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

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<ul><li><p>Physics Letters A 327 (2004) 221225</p><p>e tion</p><p>zhity, Haenzho</p><p>Received 29 March 2004; accepted 5 May 2004</p><p>Abstr</p><p>Thecondupowercan beenhancfrom teffects 200</p><p>PACS:</p><p>Keywor</p><p>Asfirst rdimentive cIn conmainsencin59 K r</p><p>* CoE-</p><p>0375-9doi:10.Available online 18 May 2004</p><p>Communicated by J. Flouquet</p><p>act</p><p>electrical resistivity and thermoelectric power S in the charge-density wave (CDW) state of the quasi-one-dimensionalctor NbSe3 under transverse magnetic field were studied systematically. The dramatic variations of the thermoelectric, as well as the resistivity, with the magnetic field H , were analyzed in a modified two-band model. The results</p><p>interpreted well in terms of the conversion of electron-like charge carrier into CDW condensed state caused by theement of CDW gap. Below 30 K, the variation of the electron-like charge carrier density with magnetic field derived</p><p>hermoelectric power data deviates from that derived from magnetoresistance data, which implies that there could be otherof magnetic field on the dynamics of charge carriers than the effect on the density of charge carrier.</p><p>4 Elsevier B.V. All rights reserved.</p><p>71.45.Lr; 72.15.Gd; 72.15.Jf</p><p>ds: Thermoelectric power; Two-band model; Charge-density wave; Density of charge carrier</p><p>early as in 1976, Monceau and Ong et al. [1,2]eported the nonlinear conductivity of quasi-one-sional metal NbSe3, which made it an attrac-</p><p>andidate for charge-density wave (CDW) study.trast to most other CDW materials, NbSe3 re-metallic or semi-metallic even after experi-</p><p>g two CDW transitions at T1 = 144 K and T2 =espectively (defined as CDW-I and CDW-II state</p><p>rresponding author.mail address: zhuan@zju.edu.cn (Z.-a. Xu).</p><p>hereafter), because its Fermi surface (FS) has not beendestroyed completely. Ong, Monceau [2] estimated theproportion () of the destroyed FS by the change of re-sistance at the CDW transition: only 20% of the FS isdestroyed by the formation of CDW gap in the uppertransition (T1 = 145 K) and about 60% of the remain-ing FS destroyed in the lower transition (T2 = 59 K).</p><p>Furthermore, a giant positive magnetoresistance(MR) was discovered in CDW-II state (T &lt; T2) underthe transverse magnetic field, and the temperature andfield dependence violates the Kohlers ruler whichholds for many normal metals [36]. Meanwhile, it</p><p>601/$ see front matter 2004 Elsevier B.V. All rights reserved.1016/j.physleta.2004.05.004Effect of magnetic field on thin the quasi-one-dimens</p><p>Jing-qin Shen a, Zhu-an Xu a,, Xue-a Department of Physics, Zhejiang Universi</p><p>b Department of Physics and Electronic Information Science, Wwww.elsevier.com/locate/pla</p><p>hermoelectric poweral metal NbSe3Chen a, Hong-tao Wang b</p><p>ngzhou 310027, PR Chinau Normal College, Wenzhou 325027, PR China</p></li><li><p>222 J.-q. Shen et al. / Physics Letters A 327 (2004) 221225</p><p>was also found that the thermoelectric power at thistemperature region is enormously affected by the mag-netic field [7]. To explain the anomalous magneticfield ehanceand Fnestinneticthe reto moThe fipowerinterpbut sosistenfoundneticsmallthe tudisagrthe meffect</p><p>IndepenCDWinvokmagnthat thwith mand Mexten</p><p>Thby a trity Ngethein oneand seslowlyture gwas m</p><p>peratutainedprocecross</p><p>scann</p><p>10 mmeasu</p><p>excita</p><p>ig. 1.wn tpend</p><p>he arr</p><p>reshoele</p><p>y usiere dFig</p><p>oeleeratuf resred</p><p>as beo C</p><p>nd Te ca</p><p>ermomm</p><p>ramae temainse S(</p><p>crea</p><p>rthent went</p><p>ve palueppro</p><p>Figermagneffect, a theory in which the CDW gap can be en-d by a magnetic field was developed by Balseiroalicov (BF) [8,9]. They proposed that the FSg builds up with the increasing transverse mag-field, therefore the CDW gap is enhanced andmaining FS is destroyed gradually, which leadsre free electrons condensed into CDW state.eld dependence of resistance and thermoelectric, as well as other transport properties could bereted qualitatively within the frame of BF theory,me experimental results are quantitatively incon-t with BF theory. For example, Tritt et al. [10,11]that the variation of electron density with mag-</p><p>field in narrow-band-noise measurement is mucher than that calculated by the BF theory. Recentlynneling spectroscopy in a high magnetic fieldees with the BF theory either [12]. Up to now,echanism of the large MR and magneto-Seebeck(MS) in NbSe3 still remains ambiguous.this Letter, we revisited the magnetic fielddence of thermoelectric power of NbSe3 in the-II state, and a modified two-band model wased to interpret both the large MR and MS in theetic field. From the fitting results, we concludede variation of the density of electron-like carriersagnetic field can almost account for both MR</p><p>S and the BF theory is still applicable to somet.e crystalline samples of NbSe3 were preparedwo-step vapor transport method [13]. High pu-b and Se powder in stoichiometric quantities, to-r with a transport agent (excess Se), were placed</p><p>end of a quartz tube, which was then evacuatedaled. The sealed tube was heated up to 700 C</p><p>in a gradient furnace and a reverse tempera-radient (i.e., the starting material end was colder)</p><p>aintained in this step. Then a forward tem-re gradient was slowly established and main-for about one week. The details of the growth</p><p>dure were reported elsewhere [14]. The typicalsection of the NbSe3 whiskers read from theiring electronic microscopy photographs is about 1 m. The electrical resistivity of NbSe3 wasred by a standard four-probe method and thetion current applied was small compared to the</p><p>FdodeT</p><p>thm</p><p>bw</p><p>m</p><p>po</p><p>su</p><p>htwa</p><p>w</p><p>thc</p><p>dthm</p><p>thinfutem</p><p>tiv</p><p>a</p><p>thmThe thermoelectric power of NbSe3 from room temperatureo 5 K at H = 0 T. The inset shows the temperatureence of resistivity for the NbSe3 sample from the same batch.ows indicate the two CDW transition temperatures.</p><p>old electrical field of CDW sliding. The ther-ctric power (Seebeck effect, S) was measuredng a steady state method. All the measurementsone in a Quantum Design PPMS-9 system.. 1 shows the temperature dependence of ther-ctric power of NbSe3 sample from room tem-re down to 10 K. The temperature dependenceistivity plotted in the inset of Fig. 1 was mea-on the whisker sample from the same batch anden reported in Ref. [6]. The arrows indicate theDW transitions at the temperatures T1 145 K2 59 K, respectively. From the S(T ) curve,n see that in the normal state (above T1), theoelectric power is small and negative, similar toon metals. However, the slope of S(T ) changestically at T T1 (the first CDW transition) andperature dependence becomes sharp. The S re-negative, but it decreases quickly. At T T2,T ) curve turns abruptly again, and it begins tose at an even larger slope to a positive value withr cooling down. This behavior of S(T ) is consis-ith the previous reports [7,15]. But our measure-at low temperature was more detailed. A posi-eak can be easily seen at around 10 K, but theof S finally tends to be zero as the temperatureaches zero.. 2 shows the temperature dependence of theoelectric power, S(T ), in different transversetic fields. In normal metal state (T &gt; T1) and</p></li><li><p>J.-q. Shen et al. / Physics Letters A 327 (2004) 221225 223</p><p>Fig. 2.NbSe3</p><p>CDWchangBut wfield dgradulargeand itmagnthat tlargerationenhanwe foappliego tozero.</p><p>Inand thincreatranspand Fthat inCDWand dmore</p><p>state eOur Mwithinmagncarrie</p><p>The thermoelectric power of common metal is usu-ally divided into two terms: one is the carriers diffu-sion term Sd and the other the phonon dragging termg . S</p><p>igh to strhig c</p><p>qell</p><p>g plaw te</p><p>ing pct p</p><p>anno</p><p>siont al. [etic fi</p><p>S =</p><p>herearamstaterm</p><p>ith ie ex</p><p>onve</p><p>owerbSe3In</p><p>as bodelassu</p><p>e sa</p><p>alvanropoe ef</p><p>arriee/nhf thee ra</p><p>e ra</p><p>arrieCD</p><p>, we</p><p>lectro</p><p>e(H)The temperature dependence of thermoelectric power ofin CDW-II state under different transverse magnetic fields.</p><p>-I state (T1 &lt; T &lt; T2), we found no observablee of S(T ) with the applied magnetic field.hen it goes into CDW-II state, the magneticependence of thermoelectric power is enhanced</p><p>ally. As the broad peak observed in MR, apeak in S(T ) appears at about T 20 Kmoves to higher temperatures with increasing</p><p>etic field. For common metals, it is impossiblehe applied magnetic field could lead to such achange of thermoelectric power, therefore it wasally suggested that the change is due to the CDWcement under magnetic field [7,15]. In addition,und that although S becomes very large when thed magnetic field is as large as 8 T, it still tends tozero when the temperature approaches absolute</p><p>CDW-II state of NbSe3, both the resistivityermoelectric power increases rapidly with thesing magnetic field. To interpret the variation ofort properties with the magnetic field, Balseiroalicov (BF) [8,9] developed a theory assuming</p><p>CDW-II state the magnetic field enhances thegap, that is, it enhances the Nesting of FS</p><p>estroys the remaining FS gradually, which meansand more free electrons condensed into CDWlectrons which causes the increase of resistivity.R data can be fitted by a modified two modelthe frame of BF theory and the effect of</p><p>etic field on the density of electron-like charger can be derived [6].</p><p>S</p><p>htoinS</p><p>(wS</p><p>logfec</p><p>fue</p><p>n</p><p>w</p><p>pIIthw</p><p>thc</p><p>pN</p><p>hm</p><p>isthgpthc</p><p>n</p><p>o</p><p>ththc</p><p>in</p><p>e</p><p>ng contributes little to thermoelectric power atemperature, because the diffusion of phonons isong to couple into charge carriers effectively. Soh temperature, Sd term play a dominant role, andel kB</p><p>ekBTF</p><p>. However, in low temperature regionbelow the Debye temperature), the phonon termys a dominant role. For some metals, the peak atmperature can be attributed to the phonon drag-art [16]. Usually the magnetic field does not af-honons considerably, thus the phonon term Sgt be affected much by magnetic field. In the dif-magneto-thermoelectric power theory of Blatt</p><p>17], the change of the diffusion term Sd in mag-eld can be expressed as</p><p>(1)2k2BT</p><p>3|e|[</p><p>/</p><p>1 + /]D,</p><p>/ is magnetoresistance and D is a fittingeter. As pointed out in Ref. [7], in the CDW-e of NbSe3, because / 1, the change ofoelectric power should be saturated very quicklyncreasing magnetic field, which is contrast toperimental observation. It is clear that neitherntional phonon drag nor diffusion thermoelectric</p><p>can account for the observed large MS in.</p><p>our previous report [6], the MR in CDW-II stateeen fitted very well by a modified two-band</p><p>in the frame of BF theory. In this model, itmed that the two types of charge carrier have</p><p>me relaxation time and mass in the two-bandomagnetic effect model which was originally</p><p>sed by Noto and Tsuzuku [18]. Furthermore,fect of magnetic field on the ratio of two typer densities is represented by a constant , i.e.,= H , where the nh (ne) is the densityhole-like (electron-like) charge carriers and </p><p>tio at H = 0. The fitting results indicate thattio of electron-like carrier density to hole-liker density decreases with decreasing temperaturesW-II state [6]. From the fitting parameter andcan estimate the effect of magnetic field on then-like carrier density, ne(H)/ne(0), viz.,</p><p>(2)/ne(0) = ( H)/.</p></li><li><p>224 J.-q. Shen et al. / Physics Letters A 327 (2004) 221225</p><p>Fig. 3.from Mfields. Sdenotes</p><p>The reFig. 3</p><p>WibandpowerbasicaFollowthermexpre</p><p>S = </p><p>whereand Stotalmagncarrieof H .</p><p>ne(T ,</p><p>ne(T</p><p>whereat zermatedthe tewere</p><p>variatfield</p><p>symbols). The triangle symbols denote the results de-rived from the MR data.</p><p>Fig. 3 shows that below T2 the density of nor-al cg of</p><p>istinconsisotesore</p><p>er, n</p><p>g teentu</p><p>avioueld eomes</p><p>ill dee(T ,</p><p>Froe(T ,</p><p>at dthere(T ,</p><p>.10,o-be co</p><p>is tef Nbee cansite sc</p><p>ccou</p><p>e un</p><p>re deith tIn</p><p>encestat</p><p>odelvedf eleompa0 K,y themet</p><p>ata iouldort pensitThe temperature dependence of ne(T ,H)/ne(T ,0) derivedS and MR data in CDW-II state under different magneticquare denotes the parameters derived from MS, and trianglethe parameters derived from the fitting result of the MR.</p><p>sults obtained according to Eq. (2) are plotted in.</p><p>thin the frame of BF theory, we also use a two-model to interpret the variation of thermoelectric</p><p>with applied magnetic field, and the results arelly consistent with the fitting results of MR.ing the approach used in Ref. [7], the total</p><p>oelectric power in the two-band model can bessed as</p><p>(3)eSe + hShe + h ,</p><p>h (e) is the conductivity of holes (electrons)h (Se) is the contribution of holes (electrons) tothermoelectric power. Since it is assumed thatetic field only affects the density of electron-likers, we can set that h, Sh and Se is independentSo we can obtain</p><p>(4)H),0)</p><p>= S(T ,0) SeS(T ,H) Se </p><p>Sh S(T ,H)Sh S(T ,0) ,</p><p>S(T ,0), S(T ,H) is the thermoelectric powero magnetic field and magnetic field H . We esti-Se = 50 V/K and Sh = 80 V/K, and thenmperature dependence of ne(T ,H)/ne(T ,0)obtained according to Eq. (4). The estimatedions of electron type density under magneticH = 4 T and 8 T are shown in Fig. 3 (square</p><p>m</p><p>indc</p><p>m</p><p>m</p><p>ev</p><p>inev</p><p>hfic</p><p>stn</p><p>n</p><p>thra</p><p>n</p><p>0twththo</p><p>frtrtha</p><p>tha</p><p>w</p><p>dIIm</p><p>rio</p><p>c</p><p>3bra</p><p>dc</p><p>pdonduction electrons reduces with the increas-magnetic field and this trend becomes more</p><p>t with the decreasing temperature, which istent with the scenario that magnetic field pro-the destroying of electron-like FS and results in</p><p>electrons condensed into CDW electrons. How-e(T ,H)/ne(T ,0) first decreases with decreas-</p><p>mperature, then saturates at about 20 K, and itally increases in lower temperatures. This be-r could be caused by the saturation of magneticnhancement of CDW gapping. So ne(T ,H) be-</p><p>less temperature dependence while ne(T ,0)creases and this leads to the increase of the ratioH)/ne(T ,0) in temperatures below 20 K.m 60 K down to 30 K, the value of ne(T ,H)/0) derived from MS data agrees well witherived from MR data. Below 30 K, there is adeviation. Furthermore, the value of ne(T ,H)/0) at 20 K estimated from Eq. (4) is only aboutwhich is unreasonably small, indicating that theand model we used is too simple to describemplicated variation of transport properties inmperature range. A recent optical investigationSe3 suggested that the scattering times of theharge carriers are suppressed by the CDWions [19]. Since the effect of magnetic field onattering times of charge carriers is not taken intont in our two-band model, it is not surprising thatreasonably small values of ne(T ,H)/ne(T ,0)rived from MS data around 20 K, which disagreehe values derived from MR data.summary, we studied the magnetic field depen-of thermoelectric power of NbSe3 in the CDW-e. Within the frame of BF theory, a two-bandis employed to account for MS data, and the de-</p><p>temperature and field dependence of the densityctron-like charge carriers, ne(T ,H)/ne(T ,0) isred with that derived from MR data. Aboveboth the MR data and MS data can be fitted welltwo-band model, and a discrepance of the pa-</p><p>er ne(T ,H)/ne(T ,0) derived from MR and MSs found as T &lt; 30 K, which implies that therebe other effects of magnetic field on the trans-roperties besides its effect on the charge carriery.</p></li><li><p>J.-q. Shen et al. / Physics Letters A 327 (2004) 221225 225</p><p>Acknowledgements</p><p>This work was supported by the National NaturalScien</p><p>Refer</p><p>[1] P.Ph</p><p>[2] N[3] P.</p><p>61[4] R</p><p>Fa[5] R</p><p>Fa[6] J.Q</p><p>C</p><p>[7] M.F. Hundley, A. Zettl, Solid State Commun. 61 (1987) 587.[8] C.A. Balseiro, L.M. Falicov, Phys. Rev. Lett. 55 (1985) 2336.[9] C.A. Balseiro, L.M. Falicov...</p></li></ul>


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