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Two-dimensional Van Hove singularity in TaS2 band structure
Volume 41A, number 3
PHYSICS LETTERS
25 September 1972
TWO-DIMENSIONAL VAN HOVE SINGULARITY IN TaS2 BAND STRUCTURE A. COUGET, L. MARTIN, F. PRADAL Laboratoire de Physique des Solides *, Universite’Paul Sabatier, Toulouse, France
and R. NITSCHE Kristallographisches Institut der Universitiit Freiburg i. Br., Germany
Received 18 July 1972 The transverse optical properties of a number of transition metal dichalcogenides have been studied in the - 12 eV range. For TaS,, a two-dimensional Van Hove singularity clearly appears at 7 eV in good agreement with the saddle point case. 2 eV
In previous papers [l-4] , the optical properties of some layer structure transition metal dichalcogenides have been reported. They covered the 2 eV - 12 eV tange and were deduced from nearly normal incidence reflectivity data using a Kramers-Kroning analysis. Among the eight different dichalcogenides we have studied (TiS2, TiSe,, VSe2, NbSe2, TaSe,, TaS,, MoS,, MoSe,) we distinguish the general case, and the peculiar case of TaS,. The optical properties are in the general case characterized by a rather smooth variation of the reflectivity for photon energies below 6 - 7 eV. In the 7 eV region, the reflectivity decreases sharply, then it increases slowly and has again a smooth variation. As expected, the computed e$ function has about the same variation as reflectivity, and the transverse energy loss function shows a well marked peak around 7 eV, known as the low energy plasmon peak and analogous to the n-electrons plasmon peak for graphite. The TaSe, is a good example of this general case. In the case of TaS,, the reflectivity starts decreasing at 2 eV till about 5 eV, so-that the low energy plasmon is shifted to lower energy. Moreover, the reflectivity is increased by a factor of about 2 between 6.5 eV and 7 eV. The real part and the imaginary part of the computed transverse dielectric function show a sharp peak in the region of the abrupt increasing of reflectivity. The energy loss function shows a very narrow dip. The width of this dip is less * Associd au C.N.R.S.
Fig. 1. TaSea and TaS, reflectivity curves.
than 0.5 eV, too weak to be observed in the electron energy loss experiments [ 5,6] . We have compared our results with mathematical models for several Van Hove singularities. We conclude that a two-dimensional saddle point in the band structure is at the origin of the observed structure. To our knowledge, TaS, is the second layer-type crystal, after graphite [7-lo] in which such a feature is clearly identified. 261
Volume
4 1A. number
PHYSICS
3
LFTTERS
25 September
1972
I
.6’
I
I
2
L
6
8
Fig. 2. TaSe* and TaSz transverse
I
10
energy
1
E ev
loss functions.
-21 Fig. 2. TaS,
complex
dielectric
transverse
function
References D.L. Greenaway and R. Nitsche, J. Phys. Chem Solids 26 (1965) 1445. I21 J.A. Wilson and A.D. Yoffe, Advances in Physics 18 (1969) 193. 131 A. Couget. L. Martin and F. Pradal, C.R. Acad. SC. Paris 272, sdrie B, (1971) 626. [41 L. Martin, A. Couget and F. Pradal, CR. Acad. SC. Paris 273, strie B, (1971) 873. S.L. Cundy. Phil. Mag. 19 (1969) 1031. I51 W.Y. Liangand [61 R. Vilanove, Thbse Paris 197 1. 171 EA. Taft and H.R. Philipp. Phys. Rev. 138 (1965) A 197 Nuovo Cimento I81 F. Bassani and G. Pastori Parravicini. 50B (1967) 95. G. Harbeke, F. Bassani and I:. Tosatti. 191 D.L. Greenaway, Phys. Rev. 178 (1969) 1340. 1101 E. Tosatti and F. Bassani, Nuovo Cimento Ser. X, 658 (1970) 161.
Ill
1, 2 and 3 show the experimentally measured reflectivity curve, and the variation of the computed dieletric and energy loss functions of TaS,. In figs. 1 and 3 we have also drawn for comparison the reflectivity and the energy loss function of TaSe,. The crustals were grown by iodine vapour transport in a gradient 850” - 750”. The smples were easily cleaved by pealing them with adhesive tape. This operation, when repeated, seems to damage the surface. The curves here shown have been obtained after the first cleavage. After two or more cleavages, the variation of reflectivity is weakened, but the positions of the singularities are not altered. Figs.
262
PHYSICS LETTERS
25 September 1972
TWO-DIMENSIONAL VAN HOVE SINGULARITY IN TaS2 BAND STRUCTURE A. COUGET, L. MARTIN, F. PRADAL Laboratoire de Physique des Solides *, Universite’Paul Sabatier, Toulouse, France
and R. NITSCHE Kristallographisches Institut der Universitiit Freiburg i. Br., Germany
Received 18 July 1972 The transverse optical properties of a number of transition metal dichalcogenides have been studied in the - 12 eV range. For TaS,, a two-dimensional Van Hove singularity clearly appears at 7 eV in good agreement with the saddle point case. 2 eV
In previous papers [l-4] , the optical properties of some layer structure transition metal dichalcogenides have been reported. They covered the 2 eV - 12 eV tange and were deduced from nearly normal incidence reflectivity data using a Kramers-Kroning analysis. Among the eight different dichalcogenides we have studied (TiS2, TiSe,, VSe2, NbSe2, TaSe,, TaS,, MoS,, MoSe,) we distinguish the general case, and the peculiar case of TaS,. The optical properties are in the general case characterized by a rather smooth variation of the reflectivity for photon energies below 6 - 7 eV. In the 7 eV region, the reflectivity decreases sharply, then it increases slowly and has again a smooth variation. As expected, the computed e$ function has about the same variation as reflectivity, and the transverse energy loss function shows a well marked peak around 7 eV, known as the low energy plasmon peak and analogous to the n-electrons plasmon peak for graphite. The TaSe, is a good example of this general case. In the case of TaS,, the reflectivity starts decreasing at 2 eV till about 5 eV, so-that the low energy plasmon is shifted to lower energy. Moreover, the reflectivity is increased by a factor of about 2 between 6.5 eV and 7 eV. The real part and the imaginary part of the computed transverse dielectric function show a sharp peak in the region of the abrupt increasing of reflectivity. The energy loss function shows a very narrow dip. The width of this dip is less * Associd au C.N.R.S.
Fig. 1. TaSea and TaS, reflectivity curves.
than 0.5 eV, too weak to be observed in the electron energy loss experiments [ 5,6] . We have compared our results with mathematical models for several Van Hove singularities. We conclude that a two-dimensional saddle point in the band structure is at the origin of the observed structure. To our knowledge, TaS, is the second layer-type crystal, after graphite [7-lo] in which such a feature is clearly identified. 261
Volume
4 1A. number
PHYSICS
3
LFTTERS
25 September
1972
I
.6’
I
I
2
L
6
8
Fig. 2. TaSe* and TaSz transverse
I
10
energy
1
E ev
loss functions.
-21 Fig. 2. TaS,
complex
dielectric
transverse
function
References D.L. Greenaway and R. Nitsche, J. Phys. Chem Solids 26 (1965) 1445. I21 J.A. Wilson and A.D. Yoffe, Advances in Physics 18 (1969) 193. 131 A. Couget. L. Martin and F. Pradal, C.R. Acad. SC. Paris 272, sdrie B, (1971) 626. [41 L. Martin, A. Couget and F. Pradal, CR. Acad. SC. Paris 273, strie B, (1971) 873. S.L. Cundy. Phil. Mag. 19 (1969) 1031. I51 W.Y. Liangand [61 R. Vilanove, Thbse Paris 197 1. 171 EA. Taft and H.R. Philipp. Phys. Rev. 138 (1965) A 197 Nuovo Cimento I81 F. Bassani and G. Pastori Parravicini. 50B (1967) 95. G. Harbeke, F. Bassani and I:. Tosatti. 191 D.L. Greenaway, Phys. Rev. 178 (1969) 1340. 1101 E. Tosatti and F. Bassani, Nuovo Cimento Ser. X, 658 (1970) 161.
Ill
1, 2 and 3 show the experimentally measured reflectivity curve, and the variation of the computed dieletric and energy loss functions of TaS,. In figs. 1 and 3 we have also drawn for comparison the reflectivity and the energy loss function of TaSe,. The crustals were grown by iodine vapour transport in a gradient 850” - 750”. The smples were easily cleaved by pealing them with adhesive tape. This operation, when repeated, seems to damage the surface. The curves here shown have been obtained after the first cleavage. After two or more cleavages, the variation of reflectivity is weakened, but the positions of the singularities are not altered. Figs.
262