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Transport properties of 2H-NbSe2: Effect of Ga-intercalation
ARTICLE IN PRESS Physica B 405 (2010) 955–957
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Transport properties of 2H-NbSe2: Effect of Ga-intercalation I. Naik a,, A.K. Rastogi b a b
Department of Physics, North Orissa University, Takatpur, Baripada – 757003, India School of Physical Sciences, Jawaharlal Nehru University, New Delhi – 110067, India
a r t i c l e in fo
abstract
Article history: Received 15 June 2009 Received in revised form 19 October 2009 Accepted 19 October 2009
We have prepared compounds of 2H-NbSe2 and 2H-GaxNbSe2 (x= 5% and 10%) at 700 1C. 2H-NbSe2 single crystal exhibits superconducting and charge density wave (CDW) transition at 7.4 K and 35 K, respectively, whereas in polycrystalline pellet of poor residual resistance ratio (RRR) value, the CDW is absent. In Ga-intercalated compounds, the rapid decrease of superconducting transition temperature was noticed. Here we report the occurrence of two-band model in which the temperature dependence of mean free path length ‘l(e)’ is the main factor for overall behavior of resistivity and thermopower. & 2009 Elsevier B.V. All rights reserved.
Keywords: Charge density wave Transition-metal compounds Superconductivity
1. Introduction Group-V transition-metal dichalcogenide compounds (TMDC) have been studied extensively for understanding the mechanism of Charge Density Wave (CDW) transition. Besides this, some of them show superconducting properties at low temperature, e.g. NbSe2, NbS2, NbTe2, TaSe2 and TaS2 [1,2]. This is a remarkable behavior, since the superconducting order is not compatible with the CDW order. The possibility of the coexistence of CDW and superconductivity in anisotropic structures has been the subject of intense studied over the last four decades as stoichiometry, intercalation and disorder significantly affect these two transitions. The original structure of TMDC is changed beyond a critical value for the intercalation, which depend on the metal atoms. Within the same symmetry, metal atom intercalation changes the c-axis and a small ( o3%) increase in a-axis. In 2H-NbSe2, a maximum of 33% and 67% tetrahedral sites are occupied by Al and Cu respectively is reported [3,4]. 2H-NbSe2 is one of them in which the CDW, expected to arise from Fermi surface nesting [5,6] or from saddle points in the electronic band [7], and superconducting transitions exist at 35 and 7.4 K respectively. Though the effect of RRR is not seen in Ts, it washes out the CDW transition for low RRR value [8]. Both the transitions get affected by stacking order and pressure in which the number density of states (DOS) increase in the conduction band through restoring of Fermi surface lost by CDW instability [9].
Corresponding author. Fax: +091 6792 255127.
E-mail address: [email protected] (I. Naik). 0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.10.028
In the present study we have attempted to prepare 2H-NbSe2, 2H-Ga0.05NbSe2 and 2H-Ga0.10NbSe2 compounds. 2H-NbSe2 with large RRR value ( 67 for single crystal) shows superconductivity (Ts =7.4 K) below a Charge Density Wave (CDW), which is vanished for lower RRR value ( 13 for pellet), at 35 K similar to reported results [8,10]. The sign of Seebeck co-efficient ‘S’ is found negative opposite to Hall coefficient ‘RH’ at room temperature and behave differently in the temperature range of 16–300 K. It, Seebeck coefficient, also exhibits anomaly around CDW transition in single crystal 2H-NbSe2 (Fig. 3).
2. Experimental details 2H-NbSe2 and its derivatives, Ga-intercalations, were prepared by direct reaction of elements, Ga= 99.99%, Nb= 99.8% and Se= 99.999%, in an evacuated sealed quartz tube at 750 1C. This is followed by grinding and pelletization in a dray box. Finally they are sintered at 700 1C for seven days. We were able to prepare single crystal flakes for 2H-NbSe2 by vapor transport technique at 750 1C. X-ray diffraction: The crystal structure of NbSe2 was confirmed to be in the 2H-phase from room temperature X-ray ˚ The diffraction with lattice constants a 3.445 A˚ and c 12.551 A. c-axis is marginally affected in the Ga-intercalated compounds (see Table 1) indicating that the Ga-ions are occupied the octahedral sites between the layers. The perfect stacking order along 10 l line makes the intensity sharp. For Ga-intercalated compounds, the peak broadening is either by stacking faults or strain. All the compounds have large intensity for 102 planes are related to orientation effect of crystallites (Fig. 1).
ARTICLE IN PRESS 956
I. Naik, A.K. Rastogi / Physica B 405 (2010) 955–957
Fig. 1. Room temperature X-ray diffraction of 2H-GaxNbSe2 (x =0, 5% and 10%).
Fig. 2. Temperature dependence of resistivity of 2H-GaxNbSe2 (x= 0, 5% and 10%). The inset figure shows the normalized resistivity for 2H-GaxNbSe2 (x= 0, 5% and 10%).
Table 1 Compound name
a
Symmentry (300 K) Latice constant (a)
b
b
b
2H –
2H
2H
2H
3.445 A˚
3.450 A˚
3.453 A˚
(c)
–
RRR value r300 (O cm) 10 4 Ts (K) S300 (mV/K) Tc (K)
66.7 0.68 7.4 4.08 35
12.551 A˚ 13.0 1.96 7.4 3.70 –
12.592 A˚ 2.9 4.18 5.6 6.33 –
12.605 A˚ 1.5 12.3 2.7 11.21 –
NbSe2
NbSe2
Ga0.05NbSe2
Ga0.10NbSe2
Ts (K)= Superconducting transition temperature. Tc (K)=CDW transition temperature. a b
For single crystal. For polycrystalline compound.
D.C. resistance measurements were carried out on single crystal and polycrystalline pellets using van-der Pauw geometry [11]. Seebeck co-efficient was measured with respect to Cu by reversing the temperature gradient at different temperatures. Finally absolute Seebeck coefficient was obtained by correcting the thermopower of Cu.
3. Results and discussions 3.1. Resistivity Fig. 2 shows the temperature dependence of resistivity for 2HNbSe2 and 2H-GaxNbSe2 (x= 5% and 10%). We have calculated residual resistance ratio (RRR) 66.7 and 13 for 2H-NbSe2 single crystal and polycrystalline pellet respectively by using the formula r300/rTs where rTs is the resistivity at Ts for superconducting compound. Although their RRR values are different, they exhibit the superconducting transition at 7.4 K. Whereas the anomaly associated with the onset of CDW transition, visible as a small bump in resistivity, around 35 K is noticed only on the compounds of 2H-NbSe2 single crystal. In polycrystalline 2H-NbSe2, both electrical conductivity and CDW get affected. To identify the origin behind it, we have plotted the normalized resistivity, after subtracting the resistivity at Ts from
Fig. 3. Temperature dependence of Abs. Seebeck co-efficient of 2H-GaxNbSe2 (x =0, 5% and 10%).
overall resitivity, in the inset Fig. 2. We interpret this in terms of the grain boundary scattering and stacking faults/strain. Ga-ion intercalations reduce the value of residual resistance ratio (see Table 1) and significantly affect the electron scattering mechanism at higher temperature. The normalized resistivity shown in the inset Fig. 2 suggests that, the observed difference in conductivity between 2H-NbSe2 and its derivatives are related to carrier doping, grain boundary scattering and stacking faults/ strain. Therefore the CDW transition, if present, is not seen in the derivatives of 2H-NbSe2. The derivatives of 2H-NbSe2, however, reduce the superconducting transition temperature ‘Ts’ by receiving extra electrons from Ga-ions. 3.2. Seebeck coefficient Fig. 3, shows the temperature dependence of absolute Seebeck coefficient ‘S’ for 2H-NbSe2 and its derivatives. Around room
ARTICLE IN PRESS I. Naik, A.K. Rastogi / Physica B 405 (2010) 955–957
temperature, all of them give negative value. In 2H-NbSe2 single crystal and polycrystalline pellet, the values of S are comparable in magnitude around 320 K. But o300 K, the temperature dependence of S exhibits the difference between them, associated with change of sign from negative to positive at low temperature. It follows by a perceptible decrease at 35 K/by a broad maximum around 50 K in single crystal/polycrystalline pellet. The behavior of polycrystalline 2H-NbSe2 is quite similar with the reported results of 2H-NbS2 [12]. These broad maxima in transition metals are not understood still today. At room temperature, the negative value of S is increased, related to the increase of electron charge carriers in conduction band, with increase of intercalate element-Ga. In two-band model, S becomes negative when the electron density of states (DOS) in one band is very high compare to the density of hole in other band. In Ga-intercalated compounds, however, S increases slowly up to 50 K and then rises rapidly up to 16 K on cooling similar to self intercalated 3R-Nb1 + xS2 and Ga0.10NbS2 [12]. We have qualitatively explained these behaviors using two-band model in next section. 3.3. Two-band model in S The energy dependence of relaxation time i.e. t(e) determines the magnitude and sign of S. This relaxation time can be related with mean free path length l(e) by the equation, l(e)= t(e)v(e), where v(e) is velocity. Around room temperature, S is negative, opposite to the Hall coefficient in 2H-NbSe2. We use the temperature dependence of l(e) to explain the complicated Seebeck coefficient of 2H-NbSe2. Since 2H-NbSe2 is a multi-band metal; we assume its complex Fermi surface is separated into two spherical surfaces with electrons and holes like character. Mathematical expression of S obtained from simultaneous action of these two bands is given below [13], S¼
sh Sh þ se Se sh þ se
ð1Þ
Here, subscripts h and e stand for the positive and negative charge carrier respectively. s is used for electrical conductivity. For simplicity, we assume both bands have equal number of charge carriers ‘N’ with identical mass ‘m’. This implies that Fermi energy 2 levels ‘z’ in two bands are same i.e. ze ¼ ð‘ =2mÞð3ne p2 Þ3=2 ¼ zh ¼ z, where ‘ ¼ h=2p and h is plank’s constant. Including the sign of charge carriers in S, the ratio of mean free path is expressed as, 8 2 2 9 > p kB T 3 dlnNh > le ðe; TÞ < 3e 2z de þS = ¼ ð2Þ 2 k2 T lh ðe; TÞ > 3 B :p 3e ; dlnNe S> 2z
in one band is very low compare to the mobility of holes in other band in two band model. As the temperature decreases, S rises slowly up to 35 K passes through the zero value around 70 K at which two mean free paths are equal. Below 70 K, le(e)olh(e) is due to the dominating nature of electrons mobility over holes which make the S positive–negative in the case of Hall coefficient ‘RH’. In case of low RRR value 13 of 2H-NbSe2, however, change in sign of S occurs around 150 K. At room temperature, the ratio of mean free path le(e)/lh(e) decreases with increasing concentration of intercalate element-Ga up to 10% irrespective of their structures. On cooling, S is increased monotonically down to 50 K after that it rapidly increases towards the positive value in Ga-intercalated compounds.
4. Conclusion We have observed a common physical mechanism of superconductivity at low temperature in 2H-NbSe2 and 2H-GaxNbSe2 irrespective of their purity. Another physical mechanism, CDW, which is shown in 2H-NbSe2 with large RRR value, is disappeared in the case of lower RRR value because of the additional scattering centers; grain boundary and stacking faults/strain. For the derivatives of 2H-NbSe2, associated with the above said scattering centers, the value of resistivity and thermopower are marginally enhanced and supported for qualitative explanation of the temperature dependence mean free path through two-band model. We therefore conclude that the electronic transport properties of 2H-NbSe2 are very sensitive to the DOS and imperfections.
Acknowledgement One of the authors (I. Naik) acknowledge to CSIR for the financial support during this work.
References [1] [2] [3] [4] [5] [6] [7] [8]
de
Here, le(e,T) and lh(e,T) are the average mean free path length for electron and hole respectively. From Eq. (2), we obtained le(e) olh(e) in 2H-NbSe2 by substituting the room temperature negative value of S. This is possible when the mobility of electrons
957
[9] [10] [11] [12] [13]
M.H. Van Maaren, G.M. Schaeffer, Phys. Lett. 20 (2) (1966) 131. M.H. Van Maaren, G.M. Schaeffer, Phys. Lett. 24A (12) (1967) 645. N. Karnezos, L.B. Welsh, M.W. Shafer, Phys. Rev. B 11 (1975) 1808. J.M. Voorhoeve-van den Berg, J. Less Common Met. 26 (1972) 399. J.A. Wilson, F.J. Disalvo, S. Mohajan, Phys. Rev. Lett. 32 (16) (1974) 882. N.J. Doran, B. Ricco, M. Schreiber, D. Titterington, G. Wexler, J. Phys. C: Solid State Phys. 11 (1978) 699. T.M. Rice, G.K. Scott, Phys. Rev. Lett. 35 (1975) 120. L.-J. Li, Z.-a. Xu, J.-q. Shen, L.-m. Qiu, Z.-h. Gan, J. Phys: Condens. Matter 17 (2005) 493. C.W. Chu, V. Diatschenko, C.Y. Huang, F.J. Disalvo, Phys. Rev. B 15 (1977) 1340. M. Naito, S. Tanaka, J. Phys. Soc. Jpn. 51 (1982) 219. L.J. van der Pauw, Philips Res. Rep. 13 (1958) 1. A. Niazi, A.K. Rastogi, J. Phys: Condens. Matter 13 (2001) 6787. F.J. Blatt, P.A. Schroeder, C.L. Foiles, D. Greig, Thermoelectric Power of Metals, Plenum Press, New York, London, 1976.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Transport properties of 2H-NbSe2: Effect of Ga-intercalation I. Naik a,, A.K. Rastogi b a b
Department of Physics, North Orissa University, Takatpur, Baripada – 757003, India School of Physical Sciences, Jawaharlal Nehru University, New Delhi – 110067, India
a r t i c l e in fo
abstract
Article history: Received 15 June 2009 Received in revised form 19 October 2009 Accepted 19 October 2009
We have prepared compounds of 2H-NbSe2 and 2H-GaxNbSe2 (x= 5% and 10%) at 700 1C. 2H-NbSe2 single crystal exhibits superconducting and charge density wave (CDW) transition at 7.4 K and 35 K, respectively, whereas in polycrystalline pellet of poor residual resistance ratio (RRR) value, the CDW is absent. In Ga-intercalated compounds, the rapid decrease of superconducting transition temperature was noticed. Here we report the occurrence of two-band model in which the temperature dependence of mean free path length ‘l(e)’ is the main factor for overall behavior of resistivity and thermopower. & 2009 Elsevier B.V. All rights reserved.
Keywords: Charge density wave Transition-metal compounds Superconductivity
1. Introduction Group-V transition-metal dichalcogenide compounds (TMDC) have been studied extensively for understanding the mechanism of Charge Density Wave (CDW) transition. Besides this, some of them show superconducting properties at low temperature, e.g. NbSe2, NbS2, NbTe2, TaSe2 and TaS2 [1,2]. This is a remarkable behavior, since the superconducting order is not compatible with the CDW order. The possibility of the coexistence of CDW and superconductivity in anisotropic structures has been the subject of intense studied over the last four decades as stoichiometry, intercalation and disorder significantly affect these two transitions. The original structure of TMDC is changed beyond a critical value for the intercalation, which depend on the metal atoms. Within the same symmetry, metal atom intercalation changes the c-axis and a small ( o3%) increase in a-axis. In 2H-NbSe2, a maximum of 33% and 67% tetrahedral sites are occupied by Al and Cu respectively is reported [3,4]. 2H-NbSe2 is one of them in which the CDW, expected to arise from Fermi surface nesting [5,6] or from saddle points in the electronic band [7], and superconducting transitions exist at 35 and 7.4 K respectively. Though the effect of RRR is not seen in Ts, it washes out the CDW transition for low RRR value [8]. Both the transitions get affected by stacking order and pressure in which the number density of states (DOS) increase in the conduction band through restoring of Fermi surface lost by CDW instability [9].
Corresponding author. Fax: +091 6792 255127.
E-mail address: [email protected] (I. Naik). 0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.10.028
In the present study we have attempted to prepare 2H-NbSe2, 2H-Ga0.05NbSe2 and 2H-Ga0.10NbSe2 compounds. 2H-NbSe2 with large RRR value ( 67 for single crystal) shows superconductivity (Ts =7.4 K) below a Charge Density Wave (CDW), which is vanished for lower RRR value ( 13 for pellet), at 35 K similar to reported results [8,10]. The sign of Seebeck co-efficient ‘S’ is found negative opposite to Hall coefficient ‘RH’ at room temperature and behave differently in the temperature range of 16–300 K. It, Seebeck coefficient, also exhibits anomaly around CDW transition in single crystal 2H-NbSe2 (Fig. 3).
2. Experimental details 2H-NbSe2 and its derivatives, Ga-intercalations, were prepared by direct reaction of elements, Ga= 99.99%, Nb= 99.8% and Se= 99.999%, in an evacuated sealed quartz tube at 750 1C. This is followed by grinding and pelletization in a dray box. Finally they are sintered at 700 1C for seven days. We were able to prepare single crystal flakes for 2H-NbSe2 by vapor transport technique at 750 1C. X-ray diffraction: The crystal structure of NbSe2 was confirmed to be in the 2H-phase from room temperature X-ray ˚ The diffraction with lattice constants a 3.445 A˚ and c 12.551 A. c-axis is marginally affected in the Ga-intercalated compounds (see Table 1) indicating that the Ga-ions are occupied the octahedral sites between the layers. The perfect stacking order along 10 l line makes the intensity sharp. For Ga-intercalated compounds, the peak broadening is either by stacking faults or strain. All the compounds have large intensity for 102 planes are related to orientation effect of crystallites (Fig. 1).
ARTICLE IN PRESS 956
I. Naik, A.K. Rastogi / Physica B 405 (2010) 955–957
Fig. 1. Room temperature X-ray diffraction of 2H-GaxNbSe2 (x =0, 5% and 10%).
Fig. 2. Temperature dependence of resistivity of 2H-GaxNbSe2 (x= 0, 5% and 10%). The inset figure shows the normalized resistivity for 2H-GaxNbSe2 (x= 0, 5% and 10%).
Table 1 Compound name
a
Symmentry (300 K) Latice constant (a)
b
b
b
2H –
2H
2H
2H
3.445 A˚
3.450 A˚
3.453 A˚
(c)
–
RRR value r300 (O cm) 10 4 Ts (K) S300 (mV/K) Tc (K)
66.7 0.68 7.4 4.08 35
12.551 A˚ 13.0 1.96 7.4 3.70 –
12.592 A˚ 2.9 4.18 5.6 6.33 –
12.605 A˚ 1.5 12.3 2.7 11.21 –
NbSe2
NbSe2
Ga0.05NbSe2
Ga0.10NbSe2
Ts (K)= Superconducting transition temperature. Tc (K)=CDW transition temperature. a b
For single crystal. For polycrystalline compound.
D.C. resistance measurements were carried out on single crystal and polycrystalline pellets using van-der Pauw geometry [11]. Seebeck co-efficient was measured with respect to Cu by reversing the temperature gradient at different temperatures. Finally absolute Seebeck coefficient was obtained by correcting the thermopower of Cu.
3. Results and discussions 3.1. Resistivity Fig. 2 shows the temperature dependence of resistivity for 2HNbSe2 and 2H-GaxNbSe2 (x= 5% and 10%). We have calculated residual resistance ratio (RRR) 66.7 and 13 for 2H-NbSe2 single crystal and polycrystalline pellet respectively by using the formula r300/rTs where rTs is the resistivity at Ts for superconducting compound. Although their RRR values are different, they exhibit the superconducting transition at 7.4 K. Whereas the anomaly associated with the onset of CDW transition, visible as a small bump in resistivity, around 35 K is noticed only on the compounds of 2H-NbSe2 single crystal. In polycrystalline 2H-NbSe2, both electrical conductivity and CDW get affected. To identify the origin behind it, we have plotted the normalized resistivity, after subtracting the resistivity at Ts from
Fig. 3. Temperature dependence of Abs. Seebeck co-efficient of 2H-GaxNbSe2 (x =0, 5% and 10%).
overall resitivity, in the inset Fig. 2. We interpret this in terms of the grain boundary scattering and stacking faults/strain. Ga-ion intercalations reduce the value of residual resistance ratio (see Table 1) and significantly affect the electron scattering mechanism at higher temperature. The normalized resistivity shown in the inset Fig. 2 suggests that, the observed difference in conductivity between 2H-NbSe2 and its derivatives are related to carrier doping, grain boundary scattering and stacking faults/ strain. Therefore the CDW transition, if present, is not seen in the derivatives of 2H-NbSe2. The derivatives of 2H-NbSe2, however, reduce the superconducting transition temperature ‘Ts’ by receiving extra electrons from Ga-ions. 3.2. Seebeck coefficient Fig. 3, shows the temperature dependence of absolute Seebeck coefficient ‘S’ for 2H-NbSe2 and its derivatives. Around room
ARTICLE IN PRESS I. Naik, A.K. Rastogi / Physica B 405 (2010) 955–957
temperature, all of them give negative value. In 2H-NbSe2 single crystal and polycrystalline pellet, the values of S are comparable in magnitude around 320 K. But o300 K, the temperature dependence of S exhibits the difference between them, associated with change of sign from negative to positive at low temperature. It follows by a perceptible decrease at 35 K/by a broad maximum around 50 K in single crystal/polycrystalline pellet. The behavior of polycrystalline 2H-NbSe2 is quite similar with the reported results of 2H-NbS2 [12]. These broad maxima in transition metals are not understood still today. At room temperature, the negative value of S is increased, related to the increase of electron charge carriers in conduction band, with increase of intercalate element-Ga. In two-band model, S becomes negative when the electron density of states (DOS) in one band is very high compare to the density of hole in other band. In Ga-intercalated compounds, however, S increases slowly up to 50 K and then rises rapidly up to 16 K on cooling similar to self intercalated 3R-Nb1 + xS2 and Ga0.10NbS2 [12]. We have qualitatively explained these behaviors using two-band model in next section. 3.3. Two-band model in S The energy dependence of relaxation time i.e. t(e) determines the magnitude and sign of S. This relaxation time can be related with mean free path length l(e) by the equation, l(e)= t(e)v(e), where v(e) is velocity. Around room temperature, S is negative, opposite to the Hall coefficient in 2H-NbSe2. We use the temperature dependence of l(e) to explain the complicated Seebeck coefficient of 2H-NbSe2. Since 2H-NbSe2 is a multi-band metal; we assume its complex Fermi surface is separated into two spherical surfaces with electrons and holes like character. Mathematical expression of S obtained from simultaneous action of these two bands is given below [13], S¼
sh Sh þ se Se sh þ se
ð1Þ
Here, subscripts h and e stand for the positive and negative charge carrier respectively. s is used for electrical conductivity. For simplicity, we assume both bands have equal number of charge carriers ‘N’ with identical mass ‘m’. This implies that Fermi energy 2 levels ‘z’ in two bands are same i.e. ze ¼ ð‘ =2mÞð3ne p2 Þ3=2 ¼ zh ¼ z, where ‘ ¼ h=2p and h is plank’s constant. Including the sign of charge carriers in S, the ratio of mean free path is expressed as, 8 2 2 9 > p kB T 3 dlnNh > le ðe; TÞ < 3e 2z de þS = ¼ ð2Þ 2 k2 T lh ðe; TÞ > 3 B :p 3e ; dlnNe S> 2z
in one band is very low compare to the mobility of holes in other band in two band model. As the temperature decreases, S rises slowly up to 35 K passes through the zero value around 70 K at which two mean free paths are equal. Below 70 K, le(e)olh(e) is due to the dominating nature of electrons mobility over holes which make the S positive–negative in the case of Hall coefficient ‘RH’. In case of low RRR value 13 of 2H-NbSe2, however, change in sign of S occurs around 150 K. At room temperature, the ratio of mean free path le(e)/lh(e) decreases with increasing concentration of intercalate element-Ga up to 10% irrespective of their structures. On cooling, S is increased monotonically down to 50 K after that it rapidly increases towards the positive value in Ga-intercalated compounds.
4. Conclusion We have observed a common physical mechanism of superconductivity at low temperature in 2H-NbSe2 and 2H-GaxNbSe2 irrespective of their purity. Another physical mechanism, CDW, which is shown in 2H-NbSe2 with large RRR value, is disappeared in the case of lower RRR value because of the additional scattering centers; grain boundary and stacking faults/strain. For the derivatives of 2H-NbSe2, associated with the above said scattering centers, the value of resistivity and thermopower are marginally enhanced and supported for qualitative explanation of the temperature dependence mean free path through two-band model. We therefore conclude that the electronic transport properties of 2H-NbSe2 are very sensitive to the DOS and imperfections.
Acknowledgement One of the authors (I. Naik) acknowledge to CSIR for the financial support during this work.
References [1] [2] [3] [4] [5] [6] [7] [8]
de
Here, le(e,T) and lh(e,T) are the average mean free path length for electron and hole respectively. From Eq. (2), we obtained le(e) olh(e) in 2H-NbSe2 by substituting the room temperature negative value of S. This is possible when the mobility of electrons
957
[9] [10] [11] [12] [13]
M.H. Van Maaren, G.M. Schaeffer, Phys. Lett. 20 (2) (1966) 131. M.H. Van Maaren, G.M. Schaeffer, Phys. Lett. 24A (12) (1967) 645. N. Karnezos, L.B. Welsh, M.W. Shafer, Phys. Rev. B 11 (1975) 1808. J.M. Voorhoeve-van den Berg, J. Less Common Met. 26 (1972) 399. J.A. Wilson, F.J. Disalvo, S. Mohajan, Phys. Rev. Lett. 32 (16) (1974) 882. N.J. Doran, B. Ricco, M. Schreiber, D. Titterington, G. Wexler, J. Phys. C: Solid State Phys. 11 (1978) 699. T.M. Rice, G.K. Scott, Phys. Rev. Lett. 35 (1975) 120. L.-J. Li, Z.-a. Xu, J.-q. Shen, L.-m. Qiu, Z.-h. Gan, J. Phys: Condens. Matter 17 (2005) 493. C.W. Chu, V. Diatschenko, C.Y. Huang, F.J. Disalvo, Phys. Rev. B 15 (1977) 1340. M. Naito, S. Tanaka, J. Phys. Soc. Jpn. 51 (1982) 219. L.J. van der Pauw, Philips Res. Rep. 13 (1958) 1. A. Niazi, A.K. Rastogi, J. Phys: Condens. Matter 13 (2001) 6787. F.J. Blatt, P.A. Schroeder, C.L. Foiles, D. Greig, Thermoelectric Power of Metals, Plenum Press, New York, London, 1976.