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Physics Letters A 327 (2004) 221–225

www.elsevier.com/locate/pla

Effect of magnetic field on the thermoelectric powerin the quasi-one-dimensional metal NbSe3

Jing-qin Shena, Zhu-an Xua,∗, Xue-zhi Chena, Hong-tao Wangb

a Department of Physics, Zhejiang University, Hangzhou 310027, PR Chinab Department of Physics and Electronic Information Science, Wenzhou Normal College, Wenzhou 325027, PR China

Received 29 March 2004; accepted 5 May 2004

Available online 18 May 2004

Communicated by J. Flouquet

Abstract

The electrical resistivityρ and thermoelectric powerS in the charge-density wave (CDW) state of the quasi-one-dimensconductor NbSe3 under transverse magnetic field were studied systematically. The dramatic variations of the thermopower, as well as the resistivity, with the magnetic fieldH , were analyzed in a modified two-band model. The rescan be interpreted well in terms of the conversion of electron-like charge carrier into CDW condensed state causeenhancement of CDW gap. Below 30 K, the variation of the electron-like charge carrier density with magnetic fieldfrom thermoelectric power data deviates from that derived from magnetoresistance data, which implies that there couldeffects of magnetic field on the dynamics of charge carriers than the effect on the density of charge carrier. 2004 Elsevier B.V. All rights reserved.

PACS: 71.45.Lr; 72.15.Gd; 72.15.Jf

Keywords: Thermoelectric power; Two-band model; Charge-density wave; Density of charge carrier

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As early as in 1976, Monceau and Ong et al.[1,2]first reported the nonlinear conductivity of quasi-ondimensional metal NbSe3, which made it an attractive candidate for charge-density wave (CDW) stuIn contrast to most other CDW materials, NbSe3 re-mains metallic or ‘semi-metallic’ even after expeencing two CDW transitions atT1 = 144 K andT2 =59 K respectively (defined as CDW-I and CDW-II sta

* Corresponding author.E-mail address: zhuan@zju.edu.cn (Z.-a. Xu).

0375-9601/$ – see front matter 2004 Elsevier B.V. All rights reserveddoi:10.1016/j.physleta.2004.05.004

hereafter), because its Fermi surface (FS) has notdestroyed completely. Ong, Monceau[2] estimated theproportion (α) of the destroyed FS by the change ofsistance at the CDW transition: only 20% of the FSdestroyed by the formation of CDW gap in the upptransition (T1 = 145 K) and about 60% of the remaiing FS destroyed in the lower transition (T2 = 59 K).

Furthermore, a giant positive magnetoresista(MR) was discovered in CDW-II state (T < T2) underthe transverse magnetic field, and the temperaturefield dependence violates the ‘Kohler’s ruler’ whiholds for many normal metals[3–6]. Meanwhile, it

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222 J.-q. Shen et al. / Physics Letters A 327 (2004) 221–225

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was also found that the thermoelectric power attemperature region is enormously affected by the mnetic field [7]. To explain the anomalous magnefield effect, a theory in which the CDW gap can be ehanced by a magnetic field was developed by Balsand Falicov (BF)[8,9]. They proposed that the Fnesting builds up with the increasing transverse mnetic field, therefore the CDW gap is enhanced athe remaining FS is destroyed gradually, which leto more free electrons condensed into CDW stThe field dependence of resistance and thermoelepower, as well as other transport properties couldinterpreted qualitatively within the frame of BF theobut some experimental results are quantitatively incsistent with BF theory. For example, Tritt et al.[10,11]found that the variation of electron density with manetic field in narrow-band-noise measurement is msmaller than that calculated by the BF theory. Recethe tunneling spectroscopy in a high magnetic fidisagrees with the BF theory either[12]. Up to now,the mechanism of the large MR and magneto-Seebeffect (MS) in NbSe3 still remains ambiguous.

In this Letter, we revisited the magnetic fiedependence of thermoelectric power of NbSe3 in theCDW-II state, and a modified two-band model winvoked to interpret both the large MR and MS in tmagnetic field. From the fitting results, we concludthat the variation of the density of electron-like carriewith magnetic field can almost account for both Mand MS and the BF theory is still applicable to soextent.

The crystalline samples of NbSe3 were preparedby a two-step vapor transport method[13]. High pu-rity Nb and Se powder in stoichiometric quantities,gether with a transport agent (excess Se), were plain one end of a quartz tube, which was then evacuand sealed. The sealed tube was heated up to∼ 700◦Cslowly in a gradient furnace and a reverse tempeture gradient (i.e., the starting material end was coldwas maintained in this step. Then a forward teperature gradient was slowly established and mtained for about one week. The details of the growprocedure were reported elsewhere[14]. The typicalcross section of the NbSe3 whiskers read from theiscanning electronic microscopy photographs is ab10 µm× 1 µm. The electrical resistivity of NbSe3 wasmeasured by a standard four-probe method andexcitation current applied was small compared to

Fig. 1. The thermoelectric power of NbSe3 from room temperaturedown to 5 K at H = 0 T. The inset shows the temperatudependence of resistivity for the NbSe3 sample from the same batcThe arrows indicate the two CDW transition temperatures.

threshold electrical field of CDW sliding. The themoelectric power (Seebeck effect,S) was measuredby using a steady state method. All the measuremwere done in a Quantum Design PPMS-9 system.

Fig. 1 shows the temperature dependence of thmoelectric power of NbSe3 sample from room temperature down to 10 K. The temperature dependeof resistivity plotted in the inset ofFig. 1 was mea-sured on the whisker sample from the same batchhas been reported in Ref.[6]. The arrows indicate thtwo CDW transitions at the temperaturesT1 ∼ 145 Kand T2 ∼ 59 K, respectively. From theS(T ) curve,we can see that in the “normal state” (aboveT1), thethermoelectric power is small and negative, similarcommon metals. However, the slope ofS(T ) changesdramatically atT ∼ T1 (the first CDW transition) andthe temperature dependence becomes sharp. TheS re-mains negative, but it decreases quickly. AtT ∼ T2,the S(T ) curve turns abruptly again, and it beginsincrease at an even larger slope to a positive valuefurther cooling down. This behavior ofS(T ) is consis-tent with the previous reports[7,15]. But our measurement at low temperature was more detailed. A potive peak can be easily seen at around 10 K, butvalue ofS finally tends to be zero as the temperatapproaches zero.

Fig. 2 shows the temperature dependence ofthermoelectric power,S(T ), in different transversemagnetic fields. In normal metal state (T > T1) and

J.-q. Shen et al. / Physics Letters A 327 (2004) 221–225 223

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Fig. 2. The temperature dependence of thermoelectric power oNbSe3 in CDW-II state under different transverse magnetic field

CDW-I state (T1 < T < T2), we found no observablchange of S(T ) with the applied magnetic fieldBut when it goes into CDW-II state, the magnefield dependence of thermoelectric power is enhangradually. As the broad peak observed in MRlarge peak inS(T ) appears at aboutT ∼ 20 Kand it moves to higher temperatures with increasmagnetic field. For common metals, it is impossithat the applied magnetic field could lead to suclarge change of thermoelectric power, therefore it wrationally suggested that the change is due to the Cenhancement under magnetic field[7,15]. In addition,we found that althoughS becomes very large when thapplied magnetic field is as large as 8 T, it still tendsgo to zero when the temperature approaches abszero.

In CDW-II state of NbSe3, both the resistivityand thermoelectric power increases rapidly withincreasing magnetic field. To interpret the variationtransport properties with the magnetic field, Balseand Falicov (BF)[8,9] developed a theory assuminthat in CDW-II state the magnetic field enhancesCDW gap, that is, it enhances the ‘Nesting’ of Fand destroys the remaining FS gradually, which memore and more free electrons condensed into Cstate electrons which causes the increase of resistivityOur MR data can be fitted by a modified two modwithin the frame of BF theory and the effectmagnetic field on the density of electron-like charcarrier can be derived[6].

The thermoelectric power of common metal is ually divided into two terms: one is the carriers’ diffusion termSd and the other the phonon dragging teSg . Sg contributes little to thermoelectric powerhigh temperature, because the diffusion of phonontoo strong to couple into charge carriers effectively.in high temperature,Sd term play a dominant role, anS ≈ cel

q≈ kB

ekBTεF

. However, in low temperature regio(well below the Debye temperature), the phonon teSg plays a dominant role. For some metals, the pealow temperature can be attributed to the phonon dging part[16]. Usually the magnetic field does not afect phonons considerably, thus the phonon termSg

cannot be affected much by magnetic field. In the dfusion magneto-thermoelectric power theory of Blet al.[17], the change of the diffusion termSd in mag-netic field can be expressed as

(1)�S = π2k2BT

3|e|[

�ρ/ρ

1+ �ρ/ρ

]D,

where�ρ/ρ is magnetoresistance andD is a fittingparameter. As pointed out in Ref.[7], in the CDW-II state of NbSe3, because�ρ/ρ � 1, the change othermoelectric power should be saturated very quicwith increasing magnetic field, which is contrastthe experimental observation. It is clear that neitconventional phonon drag nor diffusion thermoelecpower can account for the observed large MSNbSe3.

In our previous report[6], the MR in CDW-II statehas been fitted very well by a modified two-bamodel in the frame of BF theory. In this model,is assumed that the two types of charge carrier hthe same relaxation time and mass in the two-bgalvanomagnetic effect model which was originaproposed by Noto and Tsuzuku[18]. Furthermore,the effect of magnetic field on the ratio of two typcarrier densities is represented by a constantγ , i.e.,ne/nh = β − γH , where thenh (ne) is the densityof the hole-like (electron-like) charge carriers andβ

the ratio atH = 0. The fitting results indicate thathe ratio of electron-like carrier density to hole-likcarrier density decreases withdecreasing temperaturein CDW-II state[6]. From the fitting parameterβ andγ , we can estimate the effect of magnetic field onelectron-like carrier density,ne(H)/ne(0), viz.,

(2)ne(H)/ne(0) = (β − γH)/β.

224 J.-q. Shen et al. / Physics Letters A 327 (2004) 221–225

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Fig. 3. The temperature dependence ofne(T ,H)/ne(T ,0) derivedfrom MS and MR data in CDW-II state under different magnefields. Square denotes the parameters derived from MS, and triadenotes the parameters derived from the fitting result of the MR

The results obtained according toEq. (2)are plotted inFig. 3.

Within the frame of BF theory, we also use a twband model to interpret the variation of thermoelecpower with applied magnetic field, and the resultsbasically consistent with the fitting results of MRFollowing the approach used in Ref.[7], the totalthermoelectric power in the two-band model canexpressed as

(3)S = σeSe + σhSh

σe + σh

,

whereσh (σe) is the conductivity of holes (electronandSh (Se) is the contribution of holes (electrons)total thermoelectric power. Since it is assumed tmagnetic field only affects the density of electron-licarriers, we can set thatσh, Sh andSe is independenof H . So we can obtain

(4)ne(T ,H)

ne(T ,0)∼= S(T ,0) − Se

S(T ,H) − Se

· Sh − S(T ,H)

Sh − S(T ,0),

whereS(T ,0), S(T ,H) is the thermoelectric poweat zero magnetic field and magnetic fieldH . We esti-matedSe = −50 µV/K andSh = 80 µV/K, and thenthe temperature dependence ofne(T ,H)/ne(T ,0)

were obtained according toEq. (4). The estimatedvariations of electron type density under magnefield H = 4 T and 8 T are shown inFig. 3 (square

symbols). The triangle symbols denote the resultsrived from the MR data.

Fig. 3 shows that belowT2 the density of nor-mal conduction electrons reduces with the increing of magnetic field and this trend becomes mdistinct with the decreasing temperature, whichconsistent with the scenario that magnetic field pmotes the destroying of electron-like FS and resultmore electrons condensed into CDW electrons. Hever,ne(T ,H)/ne(T ,0) first decreases with decreaing temperature, then saturates at about 20 K, aneventually increases in lower temperatures. Thishaviour could be caused by the saturation of magnfield enhancement of CDW gapping. Sone(T ,H) be-comes less temperature dependence whilene(T ,0)

still decreases and this leads to the increase of thene(T ,H)/ne(T ,0) in temperatures below 20 K.

From 60 K down to 30 K, the value ofne(T ,H)/

ne(T ,0) derived from MS data agrees well withat derived from MR data. Below 30 K, there israther deviation. Furthermore, the value ofne(T ,H)/

ne(T ,0) at 20 K estimated fromEq. (4)is only about0.10, which is unreasonably small, indicating thattwo-band model we used is too simple to descrthe complicated variation of transport propertiesthis temperature range. A recent optical investigatioof NbSe3 suggested that the scattering times offree charge carriers are suppressed by the Ctransitions[19]. Since the effect of magnetic field othe scattering times of charge carriers is not takenaccount in our two-band model, it is not surprising ththe unreasonably small values ofne(T ,H)/ne(T ,0)

are derived from MS data around 20 K, which disagwith the values derived from MR data.

In summary, we studied the magnetic field depdence of thermoelectric power of NbSe3 in the CDW-II state. Within the frame of BF theory, a two-banmodel is employed to account for MS data, and therived temperature and field dependence of the denof electron-like charge carriers,ne(T ,H)/ne(T ,0) iscompared with that derived from MR data. Abo30 K, both the MR data and MS data can be fitted wby the two-band model, and a discrepance of therameterne(T ,H)/ne(T ,0) derived from MR and MSdata is found asT < 30 K, which implies that therecould be other effects of magnetic field on the traport properties besides its effect on the charge cadensity.

J.-q. Shen et al. / Physics Letters A 327 (2004) 221–225 225

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Acknowledgements

This work was supported by the National NatuScience Foundation of China (Grant No. 10225417

References

[1] P. Monceau, N.P. Ong, A.M. Portis, A. Meerschaut, J. RouPhys. Rev. Lett. 37 (1976) 602.

[2] N.O. Ong, P. Monceau, Phys. Rev. B 16 (1977) 3443.[3] P. Parilla, M.F. Hundley, A. Zettl, Phys. Rev. Lett. 57 (198

619.[4] R.V. Coleman, G. Eiserman, M.P. Everson, A. Johnson, L

Falicov, Phys. Rev. Lett. 55 (1985) 863.[5] R.V. Coleman, M.P. Everson, H.A. Lu, A. Johnson, L.M

Falicov, Phys. Rev. B 41 (1990) 460.[6] J.Q. Shen, X.Z. Chen, Y. Zheng, H.T. Wang, Z.A. Xu, J. Phy

Condens. Matter 15 (2003) 5353.

[7] M.F. Hundley, A. Zettl, Solid State Commun. 61 (1987) 587[8] C.A. Balseiro, L.M. Falicov, Phys. Rev. Lett. 55 (1985) 233[9] C.A. Balseiro, L.M. Falicov, Phys. Rev. B 34 (1986) 863.

[10] T.M. Tritt, D.J. Gillespie, A.C. Ehrlich, G.X. Tessema, PhyRev. Lett. 61 (1988) 1776.

[11] T.M. Tritt, A.C. Ehrlich, D.J. Gillespie, G.X. Tessema, PhyRev. B 43 (1991) 7254.

[12] A.A. Sinchenko, P. Monceau, Phys. Rev. B 67 (2003) 2331[13] R.E. Thorne, Phys. Rev. B 45 (1992) 5804.[14] H. Wang, Y. Zheng, X. Chen, Z. Xu, Chin. J. Mater. Res.

(2003) 247.[15] P.M. Chaikin, W.W. Fuller, R. Lacoe, Solid State Commun.

(1981) 553.[16] See, for example, F.J. Blatt, D. Greig, Thermoelectric Powe

Metals, Plenum, New York, 1976.[17] F.J. Blatt, A.D. Caplin, C.K. Chiang, P.A. Schroeder, Soli

State Commun. 15 (1974) 411.[18] K. Noto, T. Tsuzuku, Jpn. J. Appl. Phys. 14 (1975) 46.[19] A. Perucchi, L. Degiorgi, R.E. Thorne, cond-mat/0310744.