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Two-dimensional angular distribution of photoemission spectra from the valence band of 1T-TaS2
Journal of Electron Spectroscopy and Related Phenomena 78 (1996) 48S492
Two-dimensional angular distribution of photoemission spectra from the valence band of lT-TaS2 T.Matsushitaa, H.Nishimotoa, T.Okudaa, T.Nakatania, H.Daimona, S.Suga*, H.Nambab, T.Ohtab, YKagoshimac and TMiyaharac *Department Material Physics, Faculty of Machikaneyama, Toyonaka, Osaka 660, Japan
Engineering
Science,
Osaka
University,
bDepartment of Chemistry, Faculty of Science, The University of Tokyo, Bunkyo-ku, Tokyo, 113 Japan “Photon Factory, National Laboratory for High Energy Physics, Tsukuba, Ibaragi 306, Japan
Two-dimensional band structures of single-crystalline lT-TaS2 have been directly observed by using a new version of two-dimensional display-type spherical mirror analyzer. The intensity distribution patterns for linearly-polarized synchrotron radiation normally incident on the cleaved surface have shown unusual angular distributions. The non three-fold symmetry is discussed by considering the angular dependence of the dipole transition probability for the s-polarized synchrotron radiation from each atomic orbital with particular symmetry, as well as the tightbinding initial state and a free electron like final state. In addition, circular dichroism in angular distribution (CDAD) of the photoemission pattern from the valence band is predicted for lT-TaSr. 1. INTRODUCFION
2. EXPERIMENTAL
lT-TaS2 has various interesting physical properties originating from its layer crystal structure[l-41. TWO dimensional measurement of the photoelectrons emitted from the valence band by an ultra-violet light is powerful to obtain the information on the electronic energy-band structure. We have measured the two-dimensional pattern using linearly-polarized synchrotron radiation. We have also calculated the optical transition probability by using the LCAO initial state and a free electron like final state, in order to predict the two-dimensional photoelectron pattern.
The experiment was performed on the beamline BL-7B of the Photon Factory of the National Laboratory for High Energy Physics. The measurement was done at the photon energy hv =22eV by using a two-dimensional display-type spherical mirror anaIyzer[6]. The degree of the linear polarization was higher than 90%. All measurements were performed at room temperature with the s-polarized light (E I taxis) in the normal incidence conf5guration. The two-dimensional photoemiasion patterns were measured at different kinetic energies. Clean surface of the sample was obtained by in situ cleavage in a preparation chamber with a vacuum better than 1 X 10-BTorr. The cleaved sample was immediately transferred
0368-2@48/%/$15.00 0 1996 Elsevier Science B.V. All rights reserved P/I SO368- 2048 (%) 0278 1-8
490 into
an
analyxer chamber.
3. RESULTS AND DISCUSSION J?igures la-c show the observed twodimensional photoelectron patterns. The polarization of the incident light is in the horizontal direction in Fig. 1. Characteristic features do not show the three-fold symmetry. AB &I $zeases, the strong intensity in the center expands outward. From these results, one can estimate the energy dispersion of the observed bands two-dimensionally. If the patterns are compared with the result of the band calculation[6] shown in Fig. 2, the signal moves with binding Which outward energy(W) is ascribed to the Ta Usband and the signal in the central region of the twodimensional pattern in F’ig.lc is ascribed to the S 3p state.
M
r
M
K
Figure 2. Valence band of lT-TaSs from the LCAO calculation[6].
4. INTENSlTY DISTRJBUTION ANALYSIS In order to interpret the symmetry-broken dimensional properties of the two photoelectron distributions, we calculate the angular dependence of the transition probability from the tight-binding initial state. The Bloch functions are described as ~*Ar3=~~~~~““~*(~-~-~,).
(1)
i
where 4 is the atomic orbital with n, 2 and m quantum numbers, & is a lattice vector and ?, is the position vector of the j-th atom in a unit celL The eigenfunctions for lT-TaSc which are obtained from the band calculation are expressed by y%,r3
= ~&(@%Jq’,fi
(2)
-
IAh where h is the index of the band and &(a)
the eigen vectors associatedwith
is
ij.
Here we express the dipole matrix element M for the initial state i given by (2) as M=(fi(F)~.zji), (3) where f#)
(4 Figure
1. Experimental
photoelectron
patterns.
(b)w=O.‘leV, (c) W=1.2eV.
two-dimensional (a)W=O%V,
is a &ra.l state which is a Bloch
function with a wave vector k’. As the momentum of photon is much smaller than the size of the Brillouin xone (BZ) of lT-TaSz,
491
it is neglected in the present paper. A4is calculated by employing eq.(2) as M=(fi(r’)lj.+Q,?))
(4)
Here 8 is the reciprocal lattice vector. The Kronecker delta tells that i can be written as
shown in Figs.3a-c. The calculated results are with qualitative agreement the in experimental results. The calculation shows only one mirror symmetry. The symmetry line is the horizontal line passing through the center of the 1st BZ. This symmetry is caused by the coincidence of the symmetry planes of the crystal and the electric dipole operator.
q’=g-G.Thenweget
(I? can take a single value in an extended zone scheme, and 6 is taken in the 1st Brillouin zone here. Then 5 is dropped here after. Hence the intensity expressed as
=F
distribution is
(4
(8)
l~~cnM,ciqs(E,cn-~~~~-~-~~).
M”(i) = (r,(~*+.L(~) Here M,($)=&~-d*-‘J. The term
and of
energy
conservation becomes a Lorentxian function because of the life time broadening. The term M”@) represents the photoelectron angular distribution from the atomic orbital[7,8]. Here we have assumed that the final state is a free electron like outside the muEn tin sphere of the atom which emits the photoelectron, and expand f#) as I&(?)) = 4~~(i)“e-‘3’I;‘,(B,-,d,-)Y,,(B,0G,(r) lw
(9)
by means of partial wave expansion. The term M,(Z) is called “photoemission structure &tor”[9] and is very important for an interference of photoelectron waves from nonequivalent sites. Using this formula, we have calculated the two-dimensional photoelectron patterns as
(4
Figure 3. Two-dimensional photoelectron patterns by calculation. (a)W=OSeV, (II) &=0.7eV, (c) W=l&V. 5. CIRCULAR DICHROISM We have also calculated the photoelectron distribution patterns for the excitation by the circularly polarized light. The results are shown in Figs. 4a-c. Figures 4a and b show the two-dimensional photoemission distribution for the left and right helicity lights respectively. Figure 4c is their difference which is called circular dichroism in angular distribution(CDAD). The amount
492
of CDADie about 1% of the total intensityand vankhe8 along the high symmetry lines such as the mirror symmetryof the crystal. In order to elucidate the origin of the CDAD,we have hrst calculatedthe pattern by considering the Ta Sd+f optical transition only (other optical traneitionprobabilities are aesumed to be zero.) and found that CDAD disappears. The pattern calculated for the Ta Sd+sp transition neither exhibita CDAD. When we coneider both hf and d+p tran8ition8,the pattern 8hows CDAD. Thu8 CDAD ie caused by an interf&rencebetween &rent &am&ion8 to M states with difbrent symmetries. Although such an interference can&8 out in an angle integrated measurement, a 8ub8tantial interferenceis predicted for the fin& time to
appear in the angle-resolvedmeaeuwment. 6. CONCLUSION We have obeeroed the energy contour8 of the two-dimensional bands of eingle crystal lT-TaSz. The pattern8 at variou8 binding energies have shown unu8d photoelectron dktribution pattem8. Theee prominent features are well unde&ood by a model includingthe tight-bindinginitial etate and a fkee electron like m state. The non threefold symmetry ie primarily understood a8 the reek&of the angukr dependenceof the dipole transition probabiIity i?om the initial state atomic orbital with particular symmetry for the e-polarized radiation. In addition, a CDAD of photoemission pattern &om the valence band ia predictedfor the fi& time.
1. 2.
(a)
3. 4. 6.
R.L.Wither8 and JAWiI8on, J.Phy8.C 19 (1966) 1309. R.Manzke,OAnderson and M.Skiboweki, J.Phys. C 21(1966)2399. S.Tanda, T.Sambongi, T.Tani and S.Tanaka,J.Phys.Soc.Jpn.52 (1964) 476. W.Han, R.A.Pappas and E.R.Hunt,Phys. Rev. B 46 (1993) 3466. H.Daimon, Rev.Sci.In&r. 59 (1936) 646, ibid 61(1990)206.
6. 7.
8. Figure 4. Two-dimensional photoelectron pattern8 for circularly polarized light excitation. (a) Q3=0.7eV pattern for left helicie light, (b) for right helicity light, (c)difference(&rcuIardichroi8m) between (a) and (b).
9.
L.F.Mattheiee,Phy8.Rev.B8(1973) 3719. S.M.Goldberg, C.S.FadIey and S.Kono, J. Electron Speck. ReIat. Phenom. 21 (1981) 286. J.W.Gadzuk, Phye. Rev. Bl2 (1976) 6608. s.suga, H.Daimon, H.Ni&imoto, S.Imada, T.Mateushita, T.Nakatani, H.Namba, T.Ohta, YXago8hima and TMiyahara, J. Electrion Speck Relat. Phenom. (in print).
Two-dimensional angular distribution of photoemission spectra from the valence band of lT-TaS2 T.Matsushitaa, H.Nishimotoa, T.Okudaa, T.Nakatania, H.Daimona, S.Suga*, H.Nambab, T.Ohtab, YKagoshimac and TMiyaharac *Department Material Physics, Faculty of Machikaneyama, Toyonaka, Osaka 660, Japan
Engineering
Science,
Osaka
University,
bDepartment of Chemistry, Faculty of Science, The University of Tokyo, Bunkyo-ku, Tokyo, 113 Japan “Photon Factory, National Laboratory for High Energy Physics, Tsukuba, Ibaragi 306, Japan
Two-dimensional band structures of single-crystalline lT-TaS2 have been directly observed by using a new version of two-dimensional display-type spherical mirror analyzer. The intensity distribution patterns for linearly-polarized synchrotron radiation normally incident on the cleaved surface have shown unusual angular distributions. The non three-fold symmetry is discussed by considering the angular dependence of the dipole transition probability for the s-polarized synchrotron radiation from each atomic orbital with particular symmetry, as well as the tightbinding initial state and a free electron like final state. In addition, circular dichroism in angular distribution (CDAD) of the photoemission pattern from the valence band is predicted for lT-TaSr. 1. INTRODUCFION
2. EXPERIMENTAL
lT-TaS2 has various interesting physical properties originating from its layer crystal structure[l-41. TWO dimensional measurement of the photoelectrons emitted from the valence band by an ultra-violet light is powerful to obtain the information on the electronic energy-band structure. We have measured the two-dimensional pattern using linearly-polarized synchrotron radiation. We have also calculated the optical transition probability by using the LCAO initial state and a free electron like final state, in order to predict the two-dimensional photoelectron pattern.
The experiment was performed on the beamline BL-7B of the Photon Factory of the National Laboratory for High Energy Physics. The measurement was done at the photon energy hv =22eV by using a two-dimensional display-type spherical mirror anaIyzer[6]. The degree of the linear polarization was higher than 90%. All measurements were performed at room temperature with the s-polarized light (E I taxis) in the normal incidence conf5guration. The two-dimensional photoemiasion patterns were measured at different kinetic energies. Clean surface of the sample was obtained by in situ cleavage in a preparation chamber with a vacuum better than 1 X 10-BTorr. The cleaved sample was immediately transferred
0368-2@48/%/$15.00 0 1996 Elsevier Science B.V. All rights reserved P/I SO368- 2048 (%) 0278 1-8
490 into
an
analyxer chamber.
3. RESULTS AND DISCUSSION J?igures la-c show the observed twodimensional photoelectron patterns. The polarization of the incident light is in the horizontal direction in Fig. 1. Characteristic features do not show the three-fold symmetry. AB &I $zeases, the strong intensity in the center expands outward. From these results, one can estimate the energy dispersion of the observed bands two-dimensionally. If the patterns are compared with the result of the band calculation[6] shown in Fig. 2, the signal moves with binding Which outward energy(W) is ascribed to the Ta Usband and the signal in the central region of the twodimensional pattern in F’ig.lc is ascribed to the S 3p state.
M
r
M
K
Figure 2. Valence band of lT-TaSs from the LCAO calculation[6].
4. INTENSlTY DISTRJBUTION ANALYSIS In order to interpret the symmetry-broken dimensional properties of the two photoelectron distributions, we calculate the angular dependence of the transition probability from the tight-binding initial state. The Bloch functions are described as ~*Ar3=~~~~~““~*(~-~-~,).
(1)
i
where 4 is the atomic orbital with n, 2 and m quantum numbers, & is a lattice vector and ?, is the position vector of the j-th atom in a unit celL The eigenfunctions for lT-TaSc which are obtained from the band calculation are expressed by y%,r3
= ~&(@%Jq’,fi
(2)
-
IAh where h is the index of the band and &(a)
the eigen vectors associatedwith
is
ij.
Here we express the dipole matrix element M for the initial state i given by (2) as M=(fi(F)~.zji), (3) where f#)
(4 Figure
1. Experimental
photoelectron
patterns.
(b)w=O.‘leV, (c) W=1.2eV.
two-dimensional (a)W=O%V,
is a &ra.l state which is a Bloch
function with a wave vector k’. As the momentum of photon is much smaller than the size of the Brillouin xone (BZ) of lT-TaSz,
491
it is neglected in the present paper. A4is calculated by employing eq.(2) as M=(fi(r’)lj.+Q,?))
(4)
Here 8 is the reciprocal lattice vector. The Kronecker delta tells that i can be written as
shown in Figs.3a-c. The calculated results are with qualitative agreement the in experimental results. The calculation shows only one mirror symmetry. The symmetry line is the horizontal line passing through the center of the 1st BZ. This symmetry is caused by the coincidence of the symmetry planes of the crystal and the electric dipole operator.
q’=g-G.Thenweget
(I? can take a single value in an extended zone scheme, and 6 is taken in the 1st Brillouin zone here. Then 5 is dropped here after. Hence the intensity expressed as
=F
distribution is
(4
(8)
l~~cnM,ciqs(E,cn-~~~~-~-~~).
M”(i) = (r,(~*+.L(~) Here M,($)=&~-d*-‘J. The term
and of
energy
conservation becomes a Lorentxian function because of the life time broadening. The term M”@) represents the photoelectron angular distribution from the atomic orbital[7,8]. Here we have assumed that the final state is a free electron like outside the muEn tin sphere of the atom which emits the photoelectron, and expand f#) as I&(?)) = 4~~(i)“e-‘3’I;‘,(B,-,d,-)Y,,(B,0G,(r) lw
(9)
by means of partial wave expansion. The term M,(Z) is called “photoemission structure &tor”[9] and is very important for an interference of photoelectron waves from nonequivalent sites. Using this formula, we have calculated the two-dimensional photoelectron patterns as
(4
Figure 3. Two-dimensional photoelectron patterns by calculation. (a)W=OSeV, (II) &=0.7eV, (c) W=l&V. 5. CIRCULAR DICHROISM We have also calculated the photoelectron distribution patterns for the excitation by the circularly polarized light. The results are shown in Figs. 4a-c. Figures 4a and b show the two-dimensional photoemission distribution for the left and right helicity lights respectively. Figure 4c is their difference which is called circular dichroism in angular distribution(CDAD). The amount
492
of CDADie about 1% of the total intensityand vankhe8 along the high symmetry lines such as the mirror symmetryof the crystal. In order to elucidate the origin of the CDAD,we have hrst calculatedthe pattern by considering the Ta Sd+f optical transition only (other optical traneitionprobabilities are aesumed to be zero.) and found that CDAD disappears. The pattern calculated for the Ta Sd+sp transition neither exhibita CDAD. When we coneider both hf and d+p tran8ition8,the pattern 8hows CDAD. Thu8 CDAD ie caused by an interf&rencebetween &rent &am&ion8 to M states with difbrent symmetries. Although such an interference can&8 out in an angle integrated measurement, a 8ub8tantial interferenceis predicted for the fin& time to
appear in the angle-resolvedmeaeuwment. 6. CONCLUSION We have obeeroed the energy contour8 of the two-dimensional bands of eingle crystal lT-TaSz. The pattern8 at variou8 binding energies have shown unu8d photoelectron dktribution pattem8. Theee prominent features are well unde&ood by a model includingthe tight-bindinginitial etate and a fkee electron like m state. The non threefold symmetry ie primarily understood a8 the reek&of the angukr dependenceof the dipole transition probabiIity i?om the initial state atomic orbital with particular symmetry for the e-polarized radiation. In addition, a CDAD of photoemission pattern &om the valence band ia predictedfor the fi& time.
1. 2.
(a)
3. 4. 6.
R.L.Wither8 and JAWiI8on, J.Phy8.C 19 (1966) 1309. R.Manzke,OAnderson and M.Skiboweki, J.Phys. C 21(1966)2399. S.Tanda, T.Sambongi, T.Tani and S.Tanaka,J.Phys.Soc.Jpn.52 (1964) 476. W.Han, R.A.Pappas and E.R.Hunt,Phys. Rev. B 46 (1993) 3466. H.Daimon, Rev.Sci.In&r. 59 (1936) 646, ibid 61(1990)206.
6. 7.
8. Figure 4. Two-dimensional photoelectron pattern8 for circularly polarized light excitation. (a) Q3=0.7eV pattern for left helicie light, (b) for right helicity light, (c)difference(&rcuIardichroi8m) between (a) and (b).
9.
L.F.Mattheiee,Phy8.Rev.B8(1973) 3719. S.M.Goldberg, C.S.FadIey and S.Kono, J. Electron Speck. ReIat. Phenom. 21 (1981) 286. J.W.Gadzuk, Phye. Rev. Bl2 (1976) 6608. s.suga, H.Daimon, H.Ni&imoto, S.Imada, T.Mateushita, T.Nakatani, H.Namba, T.Ohta, YXago8hima and TMiyahara, J. Electrion Speck Relat. Phenom. (in print).