnclicular to thc TI chains lllay
be more conductive. Compal'ison betwcen the九H.PESspectra alld calculatecl balld
stl'ucture is l'ather l'easonable in spitc 01' thc、unccl'tainty in kょ
55
References
[4.1] D. Muller， G. E凶 nbcrger，ancl H. Hahll， Z. aωrg・allg.Chelll. 398， 207 (1973)
[4.2] M. Hanias， A. N. Anagnostopo山人 K.Kambas， and J. Spyriclelis， Phys. Rev. B
43， 4135 (1991).
[4.3] M. P. Hanias and A. ~. Anagnostopo山人 Phys.Rev B 47， 4261 (1993).
[4.4] A. Kasl刈丸山published.
[4.5] M. K. Rabinalう S.A叫泊nぅ;¥tr.O. Godazaev， N. T. Ma附 clov，and E. S. R. Gopalヲ
Phys. Stat. Solidi (b) 167， K97 (1991)
[4.6同]K. R. Allal北kl附 rd心le引¥". Sh. G. Gas句可叩y戸y守mo
E. Yu. Salaevう Sov.Phys. Semicond. 17ぅ 131(1983)
[4.7] S. Abdullaeva， and ~. ;..tlamedovぅ Tr..1. of Physicsぅ 17，568 (1093).
[4.8] N. T. Mamedov， A. :¥1. Panichぅ Phys.Stat. Solicli (a) 117う1¥15(1990).
[4.9司]F恥M.Ga剖shi廿山1lIT印I
(Sov. Phys. Semi比Cωon町吋d.15 う 757 (1981)ト川. ) )
[4.10] F. M. Gashimzadc a凶 D.G.G凶 W ぅ Phys.Stat. Solidi (b) 131， 201 (1985).
[4.11] V. A. Aliev， M. A. Aldzhanov， and S. i¥. Aliev， JETP Lett. 45， 534 (1987).
[4.12] N. Ma問
[4.13] .1. -.1. Yehand 1. Lindauヲ AtData r¥ucl. Data Tables 32ヲ 1(1985).
[4.14] D. G. Kildayぅ D.¥¥". Niles， ancl G. Marga此 ondo，Phys. Rev. B 35， 660 (1987).
57
[4.1o] E. .¥Ioos!']州 1¥¥・ 13.PearSOllぅ.J.El('ctro山日1.629 (1956). Their id州日 t!t川
Ga and Tc tttake "if? hOllds t.o fOl・mtlt<‘ (Gλ1十FLhJ2)一 IOtt礼nclthis cOlllplex ion
礼ttclt.he Tl + 1 iOtt llIake ionic honds.
[4.16] S. Hiifncr， Phofor.!echοη Spechο可COJ!!J(Sprittg(>r-Verlag;ぅ13e山 1ぅ1995)
[c1.l7] L. F. ¥I川 thei川 λlldD. l{. H礼111λllll，Pl川 n円 1333. 82.3 (1986)
[4.18] O. h. AnderSf'Il， Ph~'自 n 円. B 12う 3060(19Ti)
[4.19] E. ¥¥igner， Ph¥-s. R引・ 46ぅ 1002(1934)
58
vb r
e
4L P
a
h
c Conclusion
1ミ匂havestudied the electronic structures of one dimensional systems V02 and TIGaTe2
by means of ultraviolet photoemission spectroscopy. UPS spectra of V02 taken above
and below the metal-insulator transition temperature indicate that the electron corre-
lation e百ectis rather important both above and below the transition temperature. In
the insulating phase， the band widths of 0 2p band and V 3d band become wider as the
temperature is increased， while the bottom of the conduction band does not shift with
respect to the Fermi level. Although V02 in the insulating phase is a n-type semicon-
ductor， the Fermi level is located a little below the middle of the band gap. This can be
explained by consideration of the electron correlation e百'ect.ARPES study of TIGaTe2
indicate that the one-dimensionality of TIGaTe2 is questionable in spite of its highly
anisotropic crystal structure. 1n order to interpret the UPS results， we have performed
the band-structure calculation. The top of valence band is mainly contributed frorn Te
5p band and the direction perpendicular to the c-axis seems to be more conductive.
Comparison between UPS results and band-structure calculation is rather reasonable.
59
Acknow ledgments
Fi1'st of all， 1 would likc to cxp1'css special g1'atitude 01' Prof. A. Fujimori， who has
suggested me this ¥¥'o1'k and gi¥'ell me a lot of hclpful advice. 1 also thank Prof. T.
Mizoka¥Va， who has gi¥'eu lots of helpful achice pa1'ticularly when 1 was a undergraduate
studcnt and Dr. K. Kobayashi， ¥¥'ho has also givell lots of helpful advice particularly for
one and a half year since 1 became a graduate student. Prof. M. Onoda has provided
single crystals of V02 and given a lot of useful informations. 1 ¥Vould like to thank him
1 also would like to thank N. I¥Iamedov. ¥¥・hohas provided single crystals of TIGaTe2
and given a lot of useful informations and discussions. 1 owe my success in the band-
structure calculation to Dr. L. :¥Iattheiss. ¥¥・hohas provided program sources for our
group and given useful informations and :¥Ir. .J. Matsuno， who has taught me how to
use these sources. M1'. T. Yoshida has taught me how to deal with the photoemission
spectrometer and 1 o¥ve it to him that 1 have been to be able to measure spectra using
the spectromete1'. 1 am thallkful to ;...Ir. H. Ishii for cooperating for the photoemission
spectrometer. 1 am also gratef・ulto the members of Fujimori-groupぅ M1'. .J. Y. Son， Dr.
T. Susaki， Mr. J. Okamoto， :.-I1'. .J. Okabayashiう Mr.Y. Ishikawa， Mr. T. Nambu， Mr・-
N. Harima， and tv'Iiss. H. ¥Vakazono for encouragement.
1ょ
にU
