Features of the conductivity of the quasi-one-dimensional compound ...

ISSN 10637761, Journal of Experimental and Theoretical Physics, 2010, Vol. 111, No. 2, pp. 298–303. © Pleiades Publishing, Inc., 2010. Original Russian Text © I.G. Gorlova, V.Ya. Pokrovskii, S.G. Zybtsev, A.N. Titov, V.N. Timofeev, 2010, published in Zhurnal Éksperimental’noі i Teoreticheskoі Fiziki, 2010, Vol. 138, No. 2, pp. 335–341.

ELECTRONIC PROPERTIES OF SOLID

Features of the Conductivity of the QuasiOneDimensional Compound TiS3 I. G. Gorlovaa,*, V. Ya. Pokrovskiia, S. G. Zybtseva, A. N. Titovb, and V. N. Timofeevc,† a

Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, ul. Mokhovaya 117, Moscow, 125009 Russia email: [email protected] b Institute of Metal Physics, Ural Branch of Russian Academy of Sciences, ul. S. Kovalevskoi 18, Yekaterinburg, 620131 Russia c Baikov Institute of Metallurgy and Materials Sciences, Russian Academy of Sciences, Leninskii pr. 49, Moscow, 119991 Russia Received October 30, 2009

Abstract—The structure and transport properties of single crystal whiskers of the TiS3 quasionedimen sional semiconductor have been investigated. The anisotropy of the conductivity in the plane of layers (ab) has been measured as a function of the temperature. The anisotropy at 300 K is 5 and increases with a decrease in the temperature. Features on the temperature dependences of the conductivity along and across the chains are observed at 59 and 17 K. Near the same temperatures the form of the current–voltage characteristics mea sured along the chains is qualitatively changed. The current–voltage characteristics below 60 K exhibit non linearity and have a threshold form below 10 K. The results indicate possible phase transitions and the collec tive conduction mechanism at low temperatures. DOI: 10.1134/S1063776110080248

1.† INTRODUCTION The collective states of electrons such as charge and spin density waves, hightemperature superconductiv ity, and Wignertype charge ordering appear primarily in lowdimensional systems. This fact stimulates a permanent interest in the investigations of materials with low dimensions including quasitwodimen sional and quasionedimensional conductors. A large interest in trichalcogenides of Group V transition met als [1, 2], which are quasionedimensional conduc tors, is primarily due to the Peierls transition and motion of a charge density wave observed in some of them. Titanium trisulfide TiS3, which is studied in this work, is a representative of trichalcogenides of Group IV transition metals, which constitute another, less studied class of quasionedimensional compounds. These substances belong to diamagnetic semiconduc tors [1, 3]. They have a comparatively simple structure. A unit cell contains two metal chains of one type, which are directed along the b axis and are shifted by half the period of the crystal lattice in the direction of the b axis [4]. Chains form layers in the ab plane, which are isolated from each other by double layers of sulfur atoms and are coupled with each other by the van der Waals interaction [1, 4]. To date, the Peierls transition was observed only in ZrTe3 among the com pounds of this group. It is surprising that the charge density wave appears in the planes perpendicular to the chains [5] not along them, as usually occurs. † Deceased.

Titanium trisulfide, as well as ZrTe3, has metallic properties at high temperatures: the resistance of TiS3 in the direction of the conducting chains decreases with a decrease in the temperature. A minimum on the temperature dependence of the resistance, R(T), is observed near 250 K and the transition from the metal lic behavior to the dielectric one occurs [6, 7]. The resistance increases with a decrease in the temperature below 250 K and begins to depend on the frequency [6], which could be attributed to the appearance of the charge density wave. However, no traces of the struc tural transition in TiS3 have been observed [7]. The dielectric behavior of TiS3, as well as the frequency dependence of the resistance, at T < 200 K was explained by localization effects [6]. Nonlinear conductivity in TiS3 at T < 60 K was recently observed [8]; this observation stimulated interest in the investigation of this compound. In this work, we report the results of the structure investiga tions and the measurements of the anisotropy of the conductivity of TiS3 whiskers in the ab layer plane, generalize these new and previous results, and discuss the possibilities of the formation of a condensed state in TiS3 single crystals at low temperatures. 2. SAMPLES AND EXPERIMENTAL PROCEDURE Single crystal TiS3 whiskers were grown in quartz ampoules by the gastransport reaction method with the use of the initial TiS2 powder and sulfur excess. The

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transfer was performed to a cool end at which a tem perature of 500°C was maintained, whereas the TiS2 powder was located at the hot end of the ampoule at a temperature of 700°C. The growth process took from several days to a week. The samples are faceted belts with the sizes of (500–3000) × (10–200) × (1–20) μm along the b, a, and c directions, respectively. Such a shape of the samples is characteristic of layered quasi onedimensional compounds such as, for example, NbSe3. The lattice parameters a = 0.50 nm, b = 0.34 nm, and c = 0.88 nm [3] also indicate the layered quasionedimensional structure. The direction of the maximum growth rate of whiskers coincides with the crystallographic axis b. The cleavage plane is parallel to the ab plane. Besides, the whiskers can be easily cleft along the planes parallel to the bc plane. It is more difficult to obtain a smooth edge along the ac plane (across the metal chains). Nevertheless, we succeeded in the cleavage of the samples appropriate for the mea surements of the transverse conductivity (along the a axis). Our structure investigations of thin semitranspar ent samples in the ab plane by transmission electron microscopy show a high quality of the crystals (see Fig. 1). The density of the defects is small. Growth steps along the b axis, dislocation networks in the ab plane, and dislocation walls are observed (see Fig. 1a). The dislocations are not a growth type and are appar ently formed in the process of the splitting of the crys tal. The diffraction patterns obtained at room temper ature (see Fig. 1b) and at 155 K, i.e., above and below the metal–insulator transition temperature, are almost the same. No additional order due to the for mation of the charge density wave is observed, as in [7], which confirms the absence of the structural tran sitions in this temperature range. The crystal lattice constants (see Fig. 1b) correspond to the data known for TiS3 [3]. The temperature dependences of the resistance were measured in different crystallographic directions in the layer plane: the measuring current flows along the chains (b axis) or across the chains (a axis). The electrical contacts for the longitudinal measurements were deposited by the mechanical pressing of freshly cut indium strips to the whiskers. For transverse mea surements, we cut a whisker piece with the sizes of 100 × 100 μm in the ab plane. Gold strip contacts with a width of several micrometers were deposited on this piece by the laser sputtering method. The strips were oriented along the b axis and crossed the entire sam ple. The contact resistance in all of the cases was no higher than 10 Ω and the resistance divided by the contact area was no more than 10–6 Ω cm2. The mea surements of R(T) and current–voltage characteristic were performed using the standard fourprobe scheme in the fixedcurrent regime with a Keithley 2182A

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(b) Fig. 1. (a) The brightfield microphotograph of the TiS3 whisker. Dislocations are seen in the ab plane. A number (wall) of dislocations approaching the surface and a growth step (in the lower left corner) are directed along the b axis. (b) The electrondiffraction pattern of the same sample at room temperature.

nanovoltmeter. The current I was induced by means of a Keithley 2400 current source. To exclude the contri bution from thermopower, the measurements of each point of the R(T) dependence were carried out at two opposite current directions. A certain instability of the resistance of the samples at low temperatures is worth noting: after several cooling–heating cycles, the resis tance at T = 4.2 K was about half of the initial value and was stabilized at this level. The qualitative shape of the R(T) curves remained unchanged and all of the features were observed at the same temperatures. The temperature dependences of the longitudinal and transverse resistances were measured for seven and two samples, respectively, and the longitudinal current– voltage characteristics were measured for four sam ples. Estimates showed that the heating of the whiskers under the experimental condition is negligibly small. 3. TEMPERATURE DEPENDENCE AND THE ANISOTROPY OF THE CONDUCTIVITY OF TiS3 The temperature dependences of the resistance along the chains (b axis) and across the chains (a axis)

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Fig. 2. (a) The temperature dependences of the resistance of TiS3 that was measured in the (R||) longitudinal and (R⊥) transverse directions and was divided by the value at T = 300 K. The inset shows the temperature dependences of the logarithmic derivatives d ln R/dT . The arrows mark the temperatures at which the maxima of d ln R/dT are observed. (b, c) The temperature dependences of R|| of the TiS3 sample. The straight line corresponds to the Mott law for the hopping conductivity.

were measured from 340 to 4.2 K. Figure 2a shows the corresponding curves in the range 4.2 K < T < 300 K. The resistivity measured at T = 300 K along the chain is ρ300 ≈ 2 Ω cm, which is in agreement with the results reported in [6] and is three or four orders of magnitude higher than the value for known conductors with the charge density wave. The resistivity across the chains

(along the a axis) at room temperature is about five times higher than that along the b axis. As the temperature decreases from 340 K, the lon gitudinal resistivity decreases, reaches a minimum at 226 K, and then increases. The temperatures at which the minimum on the R(T) curves is observed are dif ferent for different samples, as in [6, 7], and are in the range of 200 K < T < 260 K. The R(T) dependences are in agreement with the results reported in [6, 7], where the R(T) dependences were presented for tempera tures above 40 K. At lower temperatures, the resistivity continues to increase. In addition to the previously known minimum at 250 K, features near 59 and 17 K are seen on the temperature dependence of the resis tance along the b axis. These temperatures correspond to the maxima (in absolute value) of the derivative dlnR/dT (inset to Fig. 2a). In contrast to the longitudinal resistance, the trans verse resistance increases monotonically with a decrease in the temperature in the region T < 300 K, and this increase is much stronger than that for the longitudinal resistance. No features are observed on the temperature dependence of the transverse resis tance in the range 200 K < T < 260 K. The minimum of R(T) corresponding to the metal–insulator transi tion is observed at a much higher temperature of T ≈ 320 K. However, the maxima of the derivative d ln R/dT in both directions are observed at about the same temperatures (see the inset in Fig. 2a). The peaks of the derivative of R(T) in the transverse direction is wider than those in the longitudinal direction and are shifted towards high temperatures by only several


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degrees of arc. Note that we report the first results of the investigation of the transverse conductivity of TiS3 and more detailed measurements in the transverse direction are required.

σnl, σ(0), Ω−1 10−4

4. ELECTRICFIELD DEPENDENCE OF THE CONDUCTIVITY OF TiS3 The current–voltage characteristics were measured in the temperature range of 4.2–125 K in electric fields up to 200 V/cm. The current–voltage character istics are almost linear at temperatures above 60 K. The resistance becomes to depend on the electric field near the temperature T ≈ 60 K, where the maximum of d ln R/dT is observed. As the temperature decreases, the nonlinearity increases, an inflection point appears on the dependences of the differential resistance Rd on the applied voltage V, and the Rd(V) dependences have the threshold character at T < 10 K. Figure 3 shows Rd(V) curves at low temperatures. The resistance at T = 4.2 K is independent of the voltage up to V = 31 mV (see the inset in Fig. 3) and then decreases sharply by an order of magnitude at a voltage of 1 V. At higher voltages, the decrease in Rd becomes slower and Rd(V) tends to saturation. The threshold field at 4.2 K is about 6 V/cm and increases with the temperature. The results were reported in more detail in [8], where the Rd(V) dependences measured at temperatures from 90 K to 4.2 K were also given (see Fig. 2 in [8]). Figure 4 shows the temperature dependences of the nonlinear part of the differential conductivity σnl ≡ σd(V) – σd(0) at fixed V values and the linear conduc tivity σ(0) measured at the current I ≤ 0.1 μA. At high temperatures, the nonlinear conductivity σnl is much lower than the linear conductivity. As the temperature decreases, σnl increases, reaches a maximum at about 50 K, and then decreases. At T < 50 K, the tempera ture dependences of σnl reproduce the features of the temperature dependence of the linear conductivity, in particular, the cusp near 17 K. At the maximum volt ages, σnl is almost independent of T.

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5. DISCUSSION OF THE RESULTS Taking into account the absence of both structural changes down to 130 K [7] and nonlinear conductivity in TiS3, the authors of [6] explained the metal–insula tor transition near 250 K by the process of the localiza tion of electrons in a disordered medium. As is seen in Fig. 2c, R(T) for our samples in the range of 75–150 K can be described by the function exp[–(TM/T)1/4] (where TM = 1.6 × 106 K), which corresponds to the variablerange hopping conductivity for the three dimensional case [9]. However, the hopping mecha nism cannot explain the threshold form of the cur rent–voltage characteristics at low temperatures. Although the hopping conductivity in high fields can be nonlinear, the deviation of Rd from a constant

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Fig. 4. Temperature dependences of (thick line) the linear conductivity σ(0) measured at the current I ≤ 0.1 μA and (circles) the nonlinear part of the differential conductivity σnl ≡ σd(V) – σd(0) at V = (from top to bottom) 1, 0.5, 0.2, 0.1, and 0.065 V. The thin lines are given as guides for eyes.

smoothly depends on the field [10]. The hopping con ductivity cannot also explain the sharp features on the R(T) dependence: in this case, the resistance should vary with temperature smoothly without peaks on the derivatives in contrast to the behavior observed for TiS3 (see the inset in Fig. 2a). The beginning of the electric field dependence of the resistance at the temperature T ≈ 60 K at which the maximum of the derivative dlnR/d(1/T) is observed indicates a structural or electronic phase transition in the system. The threshold form of the current–voltage characteristics can be associated with the collective conductivity mechanism above the threshold voltage. It can be assumed that the Peierls instability with the formation of the charge density wave appears in the TiS3 quasionedimensional compound. The nonlin ear current–voltage characteristics below 10 K, which have the form characteristic of quasionedimensional conductors, can be attributed to the depinning and sliding of the charge density wave. The formation of the charge density wave is also indicated by the tem perature dependences of σnl at various V values shown in Fig. 4. The maximum on the σnl(T) curves confirms that the phase transition occurs in the system. Below the transition, the nonlinear conductivity decreases similar to the linear conductivity, reproducing the fea tures of the latter. Such a behavior is also observed in the Peierls semiconductors [1, 2], for example, in TaS3


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[11]. Another common property of quasionedimen sional conductors with the charge density wave—the weak temperature and electric field dependences of σnl in high fields [1, 2]—is also observed for TiS3 (see Figs. 3, 4). As is well known, the conductivity of quasi onedimensional conductors with the charge density wave in high fields approaches the value of the con ductivity in the absence of the Peierls gap [1, 2]. For the case of TiS3 at T < 17 K, the asymptotic conductiv ∞ can be estimated as (0.2– ity level in the limit V 0.3 MΩ)–1, see Fig. 3. This approximately corre sponds to the linear conductivity at 17 K (see Fig. 4). Thus, it is reasonable to assume that the feature at 17 K (see Fig. 2a) is also caused by the formation of the charge density wave. Both maxima of the derivative dlnR/d(1/T) at 17 and 59 K can be attributed to the Peierls transitions as, for example, for NbSe3 [1, 2]. It is worth noting that the R(T) dependence below 59 K cannot be described by the thermal activation law R ∝ exp(Δ/T), where Δ is the Peierls gap width (see Fig. 2b). The behavior of R(T) approaches the activa tion law only below 17 K (see Fig. 2b). The activation dependence of R(T) is characteristic of many, but not all of the conductors with the charge density wave. The transition can be smeared because of fluctuations. Moreover, phase transitions in TiS3 occur against the background of the dielectrization process (possibly of localization [6]), which begins at higher temperature (~250 K). Probably, R(T) reveal both contributions to the resistance. An important characteristic of the quasione dimensional conductor, which determines the degree of its onedimensionality, is the anisotropy of the con ductivity. The relatively small anisotropy of the resis tivity ρa/ρb ≈ 5 at T = 300 K [12] (it is smaller than that in NbSe3 and TaS3 by a factor of 3 and 20, respectively) increases by two orders of magnitude with a decrease in the temperature to 50 K. This means that the TiS3 crystals at low temperatures is much more onedimen sional and, in the anisotropy value, are similar to typ ical Peierls conductors. An increase in the anisotropy with a decrease in the temperature is characteristic of conductors with the charge density wave, although such a large increase in ρa/ρb is surprising. As in the Peierls conductors, the features on the R(T) depen dence are observed for the measurements in both directions, but they are more smeared in the transverse direction (see Fig. 2c). According to [13, 14], with approaching the transition from the high temperature side, the contribution from the additional scattering by the softmode phonons becomes noticeable earlier on the transverse conductivity; for this reason, its temper ature dependence is smoother. Thus, all of the results can be explained by the for mation of the charge density wave in the quasione dimensional semiconductor TiS3 at low temperatures. At the same time, some properties significantly dis tinguish TiS3 from typical Peierls conductors. First, the resistivity of TiS3 is several orders of magnitude

higher than that of known conductors with the charge density wave. The electron density in TiS3 at room temperature determined from the Hall effect [15] is n300 ≈ 2 × 1018 cm–3. To date, the Peierls transition was observed only in quasionedimensional conductors with a relatively high carrier density (n300 ~ 1021 cm–3 at T = 300 K). This means that the period of the charge density wave in TiS3 should be much longer than that in TaS3 or NbSe3. Second, the anisotropy of the con ductivity of TiS3 in the ab plane is comparatively small. For this reason, it is not excluded that the form of the R(T) and R(V) dependences at low temperatures is attributed to the transition to another correlated state of electrons that is not associated with the charge den sity wave. At low electron densities, this state can be due to Wigner charge ordering caused by the electron– electron correlation interaction without a change in the crystal structure. Such an ordering occurs, for example, in quasionedimensional organic conduc tors (DIDCNQI)2Ag [16] and (TMTTF)2PF6 [17]. In this case, the maximum of the derivative dlnR/d(1/T) is also observed at the transition point [17]. It is assumed that the Wigner crystallization also occurs in twodimensional GaAs heterostructures [18, 19]. The thresholdtype current–voltage characteris tics, which can be attributed to the motion of the elec tron crystal, are observed in such structures [18]. It is worth noting that the electron density in such struc tures is on the order of 1011 cm–2 [19], i.e., of the same order of magnitude as in TiS3 per elementary conduct ing layer. 6. CONCLUSIONS The main results of this work are as follows. The electron microscopy investigations of the structure of TiS3 single crystal whiskers have shown the perfectness of the crystals and the absence of the struc tural transitions in the temperature range of 155– 300 K. The anisotropy of the conductivity of TiS3 in the ab plane is equal to 5 at room temperature and increases by two orders of magnitude with a decrease in the tem perature to 50 K. The temperature dependences of the conductivity measured along the b and a crystallographic directions (along and across the conducting chains) exhibit fea tures near the temperatures of 59 and 17 K, which cor respond to the maxima of the derivative d ln R/dT . Below 60 K, the nonlinear conductivity is observed along the chains and the current–voltage characteris tics have the threshold form below 10 K. The temper ature dependence of the nonlinear conductivity has features at the same temperatures as the linear con ductivity. The results indicate a transition to a correlated electron state in TiS3 at low temperatures. It can be assumed that two Peierls transitions with the forma


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tion of the charge density wave occur at 59 and 17 K. At the same time, taking into account a low freecar rier density and the dielectric behavior of the conduc tivity in the temperature range 60 K < T < 250 K, the possibility of another type of electronic ordering is not excluded.

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Translated by R. Tyapaev

ACKNOWLEDGMENTS We are grateful to A.P. Orlov for assistance in the measurements and to P. Monceau, Yu.I. Latyshev, and V.A. Volkov for the discussion of the results. This work was supported by the Russian Foundation for Basic Research (project nos. 060272551NTsNILa and 080201303a), by the Presidium of the Russian Academy of Sciences (program no. 27 “Foundations of Basic Research of Nanotechnologies and Nanoma terials”), program “Physics of New Materials and Structures” of the Department of Physics, Russian Academy of Sciences, and by the International Euro pean Laboratory “Physical Properties of Coherent Electron States in Solids” supported by the Centre national de la recherche scientifique (CNRS, France), Russian Academy of Sciences, and Russian Foundation for Basic Research including Institut Neel (Grenoble, France) and Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences. REFERENCES 1. P. Monceau, in Electronic Properties of Inorganic Quasi OneDimensional Materials, Ed. by P. Monceau (Reidel, Dordrecht, The Netherlands, 1985), Part 2, Vol. 2, p. 139. 2. G. Grüner, Density Waves in Solids (AddisonWesley, Reading, Massachusetts, United States, 1994).


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