NbS 3 : A unique quasi one-dimensional conductor with three charge density wave transitions
S.G. Zybtsev, V.Ya. Pokrovskii, V.F. Nasretdinova, S.V. Zaitsev-Zotov, V.V. Pavlovskiy, A.B. Odobesco, Woei Wu Pai, M.-W. Chu, Y. G. Lin, E. Zupanič, H.J.P. van Midden, S. Šturm, E. Tchernychova, A. Prodan, J.C. Bennett, I.R. Mukhamedshin, O.V. Chernysheva, A.P. Menushenkov, V.B. Loginov, B.A. Loginov, A.N.Titov, Mahmoud Abdel-Hafiez
NNbS : A unique quasi one-dimensional conductor with three charge density wavetransitions S.G. Zybtsev, V.Ya. Pokrovskii, ∗ V.F. Nasretdinova, S.V. Zaitsev-Zotov, V.V. Pavlovskiy, A.B. Odobesco, Woei Wu Pai, † M.-W. Chu, Y. G. Lin, E. Zupaniˇc, H.J.P. van Midden, S. ˇSturm, E. Tchernychova, A. Prodan, J.C. Bennett, I.R. Mukhamedshin, O.V. Chernysheva, A.P. Menushenkov, V.B. Loginov, B.A. Loginov, A.N.Titov, and Mahmoud Abdel-Hafiez ‡ Kotel (cid:48) nikov Institute of Radioengineering and Electronics of RAS, Mokhovaya 11-7, 125009 Moscow, Russia Center for condensed matter sciences, National Taiwan University, Taipei, Taiwan, 106 National synchrotron research center, HsinChu, Taiwan 300 Joˇzef Stefan Institute, Jamova 39, Ljubljana, Slovenia Department of Physics, Acadia University, Wolfville, N. S. Canada Institute of Physics, Kazan Federal University, 420008 Kazan, Russia National Research Nuclear University ”MEPhI” (Moscow EngineeringPhysics Institute), Kashirskoe sh. 31, 115409 Moscow, Russia National Research University of Electronic Technology (MIET), 124498, Zelenograd, Moscow, Russia Ural Federal University, Mira 19, 620002, Yekaterinburg, Russia Center for High Pressure Science and Technology Advanced Research, Beijing 100094, China (Dated: July 1, 2016)Through transport, compositional and structural studies, we review the features of the charge-density wave (CDW) conductor of NbS (phase II). We highlight three central results: 1) In additionto the previously reported CDW transitions at T P = 360 K and T P = 150 K, another CDW transi-tion occurs at a much higher temperature T P = 620-650 K; evidence for the non-linear conductivityof this CDW is presented. 2) We show that CDW associated with the T P - transition arises fromS vacancies acting as donors. Such a CDW transition has not been observed before. 3) We showexceptional coherence of the T P -CDW at room-temperature. Additionally, we report on the effectsof uniaxial strain on the CDW transition temperatures and transport. PACS numbers: Condensed Matter Physics, Materials Science, Superconductivity
I. INTRODUCTION
Since Peierls transitions, at which electrons condenseinto charge-density waves (CDWs), usually occur well be-low room temperature (RT), studies of CDWs in quasione-dimensional (1D) conductors have been usually con-sidered a branch of low-temperature physics [1, 2]. Theformation of a CDW is accompanied by dielectrization(i.e., gapping) of the electronic spectrum with a corre-sponding drop in electrical conductivity. Periodic latticedistortion accompanied with the CDW can be studiedwith both diffraction techniques in momentum space andscanning tunneling microscopy in real space. A notablebasic feature of quasi 1D CDWs is their ability to slidein a sufficiently high electric field, resulting in non-linearconductivity. This sliding is accompanied by the gener-ation of narrow- and wide-band noises. The quasi 1DCDWs also feature an enormous dielectric constant andmetastable states originating from their deformability. Inaddition to these basic effects, a number of other fea-tures have been investigated including synchronizationof CDW sliding with an external radio-frequency (RF) ∗ Electronic address: [email protected] † Electronic address: [email protected] ‡ Electronic address: [email protected] field (the so-called Shapiro steps), coherence stimulationof CDW sliding by asynchronous RF irradiation [3], theeffects of pressure [2] and uniaxial strain [4–7] on thePeierls transitions and CDW transport, and enormouselectric-field-induced crystal deformations [2, 8].Several trichalcogenides of the group V metals (MX ),namely NbSe , TaS (orthorhombic and monoclinic) andphase II NbS (hereafter NbS -II), constitute a family oftypical quasi 1D CDW conductors [1, 2]. Their crystalstructures are formed from metallic chains surroundedby trigonal prismatic cages of chalcogen atoms. Thoughthese compounds are apparently isoelectronic, their prop-erties are rather diverse. For example, they display verydifferent CDW wave vector magnitudes, indicating dif-ferent degrees of filling in conduction electronic bands.A plausible reason for this variety may be the relativepositioning of the chalcogen atoms [9]. Depending ontheir interatomic distances, chalcogen atoms can eitherbe isolated from each other or they form bonded pairs.Correspondingly, one valence electron from a chalcogenatom can either belong to the conduction band or to alocalized bond.The monoclinic polymorph NbS -II exhibits some fas-cinating CDW features. Two CDW transitions have beenreported for NbS -II. One CDW has a wave vector q =(0.5 a *, 0.298 b *, 0) [10, 11], and forms at T P =330-370K [11, 12], a temperature much beyond the traditionalrealm of low-temperature physics. While several basic ex- a r X i v : . [ c ond - m a t . s t r- e l ] J un perimental results on NbS -II were published in the 1980s[1, 2, 10, 11, 13–16], little subsequent work was under-taken until 2009. This gap was largely due to difficultieswith synthesizing the compound: NbS -II whiskers wereonly found as rare inclusions accompanying the growthof the semiconducting phase of NbS (hereafter NbS -I) [11], which was more extensively studied [1, 2, 17, 18].A new phase-III NbS with a phase transition at 150 Kwas also reported [13], which was later suggested to bea sub-phase of NbS -II [8, 12, 19]. The synthesis condi-tions of NbS -II were established from studies in the Ko-tel’nikov Institute of Radioengineering and Electronicsof RAS in 2009 [8], and were recently successfully repro-duced in the National Taiwan University. A detailed de-scription of NbS -II growth conditions is presented in [8].The most notable feature of NbS -II is its non-lineartransport at RT [1, 2, 11, 12, 19] associated with theCDW formed at T P . The RT-CDW shows an exception-ally high transport coherence with the highest reportedtransport velocities of any known sliding CDW. The cor-responding values of the fundamental frequency, f f , asrevealed by the RF interference technique [12, 19], ex-ceed 15 GHz. The coherence of this CDW can be furtherimproved by external asynchronous RF irradiation [3]and by uniaxial strain [20]. The Peierls transition at T P is clearly detected in transport and structural stud-ies: a pronounced increase of resistance, R , with de-creasing temperature is observed near T P , while its I-Vcurve becomes nearly linear above 340 K. The intensitiesof the q satellites strongly decrease significantly above350 K [11, 21], while the satellites of second modulationwave vector q = (0.5 a *, 0.352 b *, 0) remain detectableto at least 450 K.Within NbS -II two ”sub-phases” have been identi-fied: a low-ohmic and a high-ohmic sub-phase [8, 19, 22].According to [8], the low-ohmic samples are preparedat 670-700 ◦ C, and the high-ohmic ones at 715-740 ◦ C.Further experiments have shown that low-ohmic sam-ples can also be synthesized between 720 and 730 K inthe presence of at. 16% excess of S. Both sub-phasescan grow in the same run if a temperature gradient ispresent within the synthesis ampoule. Electron diffrac-tion reveals a doubling of lattice constant along the a axis for the high-ohmic crystals. Such a lattice dou-bling is absent in the low-ohmic ones [19]. In additionto the CDW transition at T P , the low-ohmic samplesundergo a further CDW transition at T P = 150 K [13]as detected in the temperature-dependent resistance, R ( T ), curves [8, 12, 19]. Below T P , a non-linear con-duction with a pronounced threshold field, E t , is ob-served. This indicates a charge transport coupled tothis low-temperature CDW (LT CDW). The presence ofShapiro steps provides definitive proof of LT CDW slid-ing [12, 19]. RF synchronization studies reveal a sur-prisingly low charge density of this LT-CDW. The so-called ”fundamental ratio”, j c / f f , appears very low andsample dependent [12, 19] (here j c is the CDW currentdensity at the 1 st Shapiro step). Electron and X-ray diffraction studies indicated that the low-ohmic sampleswere homogeneous rather than a mixture of phases. Sev-eral attempts to find structural changes below T P wereunsuccessful [10, 23]. The LT-CDW state emerges froma dielectrized state following the two CDWs formed athigher temperatures. Therefore, this CDW remains arather enigmatic charge-ordered state. The emergence ofa new CDW in this rather resistive state is very unusualand a Keldysh-Kopaev transition [24] (the formation ofan excitonic dielectric [25]) has been proposed as a pos-sible mechanism [19].In this paper we present a number of new experimen-tal results for NbS -II. Section II focuses on the fea-tures of the RT-CDW. We report unprecedentedly highvalues of CDW fundamental frequencies as revealed byShapiro steps. A high coherence of the RT-CDW slidingis shown by the nearly complete CDW synchronizationunder RF power and by Bessel-type oscillations of theShapiro steps’ width vs. RF power. In addition, weexperimentally demonstrate that the coherence can befurther improved by applying strain, (cid:15) , parallel to thechains, i.e., along the b axis. Such strain also stronglyaffects the CDW transition temperature T P which de-creases by approximately 80 K for (cid:15) ∼ III we report transport measurements at temperaturesup to about 650 K. A new feature in R ( T ) is found near620-650 K and is attributed to the onset of an the ultra-high-temperature (UHT-) CDW. Evidence for non-lineartransport provided by the UHT-CDW is given. We alsodemonstrate that by heating above ≈
800 K the high-ohmic sub-phase transforms gradually into the low-ohmicsub-phase and further into a metallic-like compound.Section IV illustrates and focuses on the LT-CDW. Un-like the transition at T P , the LT-CDW transition ap-pears nearly insensitive to strain, as is the non-linear con-duction associated with this LT-CDW. Electron-probemicroanalyses (EPMA) reveal a shortage of S in thelow-ohmic samples. This suggests a coupling betweenthe relatively high conductivity of the low-ohmic sam-ples and the presence of S vacancies. Though electrondiffraction patterns show no changes below 150 K, the T P transition is detected by TEM-based electron en-ergy loss spectroscopy (STEM-EELS) and X-ray absorp-tion near edge spectroscopy (XANES). These techniquesindicate charge transfers between states coupled with Sand Nb atoms, as well as with S vacancies. Nuclear mag-netic resonance (NMR) studies suggest ”freezing” of thecondensed electronic state near T P . In section V , wepresent an overview of the results and discuss variouspossible origins of the LT-CDW transition. The Keldysh-Kopaev (excitonic insulator) transition [24, 25] appearsmore consistent with the experimental data then othermechanisms of electronic condensation. In the conclud-ing section VI , we summarize the main features of NbS -II. -20 -15 -10 -5 0 5 10 15 202530354045 I c ( m A) s d ( M W - ) FIG. 1: The RT dependences of differential conductivity, σ d ,vs. non-linear current, I c , under RF irradiation at differentfrequencies. The sample dimensions are 1.6 µ m × µ m . II. ROOM-TEMPERATURE CDW; EFFECTSOF RF IRRADIATION AND UNIAXIAL STRAIN
The RT-CDW in NbS -II has been most thoroughlystudied to date. It is remarkable not only for the occur-rence of sliding, but also for its extremely high sliding co-herence. The ”fundamental ratio”, j c / f f , is sample inde-pendent within the experimental error (defined by the un-certainty in the sample cross-sectional area). The exper-imentally determined value j c / f f =18 A/MHz/cm [19]corresponds to one CDW chain per unit cell [12]. Theuniversality of this ”fundamental ratio” allows a pre-cise determination of the cross-section area of the sam-ples [26]. A very high coherence of the RT-CDW slidingis observed in samples with nanoscale transverse dimen-sions. In these samples the highest fundamental frequen-cies are achieved. As Fig. 1 shows, Shapiro steps (the firstharmonic) are observed at frequencies as high as 20 GHz.The large area per CDW chain, s =2 e/ ( j c / f f ) = 180˚A [27], compared to other quasi-1D CDW compounds,is consistent with the relatively small amount of Jouleheating of the NbS -II samples. They show the highestdensity of CDW current before burn-out [19]. Based onthe highest current densities ever passed through thesesamples, it is suggested [19] that fundamental frequen-cies as high as f f = 200 GHz are attainable. However,synchronization of the CDW at frequencies above 20 GHzrequires special arrangement of the samples for a betterimpedance match with RF radiation.At a sufficiently large RF power, the RT-CDW inNbS -II nano-dimensional samples show nearly completesynchronization: the differential conductivity, σ d , of theCDW is reduced by 80-90% (Fig. 2). At the same time,the widths of the Shapiro steps show a non-monotonic de-pendence on the RF power with Bessel-type oscillations.To observe such oscillations, the CDW should exhibit ahigh coherence. Previously, the Bessel-type oscillationswere observed for NbSe only [29]. The evolution of the I- -1 -0.5 0 0.5 1 11.522.533.54 V ( V ) s d (M W -1) T = 3 0 0 Kf = 4 0 0 M H z
FIG. 2: An example of σ d vs. V dependence under RF irradi-ation at RT. The sample dimensions are 50 µ m × µ m . V curves with increasing RF power is shown by the video-clip in the Supplementary Material. It shows the screenof a digital oscilloscope displaying the rapidly recordedI-V curves of a NbS -II sample. Figure 3 presents thenormalized dependence of the 1 st Shapiro step width andthe threshold voltage, V t , (half-width of the ”0-th step”)on the RF power. A non-monotonic suppression of V t has been previously reported for NbSe [29, 30].We recently developed techniques to apply controlleduniaxial strain to whisker-like samples, including nano-sized ones [19]. The NbS -II samples were stretched bybending epoxy-based substrates [19]. Studies of NbS -II at RT [20] and of orthorhombic TaS [20, 31] havedemonstrated that strain can improve the CDW coher-ence. Figure 4 summarizes a set of curves showing thedifferential conductivity of NbS -II as a function of volt-age, V . Unlike in case of the orthorhombic TaS , in whichan ultra-coherent CDW emerges through a phase transi-tion at a critical strain [20, 31], CDW coherence in caseof NbS -II grows gradually with (cid:15) (Fig. 4): the thresholdsbecome sharper, the growth of σ d above the thresholdsoccurs faster, and the value of the maximum CDW con-ductivity increases [20]. After strain removal, the thresh-old voltage decreases and the threshold becomes slightlysharper, while the value of resistance at V = 0 indicatesthat the sample is unstrained.The growth of coherence with strain is also demon-strated by the effect of RF synchronization. At a fixedRF power, the Shapiro steps are more pronounced at in-creased strain, becoming visible directly in the I-V curves(Fig. 5). The effect of strain appears similar to that ofasynchronous RF irradiation which also improves the co-herence of the CDW sliding, as observed for a numberof compounds [3, 32, 33], including NbS -II [3]. How-ever, the origins of enhanced coherence in these two casesare likely different. While RF is believed to periodicallydraw CDW back to its starting state before it loses co-herence [3], strain can change the crystal defect struc-ture [20]. As shown in Fig. 4, the irreversible growth d V / V t ( ) , V t / V t ( ) Width of the 1 st stepV t / V t (0) FIG. 3: A plot of a normalized Shapiro step width and V t vs. RF power (400 MHz). The sample dimensions are 50 µ m × µ m (see Fig. 2). The original I-V curves are in theSupplementary Material. of coherence after strain removal may be explained bya reduction in the crystal defect density after the uni-axial deformation. For example, it is known that twin-free YBCO crystals can be obtained by applying uniaxialpressure at 420 ◦ C in flowing oxygen [34]. However, themajor part of the coherence growth is reversible (Fig. 4).This could be attributed to an alignment of the metallicchains under strain. Increased velocities of the internalacoustic modes and their reduced friction in the strainedsamples can also stimulate coherence of the CDW slidingthrough CDW-lattice coupling [8, 35].Studying strain effects of CDW transitions is impor-tant to better understand how the CDW condensateforms. Uniaxial strain decreases the anisotropy; as inter-atomic distances along the conducting chains grow, theinterchain distances decrease due to the Poisson contrac-tion. The reduction in anisotropy corrugates the Fermisurfaces and decreases T P . At the same time 1D fluc-tuations are suppressed, which increases T P . The actualchanges in T P result from the competition between thesetwo effects. Applied uniaxial strain reduces T P in or-thorhombic TaS [5, 6] (but with a tendency to increaseit after exceeding a critical value of [31]), NbSe [5] andK . MoO [7]. In the monoclinic TaS the lower tran-sition is shifted downwards, while no shift was observedfor the upper transition temperature up to 1.5% [36].The effects of uniaxial strain on CDW compounds havebeen examined less thoroughly than those of hydrostaticpressure, which is in part similar to the effect of stretch-ing. In fact, a general feature of quasi 1D CDW com-pounds is also a lowering of T P under pressure, indicat-ing that the corrugation of Fermi surfaces has a dominantinfluence on T P [2, 37]. The only known exception is the -0.05 0 0.0581012141618 V (V) s d ( M W - ) FIG. 4: The RT voltage dependencies of differential conduc-tivity σ d for a sample under uniaxial strain. The strain in-creases from (cid:15) = 0 (the lowest curve) to (cid:15) = 1% (the upper-most curve) in approximately equal steps. The curve markedwith red circles was obtained after the strain was removed.The sample length, L , is 24 µ m. -0.2 -0.1 0 0.1 0.2-0.4-0.3-0.2-0.100.10.20.30.4 I ( m A) V ( V ) e = 0 e = 1 % f = 50 MHz FIG. 5: RT I-V curves at different strains, (cid:15) , under fixed RFirradiation (50 MHz). The sample dimensions are 50 µ m × µ m . The Shapiro steps become visible with increased (cid:15) . ( b )( a )
260 280 300 320 340 360010002000300040005000
T ( K ) d(log R)/d(1/T) (K) e = 1 . 4 % e = 1 . 2 % e = 1 % e = 0
100 150 200 250 300 35001234567
T ( K ) s ( M W - ) e = 1 % e = 0 ( a ) FIG. 6: a) The initial σ ( T ) curve (blue) and under 1% ofstretching strain (red). Both T P and T P are lowered understrain. b) The logarithmic derivatives of resistance vs. T forthe same sample in the vicinity of T P . The sample dimen-sions are 22 µ m × µ m . Measurements under strain werenot performed above 300 K due to problems with the epoxysubstrates at elevated temperatures. monoclinic TaS , whose upper transition temperature in-creases at small pressures. It was proposed that the sup-pression of 1D fluctuations dominates the T P variationin this strongly anisotropic TaS polytype.In the case of NbS -II, strain strongly affects the RT-CDW: (cid:15) ∼ T P from 360 K tobelow 280 K (Fig. 6). It is also obvious that strain sharp-ens the CDW transition. The decrease of T P in NbS -IImeans that, in spite of the large anisotropy [38], it isprimarily dominated by Fermi-surface nesting conditionsand less by the suppression of the 1D-fluctuations.The reduction of T P with must be taken into accountin the I-V curves under strain (Fig. 4). For larger ap-plied strains the σ d ( V ) dependencies were measured closeto T P . However, the evolution of the curves with can-not be attributed to the proximity of T P only. In theabsence of strain, the I-V curves are smeared at temper-atures close to the CDW transition [12]. Therefore, thegrowth of CDW coherence observed in Fig. 4, as well asthe increased sharpness of the Peierls transition at T P (Fig. 6b), are a direct consequence of a tensile strain.The ”inverse” electro-mechanical effects, i.e., the im- -20 -10 0 10 20-0.03-0.02-0.0100.010.020.03 I ( m A) df ( deg ) T=309 Kwithout RF ( · fl› under RF (45 MHz) FIG. 7: Current dependence of the torsional strain ampli-tude. The angle is measured with the lock-in technique ata resonance frequency of 3.75 kHz. The current applied tothe sample has the form of symmetric meanders. The datawithout RF irradiation are multiplied by 10. The sample di-mensions are 200 µ m × µ m [40] pact of electrical field on the dimensions and the form ofthe samples, have been less studied for NbS -II. Similarlyto orthorhombic TaS , K . MoO and (TaSe ) I, NbS -II also shows electric-field-induced torsional strain. Itcan be observed at RT. However, the torsional angles arerelatively small and are 1-2 orders of magnitude smallerthan those observed in TaS . The most reliable measure-ment of the torsional angle as a function of voltage isobtained with an ac voltage applied at the mechanicalresonant frequency of NbS -II samples. Figure 7 showstwo dependences of the torsional angle on current (withand without applied RF irradiation applied) measuredwith a lock-in technique at the lowest resonant frequencyof 3.75 kHz. The applied ac voltage is symmetric, with agradually sweeping amplitude. The torsional angle wasmeasured optically [8]. Without RF irradiation, a thresh-old current for the onset of torsion was observed, likein the cases of the orthorhombic TaS , K . MoO and(TaSe ) I [8, 39]. RF irradiation (45 MHz) suppressesthe thresholds and increases the torsional angles by anorder of magnitude. This effect is in line with the coher-ence stimulation by an asynchronous RF irradiation [3].
III. THE ULTRA HIGH- T P CDW:INDICATIONS OF A PEIERLS TRANSITIONAND A FRHLICH MODE.
As mentioned in the introduction section, the diffrac-tion patterns of NbS -II show at 300 K incommensuratesatellites belonging to two CDW q -vectors: q = (0.5 a *, /T (K) R ( W ) T P2 T P1 T P0 FIG. 8: A wide-range temperature dependence of NbS -IIresistance. Data from two whiskers (100 µ m × µ m - highT, 126 µ m × µ m - lower T) are combined into a singlegraph. The high-temperature points were obtained during aheating cycle in an Ar flow. b *, 0) and q = (0.5 a *, 0.298 b *, 0) [10, 11]. Whilethe first set of satellites remain visible up to 450 K, thesecond set vanishes gradually above 360 K, which is closeto T P [11]. When heated above 450 K under vacuum orambient conditions, NbS -II crystals start to degrade.In order to extend the measuring range and preventcrystal degradation, the R ( T ) measurements at elevatedtemperatures reported herein were performed in an Ar at-mosphere. The temperature was monitored with a ther-mocouple. Heating to ∼
700 K and subsequent coolingwas performed within several minutes. Figure 8 showsthe R ( T ) curve in a wide temperature range and veryclearly reveals the transitions at T P and T P . The de-pendence at high temperatures, above T P , was addedfrom a different sample during a heating cycle. Above600 K a notable degradation of sample properties begins,resulting in a growth of conductivity. However, duringfast cooling from 700 K the feature in the σ ( T ) reap-pears in the same temperature range (the dynamic errorin temperature determination was tens of K). Thereforethe σ ( T ) feature around 620-650 K is attributed to thetransition at T P .As shown in Fig. 9, heating to above about 800 K grad-ually transforms the high-ohmic sub-phase into the low-ohmic one. Further heating transforms NbS -II into acompound with metallic conductivity. As discussed be-low, the increased conductivity may be attributed to sul-fur loss and formation of S vacancies at elevated temper-ature.Figure 10 shows a series of σ d ( V ) curves for a NbS -IIsample, recorded below and above T P . At T > T P agradual growth in conductivity at fields above 0.3 kV/cm -100 -50 0 50 10040060080010001200 E (V/cm) R d / L ( W / m m ) As grown1 st anneal in Ar3 rd anneal in Ar FIG. 9: Normalized RT differential resistance vs. electricfield of an as-grown high-ohmic sample and after 3 subsequentheating/cooling cycles up to 800-850 K in an Ar atmosphere.The contact-separation L = 1050 → → µ m (becomingshorter after each heating cycle because of new contacts). is observed (e.g. the curve at 450 K). It is difficult toseparate the effects of CDW sliding and Joule heatingin these curves. However, sliding of the UHT-CDW canbe checked by the effect of RF irradiation on the σ d ( V )curves. This effect was studied at RT, where it was possi-ble to place the sample sufficiently close to the RF gener-ator output for better matching. Figure 11 illustrates the σ d ( V ) curves recorded at RT over a wide voltage range.At low voltages, the increase of σ d is attributed to RT-CDW sliding, which shows saturation for values aboveabout 1 V. However, at voltages above about 5 V ( E >
10 kV/cm), σ d grows rapidly again above the initial sat-uration level. To check whether this second rise comesfrom sliding of the UHT-CDW, the effect of coherencestimulation by RF irradiation [3] was employed. Onecan see that when the RF field is applied (with all otherconditions kept fixed) σ d grows faster and at lower elec-tric fields (Fig. 11). Thus, the σ d ( V ) diagram exhibitstypical features of a CDW conductor with a thresholdvoltage and a saturation at higher voltages. RF voltagesuperimposed onto a slowly sweeping DC voltage wouldgive a trivial opposite effect, i.e., smearing out the σ d (V)curve (see Fig. 1 in [3]). Consequently, the observed in-crease of σ d at higher voltages should be attributed tosliding of the UHT-CDW. The largest current density j c of this sliding CDW, as estimated from Fig. 11, is ∼ · A/cm ; this correspond to a fundamental frequencyof ∼
300 GHz (with j c / f f =18 A/MHz/cm ). - 2 - 1 0 1 20 1 02 03 04 05 06 0 V ( V ) s d (M W -1) FIG. 10: The σ d (V) curves for a NbS -II sample below andabove T P . The sample length is 44 µ m. IV. THE UNUSUAL CDW FORMED BELOW150 K.
The transition at T P = 150 K (Fig. 8) remains theleast understood. This transition is only observed in thelow-ohmic sub-phase, with the drop in specific conduc-tivity, σ s , near 150 K being sample dependent [12, 19].These samples show a threshold in the I-V curves andShapiro steps above the threshold voltage below T P (Figs. 12 and 13), indicating the formation of a newCDW [12, 13, 19]. However, the ”fundamental ratio” j c / f f appears rather low and also sample dependent. Theratio does not exceed 6 A/MHz/cm and is 3 times lowerthan the value for the RT-CDW (18 A/MHz/cm ). Ifthe charge density is assumed to be 2 e per λ on eachconducting chain, the highest values of j c / f f will corre-spond to about 1/3 of a chain per unit cell carrying theCDW. This value seems to be close to 1 and one mightexplain the discrepancy with an inaccuracy of the esti-mate. However the lowest ratios measured below 150 Kwere two orders of magnitude smaller [12, 19]. The dif-ference between the RT-CDW and LT-CDW transportis clearly illustrated by Fig 12a, where σ d vs. non-linearcurrent is plotted for both CDWs under the same irradi-ation frequency, 400 MHz. For the 1 st Shapiro step thecurrent of the LT-CDW is nearly 3 orders of magnitudelower than that of the RT-CDW. The LT-CDW thus hasan unreasonably low CDW current density for a classicalCDW, i.e., for a CDW formed through a Peierls transi-tion.Figure 14 shows an Arrhenius plot of specific conduc- s d ( M W - ) fl f = 4 G H z fi f = 0 . 8 G H z ‹ n o R F FIG. 11: Room-temperature σ d (V) curves with and with-out RF irradiation. Note the Shapiro steps under the 4 GHzirradiation. -30 -15 0 15 300510 I c ( A) d ( M - ) -0.06 -0.04 -0.02 0 0.02 0.04 0.060.050.10.15 I c ( A) d ( M - ) a) b) FIG. 12: The σ d vs. I c curves under 400 MHz radiation atRT (a) and 122 K (b). The horizontal scales are adjusted tomatch the positions of 1 st Shapiro steps. The dimensions ofthe sample are 170 µ m × µ m . tivities, σ s , for a number of NbS -II samples. For thesesamples, Shapiro steps at RT allow precise determina-tion of their cross-sectional areas and consequently oftheir specific conductivities. For comparison reasons thedependence for a NbS -I sample [17] is added. Thereis a large variation between the specific conductivitiesof different samples. The upper group of curves corre-sponds to the low-ohmic sub-phase and clearly reveals the150 K transition. This leads to a somewhat wider range -0.4 -0.2 0 0.2 0.400.050.10.15 V (V) s d ( M W - ) T=125 K
FIG. 13: σ d vs. V curves under 400 MHz radiation below 150K. The blue (solid) line corresponds to an undeformed samplewhile the red (broken) curve was obtained from a stretchedsample with (cid:15) >
1. The dimensions of the sample are 500 µ m × µ m . The lines are polynomial fits of the experimentalpoints. of RT specific conductivities for the low-ohmic samplesthan earlier reported [8, 19], ranging from 10 to 3 × (Ωcm) − . Despite the large differences in the actual con-ductivities, which vary by over an order of magnitude,the temperature dependence σ s ( T ) for the majority ofthe low-ohmic samples appears very similar on the log-arithmic scale. Correspondingly, the drops in σ s at T P appear approximately proportional to their values above T P . Thus, it can be concluded that all the excess elec-trons, not gapped at T P and T P , are dielectrized at T P , regardless of the actual electron concentration.The conclusion is supported by the result presentedin Fig. 15, where the fundamental ratio j c / f f of the LT-CDW is shown as a function of the drop in specific con-ductivity, ∆ σ s , at T P [41]. The CDW current densityat fixed f f thus appears approximately proportional to∆ σ s .If the single-particle conductivity above T P and theCDW conductivity below T P are provided by the sameelectrons, the mobility in the normal state can be esti-mated from the relationship between σ s and the ”fun-damental ratio” (Fig. 15). By multiplying ∆ σ s /( j c / f f )with an estimated value of λ =10 ˚A, which corresponds tothe wavelengths of the RT- and UHT-CDWs, an electronmobility of about 3 cm /Vs is obtained. For a specificconductivity ∆ σ s = 2.5 × (Ωcm) − (see Fig. 14), thismobility above T P corresponds to an electron concentra-tion of about 5 × cm − , which is about 0.3 electronsper unit cell [1, 2].Samples with σ s (300 K) <
10 (Ωcm) − belong to thehigh-ohmic sub-phase. Their pronounced dielectric be-
4 6 8 10 1210 -5 -4 -3 -2 -1 / T ( K - 1 ) s s ( W -1cm-1) P h a s e IP h a s e I I T
P 2 = 1 5 0 K
FIG. 14: A set of Arrhenius plots of σ s for a number ofNbS -II samples. For comparison, a typical σ s (1/T) curvefor NbS -I is also shown [17]. -2 -1 D s s ( W -1 cm -1 ) j /f ( A c m - M H z - ) FIG. 15: The ”fundamental ratio”, j c / f f , of the LT-CDWvs. the specific conductivity drop at T P . The straight linerepresents a linear approximation of the data. N b _ N b S Normalized Absorbance (a.u.)
P h o t o n e n e r g y ( e V )
S _ N b S Normalized Absorbance (a.u.)
P h o t o n e n e r g y ( e V )
FIG. 16: Fluorescene-detected XANES Nb L3-edge (a) andS K-edge (b) spectra between 300 K and 50 K havior of the σ s ( T ) curves at RT and below (Fig. 14) indi-cates that the free carriers arise from thermal excitationsacross the Peierls dielectric gap formed at T P . A purehigh-ohmic sample shows an activation energy of about2000 K below T P . This value is close to 2500 K, the half-value of optical gap recently reported for NbS -II [42].Evidently, the number of free electrons in these samplesis insufficient to condensate into a collective state. Alter-natively, the transition can just become invisible becauseof the insufficient electron concentration.To better understand the properties of NbS -II, we de-termined the chemical composition of these samples withelectron-probe microanalysis (EPMA). Reliable compo-sitions were only obtained for samples with transversedimensions larger than 1 µ m, which all belonged to thelow-ohmic sub-phase. It was thus impossible to establisha difference in composition between the two sub-phases.From a total of 15 measurements at several sample loca-tions, we obtained a S:Nb ratio of 2.87 ± -II indicateseither the presence of S vacancies or an excess Nb in peak intensity (normalized to 300K values) T e m p e r a t u r e ( K ) S m a i n p e a k S p r e - e d g e p e a k N b m a i n p e a k
FIG. 17: The normalized intensities of the S K-edge, pre-edge and Nb L3-edge as function of temperature. the low-ohmic samples. It has been reported previouslythat NbS is susceptible to S loss with heating [43]. It istherefore likely that the variation in specific conductiv-ity found in the NbS -II samples is a result of S vacan-cies acting as donors, similar to the observed behavior ofTiS [44, 45] and TiSe [46, 47]. Consequently, the higherconcentration of S vacancies would account for the re-duced electrical resistivity observed in samples, belongingto the low-ohmic sub-phase. Although the EPMA mea-surements were not performed on the high-ohmic sam-ples, it is reasonable to assume that these samples arecloser to the stoichiometric composition. Their transfor-mation into the low-ohmic phase under high-temperaturetreatment (Fig. 9) is then connected with a loss of S.The LT-CDW seems to further condense electrons froma state already dielectrized by the RT-CDW. This israther unusual. For a conventional RT-CDW, conden-sation of the Nb d -state electrons leads to a Peierls gap.To further condense electrons in the Nb d -state at T P ,some additional electrons can be transferred from theS p -state into the Nb d -state by forming thus ( S ) − pairs. We have used X-ray near edge absorption spec-troscopy (XANES) to probe the hole occupation in Nb d -state and S p -state from fluorescence-detected Nb L3-edge (at 2375 eV) and S K-edge(at 2476 eV) absorptionlines. From RT to 150 K, the Nb-L3 peak intensity de-creases due to reduced hole occupation of the Nb 4 d state,as shown in Fig. 16(a). Similarly, the pre-edge feature(2470 eV) of the S K-edge also decreases in intensity be-tween these temperatures, as shown in Fig. 16(b). Thispre-edge arises from the transition from 1s to a p - d mixedempty bound state when the S 3 p state takes on a ”hole”character by mixing with the Nb 4 d states. A reduc-tion of the S pre-edge intensity is consistent with theexpectation that the Nb 4 d hole occupation is reduced.However, we also found that the S K-edge main peak0decreases in intensity by lowering the temperature from300 K to 150 K. This means that a simple scenario ofelectrons transferred from S 3 p to Nb 4 d states is ques-tionable. Instead, some electrons are transferred to boththe S 3 d and Nb 4 d states. Fig. 17 shows the evolutionsof the Nb L3-edge peak, the S K-edge peak, and the SK-edge pre-edge intensities as functions of temperature.We note that the behaviour shown in Fig. 17 is reversiblewith temperature.A source of the electrons to occupy Nb 44 and S 3 p states could be the S vacancies acting as electron donors.The concentration of S vacancies is much larger thantypical doping concentrations in semiconductor materialsand therefore likely makes NbS -II a degenerate semicon-ductor. If the electronic structure of NbS -II is such thatan electron pocket (from the Nb 4 d state) and a holepocket (from the S 3 p state) both exist at the Fermi en-ergy, a slight shift of it can either decrease or increase thehole occupations of both Nb 44 and S 3 p states. Such anelectronic structure is depicted in Fig. 1(a) of Ref. [49]and is believed to exist in WTe [48]. As NbS -II iscooled from 300 K to 150 K, thermal generation of car-riers becomes less important, the Fermi level tends tomove upwards, towards the donor impurity band. Thisis revealed by the decrease of both the Nb L3-edge andS K-edge peak intensities observed in XANES.By reducing the temperature from 150 K to 50 K, weobserve that the Nb L3-edge and the S K-edge peak in-tensities recover, resulting in a broad minimum at T P .While the exact cause of this phenomenon is still uncer-tain, the removal of electrons from Nb 44 and S 3 p statescould be related to exciton formation. Reduced screen-ing is expected in low-dimensional materials and at lowertemperatures, when free carriers are fewer; this leads toenhanced exciton binding energy. If the LT-CDW hasindeed an excitonic insulator nature, exciton formationwould remove electrons below T P from the Nb 44 and S3 p states. This leads to the XANES-observed recovery ofNb L3-edge and S K-edge peaks’ intensities below T P .We also observed a similar minimum of the Ta L3-edgeXANES in the orthorhombic phase of TaS near T P =220 K, which is believed to be a ”classical” Peierls transi-tion [1]. However, in o-TaS the S K-edge was not simul-taneously measured with the Ta L3-edge. We thereforedo not yet know whether o-TaS and NbS -II exhibit sim-ilar XANES behaviours. This comparative measurementshould be undertaken in the future.In addition to XANES, preliminary data from STEM-based electron-energy loss spectra (EELS) suggest the lo-cal environments of S atoms change above and below thetransition. At 105 K the L-edge of S is characterized by asingle peak at 162 eV, while at 290 K an additional peakis formed at 167 eV. Meanwhile, the M2 and M3 edges ofNb do not show noticeable changes. The STEM-EELSdata support the suggestion that there is a change inthe local environment of sulfur atoms. It is possible thatchanges in the S positions lead to a change in the numberof S-S bonds forming S( ) − instead of 2S − states, or to
01 02 03 04 05 06 0
T2-1 (ms -1)
T ( K ) ( b )( a ) K (%) B (G) FIG. 18: a) Temperature dependence of the Knight shift ofthe Nb NMR central line. The corresponding ”extra” effec-tive magnetic field H at the Nb nuclear sites is shown onthe right scale (the external fixed field B =7.5 T). b) Tem-perature dependence of the nuclear transverse magnetizationrelaxation rate, T − . a partial activation of S donor vacancies at low tempera-tures. These processes would provide another ”degree offreedom” for the S atoms to change the number of freeelectrons without altering the Nb:S ratio.NMR studies provide an additional insight into the T P - and T P - transitions. The Nb spectrum of non-oriented NbS -II powder samples in a fixed magneticfield B =7.5 T clearly shows the presence of many in-equivalent Nb sites in this phase. The temperature de-pendence of the most intense peak of the central line(which corresponds to the -1/2 ↔ T P . InFig. 18(a) the Knight shift values, K = ( f / f -1) • f is the central line peak frequency,and f = γ • B / π is the reference frequency, whichis proportional to the external magnetic field B and tothe Nb gyromagnetic ratio γ/ π =10.4065 MHz/T. TheKnight shift corresponds to an ”extra” effective field atthe nuclear site from the polarization of the conductionelectrons in the presence of an external field. The rightscale in Fig. 18(a) shows the estimated values of this ”ex-tra” field. Therefore, Fig. 18(a) reveals a new orderedstate below T P . The most obvious reason for this is alattice distortion coupled with CDW formation, as ob-served in NbSe [50].There is no change in the Knight shift around T P =1150 K (Fig. 18(a)). However, studies of the nuclear relax-ation do reveal a feature in this temperature region. Thetemperature dependence of the nuclear transverse mag-netization relaxation rate, T − , measured on the samemost intense peak of the central Nb NMR line, is shownin Fig. 18(b). A maximum of T − ( T ) appears at about130 K. The loss (decoherence) of transverse nuclear mag-netization happens due to different time-dependent localmagnetic fields at nuclear sites. The T − ( T ) dependencecan be explained by the assumption that the character-istic time of such microscopic fluctuations causing relax-ation is increasing as temperature decreases. At low tem-peratures such fluctuations slow down and their correla-tion time becomes comparable to the spin-echo time (tensof microseconds). In such cases, decoherence of the trans-verse nuclear spin magnetization becomes faster and thecorresponding transverse magnetization relaxation time T becomes shorter. At even lower temperatures the fluc-tuations become very slow and their characteristic timeappears much longer in comparison with the time of spin-echo formation. Consequently, the fluctuations do notcontribute anymore to the transverse magnetization re-laxation and T − begins to decrease again. Thus, themaximum in T − at 130 K corresponds to a ”freezing” ofone of the fluctuation sources causing relaxation [51, 52].The most probable candidate for such a source is an elec-tronic or a lattice distortion, which exists at T P or evenabove it. Such a behavior can be expected in case ofstrong 1D fluctuations, where the transition signifies 3Dordering of the CDW fluctuations (see Ref. [53], e.g.). Asimilar behavior of T − was reported for the well-knownCDW conductor NbSe near 130 K [51], i.e. somewhatbelow the 1 st CDW transition, 145 K.Unlike the Knight shift, the relaxation of the transversemagnetization can be stimulated by fluctuation of bothmagnetic and electric fields. Therefore, the maximum in T − ( T ) at 130 K can reveal not only a lattice but also anelectronic ordering. Moreover, one can suppose that theLT-CDW is mainly an electronic ordering, with latticedistortion remaining a small, secondary effect. This isconsistent with the absence of changes in the Knight shiftat T P , as well as the failed attempts to detect a latticedistortion at 150 K, either with electron [10] or X-raypowder diffraction [23].As discussed, uniaxial strain can be considered a probefor the Peierls transition. Unlike T P , T P appears muchless sensitive to strain (Fig. 6a). Some lowering of T P can only be detected with highest applied strains. Giventhe same strain, the relative reduction of T P is an orderof magnitude smaller than that of T P . Since the suppres-sion of the fluctuations increases T P and the corrugationof Fermi surfaces has the opposite influence, a balance ofthese two effects in LT-CDW might explain why T P isless sensitive to strain than T P . We also note that dif-ferent behaviors with respect to strain were observed inother trichalcogenides with multiple CDW transitions. Inthe monoclinic TaS , the lower transition appears to bemore sensitive to strain [36] and pressure [2, 37], as com- pared to the upper one. In NbSe , another compoundwith two CDWs, the effects of pressure and strain are no-tably different; while under pressure the lower transitiontemperature decreases faster than the upper one [2, 37],the rate of decrease is much slower under uniaxial strain,especially in the range of small strains [5]. In the caseof NbS -II we can suppose that either T P is more dom-inated by fluctuations than T P , or the transition at T P has a different origin.The same effect of strain is observed for the non-linearconduction of the LT-CDW (Fig. 13): the I-V curves donot show notable changes up to about 1.5% strain (theapparent slight improvement of coherence was not re-peated in other samples). The weak dependence of theLT-CDW on strain can indicate weak coupling of thisCDW with the lattice. In view of this, the low sensitiv-ity of T P on strain would also be rather coupled withthe special nature of the LT-CDW, than to the effect of1D fluctuations. V. DISCUSSION.
The results presented show that NbS -II appears tobe a unique quasi 1D compound. It shows two high-temperature CDW transitions at T P =330-370 K and T P ∼ σ ( T ) at T P and the density of the CDW current(at given f f ) depend strongly on the sample specific con-ductivity at RT, which can vary within the low-ohmicsub-phase by more than an order of magnitude. Evi-dently, the variations in specific conductivity are con-nected with the deficiency of S atoms. The excess freeelectrons, induced by ”doping” from S vacancies, do notcondense into a CDW until below 150 K. The concentra-tion of these electrons is comparable with the metallicvalue, so that the electronic gas can be considered as de-generate. Consequently, the electronic structure can betreated in terms of new Fermi surfaces, which survivedthe two upper CDW transitions. The 150 K transitionthus corresponds to condensation of these free electronsand, presumably, of additional electrons released duringredistribution of S bonding, into a CDW, or a CDW-likeformation. However, even for the low-ohmic samples thespecific conductivity above T P is far from being metal-lic. The free carriers are gapped by two already exist-ing CDWs, and the resistivity is 2-3 orders of magnitudeabove the estimated value above T P (Fig. 8). Both, the T P value and the form of the feature in σ ( T ) at T P (Fig. 14) show no obvious correlation with σ s . Conse-quently, the transition at T P is similar for the electronconcentrations varying between samples by up to one and2half orders of magnitude. In other words, the concentra-tion of electrons condensed into the LT-CDW can vary alot, but the characteristics of this CDW remain similar.The transition disappears or becomes invisible only if σ s is less than ∼
10 (Ωcm) − .The possibility of forming a separate CDW by elec-trons from dopants has not been considered yet. In thecases of NbSe and the monoclinic phase of TaS , wheremultiple Peierls transitions are also observed, differenttransitions dielectrize the electrons belonging to differenttypes of chains. In the case of NbS -II, some electronsoriginate from the S vacancies acting as donors, and theyare not expected to occupy a separate band. In case ofthe CDW compound K . MoO doping with V results inextra holes, but these are gapped by the same CDW [54].Contrary to NbS -II, doping in this case only results ina variation of the q -vector.No hysteresis was found in case of NbS -II in the R ( T ), R ( V ) and R ( (cid:15) ) measurements. Similar curves for nano-sized samples did not show steps coupled with the addi-tion/removal of a CDW period ( [7, 55] and referencestherein). This could mean that the q -vectors of the twoupper CDWs do not vary. NbS -II might have featuresin common with (TaSe ) I, where the CDW also showsno metastable states (see [2], pp. 357-360 and 364-367]).It seems that that the CDWs cannot deform in NbS -IIlike they do in K . MoO , TaS and a number of othercompounds, probably because of topological reasons [56].If this is the case, extra free electrons cannot be incorpo-rated in the UHT- or RT-CDWs. Thus, ”doping” withS-vacancies results in a growth of conductivity at T >T P , while at T P the extra electrons become condensedinto a separate CDW.While the structure of NbS -I is well known [57], thestructure of NbS -II has not been determined yet. Toanalyze possible lattice instabilities of known phases ofNbS ab initio density functional theory (DFT) calcu-lations of a band structure were performed for a modelstructure consisting of symmetrized monoclinic unit cellsof NbS -I. That is, we just manually removed the knowndimerization of NbS -I and placed the atoms at the meanpositions of a dimerized NbS -I unit cell [57]. This con-verted the compound into a metallic state. The DFTcalculations were performed in both the local density ap-proximations by the PAW (Projector Augmented-Wave)method [58], as well as by the generalized gradient ap-proximation [59], as implemented in the Abinit simula-tion package [60]. Four bands were found to cross theFermi level in the initial filling. Two of them have rela-tively large flat regions corresponding approximately to1/2 and 2/3 filling of the respective bands. The corru-gation of Fermi surfaces appears sensitive to the electronconcentration: a reduced filling of these bands flattensthe Fermi surfaces and makes the compound suscepti-ble to CDW instability. These bands may be responsiblefor two transitions with two q -vectors. Two other bandsform small near-cylindrical pockets around the Y point ofthe Brillouin zone and are aligned in the Y-H direction. They are more sensitive to doping and may eventuallydisappear in case of excessive doping. Extra electronsbelonging to these pockets will not be condensed in theRT- or UHT-CDW, but may form a new condensed CDWstate.Several possibilities for the formation of the LT-CDWcan be considered. The first is the Peierls transition.This would require electrons, not condensed by the CDWtransitions at T P and T P , to be in nested sections of theFermi surface. This is not a very likely scenario, becauseof the strong dependence of the ”fundamental ratio” onthe electron concentration. There is a bigger probabilitythat electrons belonging to these pockets will condenseinto a state in which the distance between the electronsdepends on their concentration, both along and perpen-dicular to the chains. A candidate case in a Wigner crys-tal (WC), which is stabilized by the repulsive Coulombforces. Unlike conventional CDWs, a WC is relativelyweakly coupled with the lattice. This might be the rea-son, why the LT-CDW was not detected by TEM [61].However, T P , as well as the form of the σ ( T ) curvein the logarithmic scale (Fig. 14), remain stable over awide range of electronic concentrations (nearly one anda half orders of magnitude). Since the temperature of aWigner crystallization depends on the concentration ofelectrons as a power law, the observation argues againsta WC formation at 150 K.The stability of T P might indicate that the transitionat 150 K, forming a periodic potential, is not directly cou-pled with the electrons induced by doping. Nonetheless,these electrons, irrespective to their concentration, areaccommodated into this potential and form a CDW elec-tronic crystals. In case of the high-ohmic samples thiscondensation remains invisible in the σ ( T ) curves. Thetransition at T P can however show up in some othermeasurements like e.g. in σ ( T ) studies at sufficientlyhigh frequencies (see Fig. 4 in Ref. [15]). A kind of metal-dielectric transition was also observed close to 150 K inthe NbS -I polytype, where the transition temperatureappears stable in a wide range of pressures [62]. Thus,the 150 K transition seems to be an intrinsic feature ofboth NbS polytypes and appears rather robust againstpressure, strain and doping.Apart from Wigner crystallization and Peierls transi-tion, the Keldysh-Kopaev transition [24] (known also asthe formation of excitonic dielectric [25]) has been sug-gested as a possible mechanism for electron condensationin NbS -II at T P [19]. This transition represents a gener-alization of the Peierls transition, which can occur if theelectron’s and hole’s Fermi surfaces have shapes, whichallow nesting. It may take place in a semiconductor, ifthe gap between the hole and electron bands is smallerthan the binding energy of an exciton; then spontaneousexciton formation begins and a new electronic state de-velops. If the maximum and minimum of the hole andelectron bands are displaced in the k -space, the vectorconnecting them defines the wave vector of the possiblecharge modulation, i.e. an excitonic CDW. Among re-3lated compounds such an origin of CDW formation hasbeen suggested for TiSe [63], which is also semiconduct-ing above the transition. The nesting of electrons andholes with formation of excitons can proceed in a similarway for various degrees of doping. The dielectrization ispronounced if one of the bands (the electronic one in ourcase) is partly filled above T P . However, if the Fermienergy is located in the gap separating the bands, likeit would be in case of a stoichiometric composition, onecan expect a dielectric state already above T P with thetransition remaining practically invisible in σ ( T ).Neither the possibility of sliding nor the possible val-ues of j c / f f have been discussed for an excitonic CDW.One can consider a simple case of a ”symmetric” exci-tonic CDW, which originates from the nesting of twosimilar electronic and hole bands, with a symmetricallypositioned Fermi level ( p = n ). Such an excitonic CDWwill not be charged. However, in case of doping, a slidingexcitonic CDW can transfer charge proportional to thedegree of doping. VI. CONCLUSIONS.
Our studies show that NbS -II is an outstanding mem-ber of the MX group. It has three CDWs: a near roomtemperature RT-CDW at T P = 360 K, a low tempera-ture LT-CDW at T P = 150 K, and another CDW at amuch higher temperature T P = 620-650 K. Each CDWpresents peculiar salient features. First, the RT-CDWhas exceptionally high coherence and the utmost veloc-ity of all known sliding CDWs. This suggests that thisRT-CDW can be considered for practical applications.Second, the fields and currents of the UHT-CDW areimpressive. Third, the LT-CDW is most unusual and aphysical picture of its formation is still incomplete.For readers’ references we opt to summarize the fea-tures of NbS -II as a list:1. The properties of NbS - II depend strongly on thegrowth conditions. The RT conductivity, σ s (300K), of the samples varies from 2 to 3 × (Ωcm) − .2. The ”low-ohmic” samples ( σ s (300 K) = 10–3 × (Ωcm) − are S deficient with the S vacancies act-ing as electron donors. The gradual transformationof the ”high-ohmic” into the ”low-ohmic” ones un-der heating above ∼
800 K is consistent with thisconclusion.3. The ”high-ohmic” sub-phase ( σ s (300 K) = 2–10(Ωcm) − of NbS -II shows two CDW transitions,at T P =340-370 K and at T P ≈ T P and T P , the”low-ohmic” samples show a CDW transition at T P = 150 K. The specific conductivity drop at T P is proportional to the specific conductivity above T P . This LT-CDW is a condensate of the elec-trons donated by the S vacancies. 5. All three CDWs exhibit sliding at E > E t .6. RF interference shows that the fundamental fre-quency of the RT-CDW sliding can be at least 20GHz. The extremely high coherence of this CDWis manifested in Bessel-type oscillations of E t andof the Shapiro steps’ width as a function of the RFpower.7. At RT the NbS -II samples show torsional strain.The strain grows abruptly for E > E t and can beincreased by an order of magnitude with RF irra-diation.8. Under uniaxial stretching NbS -II samples the RT-CDW demonstrates many features of coherence en-hancement, i.e., the threshold decreases and be-comes sharper, the growth of σ d above E t is faster,the value of the maximum CDW conductivity in-creases, and the Shapiro steps under RF irradiationbecome more pronounced.9. T P is extremely sensitive to uniaxial stretching: (cid:15) ∼
1% can reduce T P to below RT. The transitionat T P becomes sharper with strain, in line with thegrowth of the CDW coherence.10. Sliding of the UHT-CDW can be observed belowand above T P . This is proven by the effect of RF-induced coherence stimulation. The E t value forthis CDW can be on the order of 10 kV/cm at RT.11. The LT-CDW is nearly insensitive to tensile strain.At equal strain the relative decrease of T P is 10times lower than that of T P . The I-V curves showno regular changes under strain up to 1%12. The charge density of the LT-CDW transport, i.e.,the j c / f f value revealed by RF interference, is from3 to 1000 times smaller than that of the RT-CDWand scales with the specific conductivity above T P .The value j c / f f appears to be well below 2 e /s ,which is impossible for a normal CDW.13. Unlike in cases of RT- and UHT- CDWs, no latticedistortion is observed at T P by means of diffractiontechniques. The Nb NMR study reveals a Knightshift at T P , but not at T P .14. A clear maximum near T P is observed in the tem-perature dependence of the nuclear transverse mag-netization relaxation rate, T − , measured at thecentral Nb NMR line. The feature in T − ( T ) isinterpreted by a freezing of the electronic densitydistortion (ordering) with cooling.15. Near T P , minima are observed in XANES spectraof the S K-edge, K-line pre-edge, and the Nb L3-edge. The result reveals electron transfer to both S3 p and to Nb 4 d states down to T P . Further cool-ing below T P reverses the trend of XANES inten-sity variation. A plausible cause for the observedXANES below T P is a formation of excitons.416. The condensation of the excess electrons in the”low-ohmic” samples into a separate LT-CDW isexplained with the rigidity of the RT- and UHT-CDWs, which does not allow changes of their q -vectors and condensation of extra electrons. In ad-dition, ab initio calculations show that these elec-trons may belong to additional small pockets in theFermi surfaces, and a formation of a new condensedphase.17. The nature of the LT-CDW is not completely un-derstood. The concept of an excitonic dielectricmight explain the low sensitivity of T P to the con-centration of electrons, condensed into this CDW.Further studies of this compound, including structuraland scanning-probe ones are in progress [23]. Acknowledgments
We are grateful to A.A. Sinchenko and A.P. Orlov forthe help in the strain experiments. The support of RFBR (grants 14-02-01240, 14-02-92015, 16-02-01095) and theprogram ’New materials and structures’ of RAS is ac-knowledged. The elaboration of the ”bending technique”of the uniaxial expansion was supported by the RussianScientific Foundation (Grant No14-19-01644). The workof I.R.M. was supported by the Program of Competi-tiveness Growth of Kazan Federal University funded bythe Russian Government. The support by MOST, Tai-wan (103-2923-M-002 -003 -MY3) and by the SlovenianResearch Agency (ARRS) under the Slovenia-Russia bi-lateral project BI-RU/14-15-043 is also acknowledged.EPMA was performed, in part, using the equipment ofMIPT Center of Collective Usage. [1] P. Monceau, in Electronic Properties of Inorganic Quasi-One-Dimensional Conductors, edited by P. Monceau (D.Reidel Publishing Company, Dordrecht, 1985).[2] P. Monceau. ”Electronic crystals: an experimentaloverview”. 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