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Full-potential calculations of the electronic and optical properties for 1T and 2H phases of TaS2 and TaSe2
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Physica B 358 (2005) 158–165 www.elsevier.com/locate/physb
Full-potential calculations of the electronic and optical properties for 1T and 2H phases of TaS2 and TaSe2 Ali Hussain Reshak, S. Auluck Physics Department, Indian Institute of Technology, Roorkee, Uttaranchal 247667, India Received 20 July 2004; received in revised form 12 November 2004; accepted 4 January 2005
Abstract The band structure, density of states and anisotropic frequency-dependent optical properties have been calculated for the 1 T and 2 H phases of TaS2 and TaSe2 using the full-potential linear augmented plane wave (FPLAPW) method. In the 1 T and 2 H phases, when S is replaced by Se, the unoccupied Ta-5d and chalcogen-p bands move closer to the Fermi energy EF and the bandwidth of the chalcogen-s group decreases. Compared to the 1 T phase, in the 2 H phase the occupied/unoccupied bands move towards higher/lower energies with respect to EF. In the 1 T phase, when S is replaced by Se, the peak positions in the imaginary part of the frequency-dependent dielectric function 2 ðoÞ move towards lower energies by 0.5 eV. The single peak at 6 eV in 2 ðoÞ of the 1 T phase is split into two peaks in the 2 H phase. We make a detailed comparison of the frequency-dependent reflectivity and absorption coefficient with the available experimental data. The linear muffin tin orbital method within the atomic sphere approximation (LMTOASA) shows poor agreement with the experimental data while our FPLAPW results give excellent agreement with the experimental data suggesting that a better representation of the potential is essential for calculating optical properties accurately. r 2005 Elsevier B.V. All rights reserved. PACS: 70 Keywords: Electronic structure; Optical properties; Transition metal dichalcogenides; FPLAPW
1. Introduction The group VB transition metal dichalcogenides (TMDCs) TaS2 and TaSe2 are members of the Corresponding author. Tel.: +011 0091133272344;
fax: +011 91133273560. E-mail address: [email protected] (A.H. Reshak).
large family of TMDCs, whose optical and electrical properties have been reviewed by Wilson and Yoffe [1]. These compounds are interesting because they exhibit a rich variety of phase transitions produced by commensurate and incommensurate charge density waves [2]. The optical and photoelectron spectra of these compounds have been extensively studied
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.01.051
ARTICLE IN PRESS A.H. Reshak, S. Auluck / Physica B 358 (2005) 158–165
experimentally [3–10]. Liang et al. [3] measured the room temperature reflectance of 1T-TaS2 and 2H~ perpendicular to c-axis TaS2 for the electric field E ~ ðE ? cÞ: Beal et al. [4] measured the reflectivity spectra of single crystals of 1T-TaS2 and 2H-TaS2/ ~ ? c: Ruzicka et al. [5] present an optical Se2 for E study of 2H-TaSe2 along the less conducting caxis. Bell et al. [6] calculated the joint density of states (JDOS) by performing a Kramers–Kroning analysis of the electron energy loss measurements. Smith and his co-workers [7,8] have measured the photoelectron energy spectra of 1T-TaS2, 1TTaSe2 and 2H-TaSe2 as a function of both polar and azimuthal angle emission. Okuda et al. [9,10] have performed angle-resolved photoelectron spectroscopy on 1T-TaS2 to obtain a very clear dependence of the photoelectron angular distribution (PEAD) pattern on the incident photon polarization. Mattheiss [11] has used the augmented plane wave (APW) method to determine the band structures of 1T and 2H phases of TaS2. Wexler and Woolley [12] have performed nonrelativistic calculations of the band structure of 2H-TaS2/Se2 using the layer method within the muffin tin approximation. Myron et al. [13] have used the Korringa–Kohn–Rostoker (KKR) method in the muffin tin approximation to calculate the band structure and Fermi surface of 1T-TaS2/Se2. Woolley et al. [14] have used the APW method to calculate the band structures and Fermi surfaces for 1T-TaS2 and 1T-TaSe2. Sharma et al. [15] calculated the anisotropic frequency-dependent dielectric function for the 1T and 2H phases of TaS2/Se2 using the linear muffin tin orbital method within the atomic sphere approximation (LMTO-ASA). The nonmagnetic 1T and 2H phases of TaS2/Se2 exhibit a range of charge density wave (CDW) transitions [16]. Studies of the electronic properties have been carried out to highlight the CDW phenomena that are encountered in these compounds [17]. Wilson et al. [16] were the first to observe the CDW in 1T-TaS2. The undistorted phase for 1T-TaS2 exists for a very small temperature range above 550 K. Upon cooling, it shows a CDW distortion that is incommensurate with the underlying lattice [16]. Demsar et al. [17]
159
have calculated the time-resolved optical spectroscopy of collective and single-particle excitation of 1T-TaS2 and 2H-TaSe2 and find the presence of a large gap in the excitation spectrum, associated with the formation of various degrees of CDW order. Sharma et al. [18] investigated the effect of the CDW on the Fermi surface of 1T-TaS2/Se2/Te2 using the full-potential linear augmented plane wave (FPLAPW) method. They find that these compounds are unstable towards the formation of a CDW state. Bayliss et al. [24] reported that in the high-temperature region, 1T-TaS2 slowly transforms into the 2H modification. Recently, Pillo et al. [23] examined the CDW compound 1T-TaS2 as a function of photon energy. In this paper, we would like to focus our attention on the optical properties. Although there exist many measurements of the optical properties, there is a dearth of theoretical calculations. To the best of our knowledge, there is only one reported calculation in the literature by Sharma et al. [15]. Agreement with the experimental data was not good. We would like to address the question whether a better representation of the potential can lead to better agreement with the experimental data. With this in mind, we present calculations of the optical properties using the FPLAPW method. To quote from our conclusions, we find that this leads to a better representation of the optical properties and hence better agreement with the experimental data. In Section 2, we give details of our calculations. The band structure and density of state are presented and discussed in Section 3. The frequency-dependent dielectric function and other optical properties are given in Section 4, and Section 5 summarizes our conclusions.
2. Details of calculations The materials we are concerned with here, TaS2 and TaSe2, have a hexagonal Bravais lattice with undistorted trigonal prismatic coordination in 2H polytypes and octahedral coordination in 1T polytypes. The 1T phase is stable at 800 1C, while the 2H phase is stable at room temperature. In the 1T phase (space group D33d (P3m1)), Ta atoms are
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Table 1 The room temperature lattice parameters and the atomic positions for 1T and 2H phases of TaS2 and TaSe2 Compounds
a (A˚)
c (A˚)
z
Position of TM
Position of chalcogen
1T-TaS2 1T-TaSe2 2H-TaS2
3.365a 3.477a 3.316b
5.892a 6.272a 12.0702b
0.257d 0.261d 0.123d
(0 0 0)a (0 0 0)a 7(0 0 1/4)b
2H-TaSe2
c
3.434
c
12.696
d
0.1217
7(0 0 1/4)
c
12 a 3 3 z 12 a 3 3 z 12 33z ; 12 1 3 3 ð2 12 33z ; 12 1 3 3 ð2
zÞ
b
zÞ
c
a
Ref. [18]. Refs. [13,15]. c Ref. [15]. d Optimized. b
octahedrally coordinated with chalcogen atoms with only one sandwich in the unit cell while in the 2H phase (space group D46h (P63/mmc)), the unit cell spans two sandwiches. The experimental structural parameters at room temperature of TaS2 and TaSe2 along with the atomic positions are given in Table 1. We have performed calculations at these experimental lattice constants. In the absence of any experimental value of z, we have optimized the value of z as corresponding to the minimum total energy. These are listed in Table 1 and were very close to the ideal values of 0.25 and 0.125 for 1T and 2H phases, respectively. The calculations are based on the density functional theory (DFT) within the local density approximation (LDA). The density functional equations are solved using the first principles FPLAPW method as embodied in the WIEN97 code [19]. We used the muffin tin (MT) sphere radii R ¼ 2 a.u. for all atoms. Self-consistency was obtained using 200k points in the irreducible Brilloun zone (IBZ), and the BZ integration was carried out using the [20], tetrahedron method. The density of states (DOS) and the optical properties are calculated with 500k points in the IBZ.
3. Results and discussions 3.1. Band structure and density of states In Fig. 1, we show the FPLAPW calculations of the band structures, total and partial
DOS of 1T and 2H phases of TaS2/Se2. We can distinguish three main regions, which we call A, B and C. These correspond to the chalcogen-s states, chalcogen-p and Ta-d states, respectively. We find a strong hybridization between the Ta-d states and chalcogen-p states near the Fermi energy (EF). Our DOS is in agreement with the calculations of Myron and Freeman [13] and Mattheiss [11] and in disagreement with LMTO-ASA method [21] in the matter of peak heights, peak positions and the values of N(EF). In general, replacing S by Se in 1T and 2H phases, the bandwidth of the chalcogen-s states is reduced and the unoccupied Ta-5d and chalcogen-p bands shift slightly towards lower energies to be closer to EF. This is consistent with the work of Myron and Freeman [13]. On going from 1T to 2H phase, we note that the chalcogen-s group is shifted towards higher energies by around 1 eV. The chalcogen-p group and Ta-5d group are shifted towards EF. In Table 2, we compare our calculated DOS at EF (N(EF)) with other calculations and with the low-temperature specific heat data [16]. In agreement with the KKR, FPLAPW and LMTO-ASA calculations, we find that N(EF) increases when S is replaced by Se in the 1T phase. The experimental data do not show this trend. The experimental values [16] of N(EF) are always larger than our calculated N(EF) indicating the presence of many body interactions.
ARTICLE IN PRESS A.H. Reshak, S. Auluck / Physica B 358 (2005) 158–165
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Fig. 1. Band structures and total density of states (————) in states/eV unit cell, along with the partial DOS, where (- - - - - -) denotes chalcogen-s, ( . . . . . . . .) chalcogen-p, and (. . . . . . . ) Ta-d, in 1T and 2H phases of TaS2/Se2. The partial DOS in 1T phase is multiplied by 2 and in 2H phase by 3.
Table 2 The DOS at EF, N(EF) in states/eV unit cell Compound
FPLAPW
APW
KKR
1T-TaS2 1T-TaSe2 2H-TaS2 2H-TaSe2 Ref.
1.7 2.0 4.8 5.2 This work
1.4
1.6 2.5
FPLAPW 1.4 1.6
5.9 11
13
18
LMTO-ASA 0.7 1.2 3.9 4.2 21
Exp. 5.33 4.05 6.48,10.8 16
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4. Optical properties The optical properties are calculated using expressions given in our earlier work [22]. As these compounds are metallic, we must include the Drude term (intraband transitions). The Drude term is given by int ra ðoÞ ¼
o2P t oð1 þ o2 t2 Þ
where oP is the plasma frequency and t is the relaxation time. The calculated values of _oP corresponding to the two polarizations parallel and perpendicular to c-axis are given in Table 3. Fig. 2 shows the calculated frequency-dependent dielectric functions ? 2 ðoÞ along with the experimental data of Beal et al. [4] and the LMTO-ASA results [15]. Using _=t ¼ 0:1 eV; we have performed calculations of 2 ðoÞ with and without the Drude term. The sharp rise in 2 ðoÞ at energies less than 0.5 eV is due to the Drude term. As the LMTO-ASA calculations do not include the Drude term, there is no sharp rise at very low energies. The LMTO-ASA results do not show good agreement with the experimental data. A significant improvement is obtained using the FPLAPW method, resulting in very good agreement with the experimental data. This is attributed to the fact that the LMTO-ASA calculations are based on the muffin tin approximation, which is known to give a poor representation of the wave functions. On going from the disulphide to the diselenide, in the 1T-phase, we find that the peak positions shift towards lower energies by around 1 eV. On comparing 1T-TaS2 with the experimental data, we note that the 2 eV peak is shifted towards the higher energies by around 1 eV, while the peak around 7 eV is shifted towards lower Fig. 2. Calculated ? 2 ðoÞ using FPLAPW method (————) compared with the LMTO-ASA calculations [15] (————) and the experimental data (- - - - - -) of Beal et al. [4].
Table 3 The plasma energy in eV Compounds
_o? P
_okP
1T-TaS2 1T-TaSe2 2H-TaS2 2H-TaSe2
5.83 5.36 3.87 3.70
2.17 2.73 1.16 1.47
energies by around 1 eV. At higher energies (X10 eV) both experimental and theoretical data show a monotonically decreasing behavior. There are no experimental data for 1T-TaSe2. In 2HTaSe2 we note that the structures in the energy
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range 2.5–5 eV are shifted towards higher energies by around 1 eV with respect to the experimental data. Moving from 1T to 2H phase, the single peak around 6 eV in 2 ðoÞ for 1T phase is split into
two peaks in the 2H phase which is in agreement with the experimental data. This is attributed to the changes in the wave character of bands and to the number of atoms in the unit cell being doubled.
Fig. 3. Calculated (FPLAPW) reflectivity spectrum (————) along with the experimental data (- - - - - -) of Beal et al. [4] for ~ ? c: E
Fig. 4. Calculated (FPLAPW) absorption coefficient (————) along with the experimental data (- - - - - -) of Beal et al. [4] for ~ ? c: E
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Our analysis shows that the transitions from chalcogen-p (occupied) to Ta-d (unoccupied) states are responsible for the structures in ? 2 ðoÞ: In Figs. 3 and 4, we show the calculated perpendicular reflectivity spectra and absorption coefficient for 1T and 2H phases of TaS2/Se2. We find excellent agreement with the experimental data of Beal et al. [4].
bands and to the number of atoms in the unit cell being doubled. The frequency-dependent reflectivity and absorption coefficient for the perpendicular polarization are in excellent agreement with experimental data. The band transitions that contribute to the structures of the frequencydependent dielectric function are primarily from chalcogen-p states to Ta-5d states.
5. Conclusions
Acknowledgements
Our calculations show that the 1T and 2H phases of TaS2 and TaSe2 are metallic. The FPLAPW band structure and DOS show good agreement with the earlier calculations based on KKR [13] and APW [11] methods and disagreement with the LMTO-ASA calculations [21] in the matter of peak heights, peak positions and the values of N(EF). When S is replaced by Se in 1T and 2H phases, the unoccupied Ta-5d and chalcogen-p bands move slightly towards EF and the bandwidth of chalcogen-s decreases, while the occupied Ta-5d bands are unchanged. On going from 1T to 2H phase, the occupied bands move towards higher energies while the unoccupied move towards lower energies with respect to EF and the bandwidth of chalcogen-s group and the occupied Ta-5d bands increases. Our calculations show that the DOS at EF increases on moving from S to Se and from 1T to 2H. A strong hybridization between Ta-5d states and chalcogenp states was found. Our calculated FPLAPW frequency-dependent ~ ? c shows dielectric function corresponding to E good agreement with the experimental data of Beal et al. [4] while the LMTO-ASA results [15] do not show good agreement. This is attributed to the fact that the LMTO-ASA calculations are based on the muffin tin approximation, which is known to give a poor representation of the wave functions. When S is replaced by Se in the 1T phase, we note that the peak positions shift towards lower energies by around 1 eV, while in the 2H phase, the first peak in 2 ðoÞ is sharp. On moving from 1T to 2H phase, the single peak at 6 eV in 2 ðoÞ for 1T phase is split into two peaks in the 2H phase which is in agreement with the experimental data. This is attributed to the changes in the wave character of
We would like to thank the Institute Computer Center and Physics Department for providing the computational facilities. References [1] J.A. Wilson, A.D. Yoffe, Adv. Phys. 18 (1969). [2] J.A. Wilson, F.J. Di Salvo, S. Mahajan, Adv. Phys. 24 (1975) 117. [3] W.Y. Liang, G. Lucovsky, R.M. White, W. Stutius, K.R. Pisharody, Philos. Mag. 33 (1976) 493. [4] A.R. Beal, H.P. Hughes, W.Y. Liang, J. Phys. C 8 (1975) 4236. [5] B. Ruzicka, L. Degiorgi, H. Berger, R. Gaal, L. Forro, Phys. Rev. Lett. 86 (2001) 4136. [6] M.G. Bell, W.Y. Liang, Adv. Phys. 25 (1976) 52. [7] M.M. Traum, N.V. Smith, F.J. Di Salvo, Phys. Rev. Lett. 32 (1974) 1241. [8] N.V. Smith, M. Traum, Phys. Rev. B 11 (1975) 2087. [9] T. Okuda, H. Daimon, K. Nakatsnji, M. Kotsngi, S. Suga, Y. Tezuka, S. Shin, T. Hasegawa, K. Kitazawa, J. Elect. Spectrosc. Related Phenomena 88–91 (1998) 287. [10] T. Okuda, Kan Nakatsuji, Shigemasa Suga, Yasuhisa Tezuka, Shik Shin, Hiroshi Daimon, J. Elect. Spectrosc. Related Phenomena 101–103 (1999) 355. [11] L.F. Mattheiss, Phys. Rev. B 8 (1973) 3719. [12] G. Wexler, A.M. Woolley, J. Phys. C 9 (1976) 1185. [13] H.M. Myron, A.J. Freeman, Phys. Rev. B 11 (1976) 2735. [14] A.M. Woolley, G. Wexler, J. Phys. C 10 (1977) 2601. [15] Sangeeta Sharma, S. Auluck, M.A. Khan, Pramana, J. Phys. 54 (1999) 431. [16] J.A. Wilson, F.J. Di Salvo, S. Machajan, Adv. Phys. 24 (1975) 117; J.A. Wilson, F.J. Di Salvo, S. Machajan, Phys. Rev. Lett. 32 (1974) 882. [17] J. Demsar, L. Forro, H. Berger, D. Mihailovic, Phys. Rev. B 66 (2002) 041101. [18] S. Sharma, L. Nordstrom, B. Johansson, Phys. Rev. B 66 (2002) 195101.
ARTICLE IN PRESS A.H. Reshak, S. Auluck / Physica B 358 (2005) 158–165 [19] P. Blaha, K. Schwarz, J. Luitz, WIEN97, Vienna University of Technology, 1997 (improved and updated unix version of the original copyright WIEN Code) which was published by P. Blaha, K. Schwartz, P. Sorantin, S.B. Trickey, Comput. Phys. Commun. 59 (1990) 399. [20] O. Jepson, O.K. Anderson, Solid State Commun. 9 (1971) 1763. [21] Sangeeta Sharma, Ph.D. Thesis, 1999.
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[22] Ali Hussain Reshak, S. Auluck, Phys. Rev. B 68 (2003) 245113. [23] Th. Pillo, J. Hayoz, D. Naumovic, H. Berger, L. Perfetti, L. Gavioli, A. Taleb-Ibrahimi, L. Schlapbach, P. Abi, Phys. Rev. B 64 (2001) 245105. [24] S.C. Bayliss, A. Clarke, W.Y. Liang, J. Phys. C 16 (1983) L831.
Physica B 358 (2005) 158–165 www.elsevier.com/locate/physb
Full-potential calculations of the electronic and optical properties for 1T and 2H phases of TaS2 and TaSe2 Ali Hussain Reshak, S. Auluck Physics Department, Indian Institute of Technology, Roorkee, Uttaranchal 247667, India Received 20 July 2004; received in revised form 12 November 2004; accepted 4 January 2005
Abstract The band structure, density of states and anisotropic frequency-dependent optical properties have been calculated for the 1 T and 2 H phases of TaS2 and TaSe2 using the full-potential linear augmented plane wave (FPLAPW) method. In the 1 T and 2 H phases, when S is replaced by Se, the unoccupied Ta-5d and chalcogen-p bands move closer to the Fermi energy EF and the bandwidth of the chalcogen-s group decreases. Compared to the 1 T phase, in the 2 H phase the occupied/unoccupied bands move towards higher/lower energies with respect to EF. In the 1 T phase, when S is replaced by Se, the peak positions in the imaginary part of the frequency-dependent dielectric function 2 ðoÞ move towards lower energies by 0.5 eV. The single peak at 6 eV in 2 ðoÞ of the 1 T phase is split into two peaks in the 2 H phase. We make a detailed comparison of the frequency-dependent reflectivity and absorption coefficient with the available experimental data. The linear muffin tin orbital method within the atomic sphere approximation (LMTOASA) shows poor agreement with the experimental data while our FPLAPW results give excellent agreement with the experimental data suggesting that a better representation of the potential is essential for calculating optical properties accurately. r 2005 Elsevier B.V. All rights reserved. PACS: 70 Keywords: Electronic structure; Optical properties; Transition metal dichalcogenides; FPLAPW
1. Introduction The group VB transition metal dichalcogenides (TMDCs) TaS2 and TaSe2 are members of the Corresponding author. Tel.: +011 0091133272344;
fax: +011 91133273560. E-mail address: [email protected] (A.H. Reshak).
large family of TMDCs, whose optical and electrical properties have been reviewed by Wilson and Yoffe [1]. These compounds are interesting because they exhibit a rich variety of phase transitions produced by commensurate and incommensurate charge density waves [2]. The optical and photoelectron spectra of these compounds have been extensively studied
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.01.051
ARTICLE IN PRESS A.H. Reshak, S. Auluck / Physica B 358 (2005) 158–165
experimentally [3–10]. Liang et al. [3] measured the room temperature reflectance of 1T-TaS2 and 2H~ perpendicular to c-axis TaS2 for the electric field E ~ ðE ? cÞ: Beal et al. [4] measured the reflectivity spectra of single crystals of 1T-TaS2 and 2H-TaS2/ ~ ? c: Ruzicka et al. [5] present an optical Se2 for E study of 2H-TaSe2 along the less conducting caxis. Bell et al. [6] calculated the joint density of states (JDOS) by performing a Kramers–Kroning analysis of the electron energy loss measurements. Smith and his co-workers [7,8] have measured the photoelectron energy spectra of 1T-TaS2, 1TTaSe2 and 2H-TaSe2 as a function of both polar and azimuthal angle emission. Okuda et al. [9,10] have performed angle-resolved photoelectron spectroscopy on 1T-TaS2 to obtain a very clear dependence of the photoelectron angular distribution (PEAD) pattern on the incident photon polarization. Mattheiss [11] has used the augmented plane wave (APW) method to determine the band structures of 1T and 2H phases of TaS2. Wexler and Woolley [12] have performed nonrelativistic calculations of the band structure of 2H-TaS2/Se2 using the layer method within the muffin tin approximation. Myron et al. [13] have used the Korringa–Kohn–Rostoker (KKR) method in the muffin tin approximation to calculate the band structure and Fermi surface of 1T-TaS2/Se2. Woolley et al. [14] have used the APW method to calculate the band structures and Fermi surfaces for 1T-TaS2 and 1T-TaSe2. Sharma et al. [15] calculated the anisotropic frequency-dependent dielectric function for the 1T and 2H phases of TaS2/Se2 using the linear muffin tin orbital method within the atomic sphere approximation (LMTO-ASA). The nonmagnetic 1T and 2H phases of TaS2/Se2 exhibit a range of charge density wave (CDW) transitions [16]. Studies of the electronic properties have been carried out to highlight the CDW phenomena that are encountered in these compounds [17]. Wilson et al. [16] were the first to observe the CDW in 1T-TaS2. The undistorted phase for 1T-TaS2 exists for a very small temperature range above 550 K. Upon cooling, it shows a CDW distortion that is incommensurate with the underlying lattice [16]. Demsar et al. [17]
159
have calculated the time-resolved optical spectroscopy of collective and single-particle excitation of 1T-TaS2 and 2H-TaSe2 and find the presence of a large gap in the excitation spectrum, associated with the formation of various degrees of CDW order. Sharma et al. [18] investigated the effect of the CDW on the Fermi surface of 1T-TaS2/Se2/Te2 using the full-potential linear augmented plane wave (FPLAPW) method. They find that these compounds are unstable towards the formation of a CDW state. Bayliss et al. [24] reported that in the high-temperature region, 1T-TaS2 slowly transforms into the 2H modification. Recently, Pillo et al. [23] examined the CDW compound 1T-TaS2 as a function of photon energy. In this paper, we would like to focus our attention on the optical properties. Although there exist many measurements of the optical properties, there is a dearth of theoretical calculations. To the best of our knowledge, there is only one reported calculation in the literature by Sharma et al. [15]. Agreement with the experimental data was not good. We would like to address the question whether a better representation of the potential can lead to better agreement with the experimental data. With this in mind, we present calculations of the optical properties using the FPLAPW method. To quote from our conclusions, we find that this leads to a better representation of the optical properties and hence better agreement with the experimental data. In Section 2, we give details of our calculations. The band structure and density of state are presented and discussed in Section 3. The frequency-dependent dielectric function and other optical properties are given in Section 4, and Section 5 summarizes our conclusions.
2. Details of calculations The materials we are concerned with here, TaS2 and TaSe2, have a hexagonal Bravais lattice with undistorted trigonal prismatic coordination in 2H polytypes and octahedral coordination in 1T polytypes. The 1T phase is stable at 800 1C, while the 2H phase is stable at room temperature. In the 1T phase (space group D33d (P3m1)), Ta atoms are
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Table 1 The room temperature lattice parameters and the atomic positions for 1T and 2H phases of TaS2 and TaSe2 Compounds
a (A˚)
c (A˚)
z
Position of TM
Position of chalcogen
1T-TaS2 1T-TaSe2 2H-TaS2
3.365a 3.477a 3.316b
5.892a 6.272a 12.0702b
0.257d 0.261d 0.123d
(0 0 0)a (0 0 0)a 7(0 0 1/4)b
2H-TaSe2
c
3.434
c
12.696
d
0.1217
7(0 0 1/4)
c
12 a 3 3 z 12 a 3 3 z 12 33z ; 12 1 3 3 ð2 12 33z ; 12 1 3 3 ð2
zÞ
b
zÞ
c
a
Ref. [18]. Refs. [13,15]. c Ref. [15]. d Optimized. b
octahedrally coordinated with chalcogen atoms with only one sandwich in the unit cell while in the 2H phase (space group D46h (P63/mmc)), the unit cell spans two sandwiches. The experimental structural parameters at room temperature of TaS2 and TaSe2 along with the atomic positions are given in Table 1. We have performed calculations at these experimental lattice constants. In the absence of any experimental value of z, we have optimized the value of z as corresponding to the minimum total energy. These are listed in Table 1 and were very close to the ideal values of 0.25 and 0.125 for 1T and 2H phases, respectively. The calculations are based on the density functional theory (DFT) within the local density approximation (LDA). The density functional equations are solved using the first principles FPLAPW method as embodied in the WIEN97 code [19]. We used the muffin tin (MT) sphere radii R ¼ 2 a.u. for all atoms. Self-consistency was obtained using 200k points in the irreducible Brilloun zone (IBZ), and the BZ integration was carried out using the [20], tetrahedron method. The density of states (DOS) and the optical properties are calculated with 500k points in the IBZ.
3. Results and discussions 3.1. Band structure and density of states In Fig. 1, we show the FPLAPW calculations of the band structures, total and partial
DOS of 1T and 2H phases of TaS2/Se2. We can distinguish three main regions, which we call A, B and C. These correspond to the chalcogen-s states, chalcogen-p and Ta-d states, respectively. We find a strong hybridization between the Ta-d states and chalcogen-p states near the Fermi energy (EF). Our DOS is in agreement with the calculations of Myron and Freeman [13] and Mattheiss [11] and in disagreement with LMTO-ASA method [21] in the matter of peak heights, peak positions and the values of N(EF). In general, replacing S by Se in 1T and 2H phases, the bandwidth of the chalcogen-s states is reduced and the unoccupied Ta-5d and chalcogen-p bands shift slightly towards lower energies to be closer to EF. This is consistent with the work of Myron and Freeman [13]. On going from 1T to 2H phase, we note that the chalcogen-s group is shifted towards higher energies by around 1 eV. The chalcogen-p group and Ta-5d group are shifted towards EF. In Table 2, we compare our calculated DOS at EF (N(EF)) with other calculations and with the low-temperature specific heat data [16]. In agreement with the KKR, FPLAPW and LMTO-ASA calculations, we find that N(EF) increases when S is replaced by Se in the 1T phase. The experimental data do not show this trend. The experimental values [16] of N(EF) are always larger than our calculated N(EF) indicating the presence of many body interactions.
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Fig. 1. Band structures and total density of states (————) in states/eV unit cell, along with the partial DOS, where (- - - - - -) denotes chalcogen-s, ( . . . . . . . .) chalcogen-p, and (. . . . . . . ) Ta-d, in 1T and 2H phases of TaS2/Se2. The partial DOS in 1T phase is multiplied by 2 and in 2H phase by 3.
Table 2 The DOS at EF, N(EF) in states/eV unit cell Compound
FPLAPW
APW
KKR
1T-TaS2 1T-TaSe2 2H-TaS2 2H-TaSe2 Ref.
1.7 2.0 4.8 5.2 This work
1.4
1.6 2.5
FPLAPW 1.4 1.6
5.9 11
13
18
LMTO-ASA 0.7 1.2 3.9 4.2 21
Exp. 5.33 4.05 6.48,10.8 16
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4. Optical properties The optical properties are calculated using expressions given in our earlier work [22]. As these compounds are metallic, we must include the Drude term (intraband transitions). The Drude term is given by int ra ðoÞ ¼
o2P t oð1 þ o2 t2 Þ
where oP is the plasma frequency and t is the relaxation time. The calculated values of _oP corresponding to the two polarizations parallel and perpendicular to c-axis are given in Table 3. Fig. 2 shows the calculated frequency-dependent dielectric functions ? 2 ðoÞ along with the experimental data of Beal et al. [4] and the LMTO-ASA results [15]. Using _=t ¼ 0:1 eV; we have performed calculations of 2 ðoÞ with and without the Drude term. The sharp rise in 2 ðoÞ at energies less than 0.5 eV is due to the Drude term. As the LMTO-ASA calculations do not include the Drude term, there is no sharp rise at very low energies. The LMTO-ASA results do not show good agreement with the experimental data. A significant improvement is obtained using the FPLAPW method, resulting in very good agreement with the experimental data. This is attributed to the fact that the LMTO-ASA calculations are based on the muffin tin approximation, which is known to give a poor representation of the wave functions. On going from the disulphide to the diselenide, in the 1T-phase, we find that the peak positions shift towards lower energies by around 1 eV. On comparing 1T-TaS2 with the experimental data, we note that the 2 eV peak is shifted towards the higher energies by around 1 eV, while the peak around 7 eV is shifted towards lower Fig. 2. Calculated ? 2 ðoÞ using FPLAPW method (————) compared with the LMTO-ASA calculations [15] (————) and the experimental data (- - - - - -) of Beal et al. [4].
Table 3 The plasma energy in eV Compounds
_o? P
_okP
1T-TaS2 1T-TaSe2 2H-TaS2 2H-TaSe2
5.83 5.36 3.87 3.70
2.17 2.73 1.16 1.47
energies by around 1 eV. At higher energies (X10 eV) both experimental and theoretical data show a monotonically decreasing behavior. There are no experimental data for 1T-TaSe2. In 2HTaSe2 we note that the structures in the energy
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range 2.5–5 eV are shifted towards higher energies by around 1 eV with respect to the experimental data. Moving from 1T to 2H phase, the single peak around 6 eV in 2 ðoÞ for 1T phase is split into
two peaks in the 2H phase which is in agreement with the experimental data. This is attributed to the changes in the wave character of bands and to the number of atoms in the unit cell being doubled.
Fig. 3. Calculated (FPLAPW) reflectivity spectrum (————) along with the experimental data (- - - - - -) of Beal et al. [4] for ~ ? c: E
Fig. 4. Calculated (FPLAPW) absorption coefficient (————) along with the experimental data (- - - - - -) of Beal et al. [4] for ~ ? c: E
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Our analysis shows that the transitions from chalcogen-p (occupied) to Ta-d (unoccupied) states are responsible for the structures in ? 2 ðoÞ: In Figs. 3 and 4, we show the calculated perpendicular reflectivity spectra and absorption coefficient for 1T and 2H phases of TaS2/Se2. We find excellent agreement with the experimental data of Beal et al. [4].
bands and to the number of atoms in the unit cell being doubled. The frequency-dependent reflectivity and absorption coefficient for the perpendicular polarization are in excellent agreement with experimental data. The band transitions that contribute to the structures of the frequencydependent dielectric function are primarily from chalcogen-p states to Ta-5d states.
5. Conclusions
Acknowledgements
Our calculations show that the 1T and 2H phases of TaS2 and TaSe2 are metallic. The FPLAPW band structure and DOS show good agreement with the earlier calculations based on KKR [13] and APW [11] methods and disagreement with the LMTO-ASA calculations [21] in the matter of peak heights, peak positions and the values of N(EF). When S is replaced by Se in 1T and 2H phases, the unoccupied Ta-5d and chalcogen-p bands move slightly towards EF and the bandwidth of chalcogen-s decreases, while the occupied Ta-5d bands are unchanged. On going from 1T to 2H phase, the occupied bands move towards higher energies while the unoccupied move towards lower energies with respect to EF and the bandwidth of chalcogen-s group and the occupied Ta-5d bands increases. Our calculations show that the DOS at EF increases on moving from S to Se and from 1T to 2H. A strong hybridization between Ta-5d states and chalcogenp states was found. Our calculated FPLAPW frequency-dependent ~ ? c shows dielectric function corresponding to E good agreement with the experimental data of Beal et al. [4] while the LMTO-ASA results [15] do not show good agreement. This is attributed to the fact that the LMTO-ASA calculations are based on the muffin tin approximation, which is known to give a poor representation of the wave functions. When S is replaced by Se in the 1T phase, we note that the peak positions shift towards lower energies by around 1 eV, while in the 2H phase, the first peak in 2 ðoÞ is sharp. On moving from 1T to 2H phase, the single peak at 6 eV in 2 ðoÞ for 1T phase is split into two peaks in the 2H phase which is in agreement with the experimental data. This is attributed to the changes in the wave character of
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