Charge Density Wave Transitions and Transport Properti esof n-M0401 1 Crystals-

Shigeo Ohara

Charge Density Wave Transitions and Transport Propertiesof n-M0401 I Crystals

Shigeo Ohara

Department of Materials Science, Faculty of Science,
Hiroshima University, Higashi-Hiroshima 724, Japan

Electrical resistivity p, Hall coefficient RH, and thermoelectric
power S have been measured over the wide temperature range 1.5-300 K for
quasi-two-dimentional crystals of monoclinic n-M0401 I , which undergoes two
charge density wave (CDW) transitions at Tel =105 and Te2=35 K.

The effectof hydrostatic pressure on the resistivity, Hall coefficient, and magnetoresistance ~p/pe is also studied up to 1.2 GPa.

The applied pressure

enhances the 1st CDW transition temperature Tel, while it suppresses the
2nd one Te 2.

The detailed analysis gives the temperature dependences of

the CDW gap energies ~I (T) below Tel and ~2 (T) below Te2, which obey asingle universal curve, independent of applied pressures.

The observed

Hall coefficient is positive in the temperature ranges studied but thethermoelectric power is mostly negative, which indicate that the conduction carriers are due to electrons and holes.

Shubnikov-de Haas oscilla-tions are also observed in the ~p/pe- and RH-H curves below Te:~, where
three main frequencies are found, which also depend on the appliedpressure, indicating that the Fermi surfaces of holes and/or electrons arepressure sensitive.

Based on these experimental data, together with themagnetic field dependence of RH below Te2, we have proposed a possible
band scheme for conduction electrons and holes of this unique material
system that have remained after the CDW transitions.

11. Introduction

Molybdenum oxides of the Magncli phase: monoclinic n- and orthorhombic y-M0401 I crystals, which are primarily built up of MoOs octahedralslabs separated by layers of Mo04 tetrahedra, parallel to the bc
plane,I.2) have quasi-two-dimensional structures and thus their Fermi
surfaces are strongly anisotropic with cylindrical shapes elongated along
the a -axis. 3 )t

In particular, n-M0401 I undergoes twice the mctal -semiconductor transitions at the characteristic temperatures Te l =105 andTC2=35 K associated with charge density wave (CDW) instabilities; dlffllse

X-ray and electron scattering studies show that the nesting vector at Te l
is Q=0.23b ,4) but the one at Te2 is not yet known.
t

Experimentally,

anomalous behaviors have been found at Tel and Te2 in the temperaturedependences of various transport properties, such as electrical resis tivity, Hall coefficient, transverse magnetoresistance,
power, and transient thermoelectric effect. 5- 9 )thermo(~ lectric

Recent band calculations

for this material using a tight-binding (block-band) method lB ) have shown
the existence of both electron and hole pockets in the Brillouin zone,
whose Fermi surfaces are two-dimensional, which favors the partial nestingof the Fermi surfaces with the nesting vector Q=0.25bwith the above experiments.

t,in good agreement

Furthermore, in the low temperature CDW state(T<T e 2), two periodicities fl and f2 in the de Haas-van Alphen oscilla-tions under magnetic fields up to 5 T are found (fl =17 T and f:?=50 T;4)
fl =17.5 T and f2=43 T5»), which are regarded as due to small electron

and/or hole pockets.

However, much less is still certain as to the natureof the Fermi surfaces of this material system.
In the present work, we have measured the dc electrical resistivity p(under hydrostatic pressures up to 1.2 GPa), Hall coefficient RH, and2thermo el ectric power S ove r t he t emp er atu r e r ange f r om 1.5-300 K.

We havealso studied RH and transvers e magn et oresistance ~p/pe at liquid He
temperatures under hydrostatic pressures up to 1 . 2 GPa an d magneti c fiel ds
up to 6 T.

These transport data will provide us wit h val uabl e i nf orm ati onon the nature of the Fermi surfaces of transport carri ers.

Taking i nt oaccount available information, we shall propose a poss i ble band sch eme ofthis unique materials system.

2 . Experimental

Crystal growth of n-Mo.Ot t was made by a ch emical vapor tr ansporttechnique in a two-zone furnace starting from a mixture of powd ers of
M002 :Mo03=1:3 using TeCl. as a transporter, in the temp erature range of
TL=510 and TH=560 °C.7)

The crystal structures and lattice parameter s ofthis crystal were examined by X-ray diffraction to agree with the r eported
data;2) a=2.46 nm, b=0.544 nm, c=0.670 nm, and ~=94.4 o.

The grown

crystals were thin platelets elongated along the bc-plane, and thetransport measurements were made on the cleaved crystals (typically 2 x
0.5 x 0.1 mm 3 ).

In particular, the dc electrical resistivity measurem ents

along the c-axis were made using mechanically polished samples.

The

crystal orientation was determined by X-ray Laue patterns.
The galvanomagnetic measurements under magnetic fi elds up to 2.0 T
using an electromagnet applied along the a'-axis were performed using a
conventional dc potentiometric method over the temp erature range from 1.5300 K.

The thermoelectric power measurements were also carried out in thesame temperature range as above with a usual technique.

The pressur eeffects on the electrical resistivity over the t emperatur e range from 4.2 300 K and Hall coefficient and transverse magnetoresistanc e at 4.2 K und er3the magnetic fields up to 6.0 T with a superconducting magnet were
measured up to 1.2 GPa using a nonmagnetic clamp-type pressure cell (Be-Cu
and SiAION).8l

The various transport properties of these crystals dependon sample-to-sample, due to different amounts of various lattjce imperfections produced during the crystal growth, such as oxygen vacancies, excess
oxygen, dislocations, impurities, etc., so that we specify a sample by thevalue of its resistivity along b- and c-axes at room temperature PbR (0)and peR (0), respectively (see figure captions and Table 1).

3. Experimental Results and Discussions

3.1

DC Transport Quantities at Ambient Pressure

The temperature dependence of the electrical resistivities Pb and Pc
for monoclinic n-M0401 I along b- and c-axes at ambient pressure isillustrated in Figs. l(a) and (b), respectively.

As can be seen clearly

from Fig. l(a), this material undergoes the CDW-related transitions at two
distinct temperatures Tel =105 and Te2=35 K.

In the case of the c-axis

resistivity [Fig. l(b)], only a small shoulder is observed at the second
transition temperature Te2.

The inset shows the temperature variation of

the ratios of the c-axis resistivity pc to the b-axis one Pb, Pe/Pb.

We

note that in the metallic region (T>Tet; normal state) the resistivity
anisotropy is temperature independent, whereas in the CDW state below Tel
it is enhanced, attaining a maximum near Te2, which indicates that theelectronic anisotropy is appreciable after the CDW transition below Tet
due to the nesting of the Fermi surfaces of conduction carriers.
As shown later (Fig. 15), the Hall coefficients of n-M0401 I in the
CDW states depend strongly on an applied magnetic fjeld H, while in the4normal state they are field independent.

In order to see an overallbehavior, here we shall show the Hall effect data taken at the f i eld of
2.0 T.

Figure 2 shows the temperature dependence of the Ilall coefficient

RH at 2.0 T for the typical samples of n-M0401 I [No. bl (squares) andcl(circles)], where the electrical currents were passed along the b- andc-axes, respectively, as done for the resistivity measurements.

At hightemperature T>Tcl the Hall coefficients of both crystals are very small
but not zero

(RH~10-4

cm 3 /C) and almost temperature independent.

Withdecreasing temperature RH sharply increases just below Te l, levels off tonearly a constant value(~10-2cm 3 /C), and continue to increase again

below its second CDW transition temperature TC2, followed by approaching a
constant value(~5xl0-1

cm 3 /C) at low temperature.

It should be notedthat there is no appreciable difference in RH for the b- and c-axes, jn
sharp contrast to their resistivities (Fig. 1).

The positive sign of RH

indicates conduction "holes" contributing to the dc transport.
The Hall mobilities #H (=RH/p) for the above samples are plotted as afunction of temperature in Fig. 3.

With lowering of temperature theappreciable increases in #H are seen near Tel and Te2; at high temperatures #H are of the order of 1 cm 2/Vs, but at low temperatures they areexceedingly enhanced by 10 4 times as large as those at T>Tel.

Also wenote that #H is strongly anisotropic below Tel (CDW state).
In contrast to the positive Hall coefficient observed over the wholetemperature range studied, the thermoelectric power S of these crystals is
almost negative, except at low temperatures.

Typical results of various

samples are presented in Fig. 4 for n-M0401 I (one sample along the c-axis,
No. c2, and two samples along the b-axis, No. b2 and b3).

At hIghtemperatures T>Tel (normal state), all crystals show a Ijnear dependenceof S on temperature, and below Tet the thermoelectric power is enhanced,

5

followed by a gradual decrease toward zero.

Furthermore, with decreasing

temperature the thermoelectric powers along the b-axis exhibit their sign
reversals from negative to positive and vice versa.
are also depend on sample-to-sample.

As can be seen, they

However, our overall behaviors of

the S-T curves are in good agreement with the results by Guyot et al. 3 )It should be emphasized that the thermal processes are predominantly
due to electrons.

At first sight, the appearance of a pronounced minimum

below Tcl seems to be due to a phonon drag effect through a strong
electron-phonon coupling, but the detailed examination of the observed S-T
curves reveals that this mechanism is ruled out.
analysis seems to be more appropriate.

Instead, the following

Since the thermoelectric powers at

high and low temperatures are nearly linear to temperature T and oursystem is a degenerate electron system, the thermoelectric power S6 can be
written by(1 )where e (>0) is the electron charge, EF e the electron Fermi energy, and ~a dimensionless parameter characterizing scattering mechanism;
phonon scattering. 1 I)
EFl e

for

Assuming ~=3, we can evaluate the Fermi energies

and EF2 e from the slopes of the S-T curves at high and low

temperatures, respectively.
EFl e

~=3

As listed in Table 1, the estimated values ofare of the order of a few electron volts, which are one order ofmagnitude as large as EF2 e ;with ~=1.3)

Guyot et ale have underestimated EFle~0.5 eVSuch a drastic decrease in the electron Fermi energy is

considered to arise from the CDW transitions due to nesting of theelectron Fermi surface.
Furthermore, we should note that the thermoelectric powers below Tc2
show a sign reversal from negative to positive or vice versa (Fig. 4),

6

which strongly suggests that positive holes are also responsible for thethermal process.

Considering the appreciable increase in the (positive)

Hall coefficients of n-M0401 I with decreasing temperature T<Te2 (indicating the decrease in the number of conduction holes), we may infer that thenesting of the hole Fermi surface takes place through the second CDW
transition at Te2, thereby accompanying the formation of the energy gap of
the hole band.

Thus it is expected that the hole Fermi energy EFh a]sochanges drastically at Te2.

In our picture, the hole system is also

degenerate, and then its thermoelectric power Sh is expressed in the form
Sh=+(rr2/3)(kB2/e)~T/EFh.

However, it is difficult to estimate the valuesof EFh from the observed curves, since the measured thermopower S is thesum of two contributions from electrons and holes, as(2 )S

where ae and ah are the electronic conductivity of electrons and holes,
respectively.

3.2

Effect of Pressure on the CDW Transitions

Figure 5 shows the temperature dependence of the electrical resistivities Pb for sample No. b4 at ambient pressure (P=O) and variouspressure p up to 1.2 GPa.

The resistivities Pb show characteristic minima

at the CDW transition temperatures Tel and Tc2, indicated by arrows.

With

increasing pressure the first transition temperature Tel and the resistivity maximum just below Tel are both increased, while the second CDW
transition temperature Te2 is shifted to a lower temperature and theresistivity maximum below Te2 is decreased appreciably.

The variations of

Tel and Tc 2 wit h pre s sur ePa res h0 wn i n Fig. 6, wher ewe see t hat Tel i S

7increasing almost linearly with p, while Te2 is decreasing gradually up to
about P=O.7 GPa and more drastically at high pressure P>O.7 GPa.

Most ofthe low dimensional conductors, such as TiSe2, 12) NbSe 3 , 13) and TaS3 , 14 )show a decrease of the CDW transition temperature Te as the pressure
increases, due to a change in the nesting condition.

On the other hand,an increase in Te with increasing pressure has been reported by Fujishita
et al. in purple bronze Nae.9MosOl7 .15)
In the present work, we have analyzed the observed p-T curves helow
the transition temperatures Tel and Te2 using the following semiempiricalexpressions to estimate the apparent CDW gap energies for 17-MOAI011, .11 (T)below Te 1 and.12 (T) below Te 2.

The electr ical conduct i vi ty (Jj :=1/ Pi (i =1

for T<Tel and i=2 for T<Te2) can be well approximated by the expression

(Jj

(Ja j

+

Ai ex p [ -.1 j (T) / kB T] ,(3)

where (Jei is the temperature-dependent conductivity due to normal conduction carriers, which can be empirically expressed by the following
polynomial forms:

(Ja

1-' =

a 1 + {31 T

and

-I
(Je 2

= a2

+ {3 2 T +

yT2,

(4)

where Ai, ai , {3i (i=l, 2), and r are some constants, and kB is theBoltzmann constant.

Figure 7(a) and (b) show the temperature dependences

oft he be s t - fit ted val ue s 0f the a ppar e nt gap en erg i e s .11 (T) and .12 (T) at
various pressures p, respectively.

The value of .11 (T) increases withlowering of temperature, and the .11 (T)-T curve is shifted toward hjgher
temperatures with increasing pressure.

Here it is of interest to notethat the .11 (T)-T curve at p=o is in good agreement with the temperaturedependence of the satellite intensities of the X-ray diffraction for '17M0401 I found by Guyot et al. ,4) as shown later.

8

On the other hand, thegap en ergy .12 (T) is also incr eased wit h decreasi ng te mperature, whose
behavior is quite differ ent from that of .1 1 ( T ) [Fig . 7 (a)] .

Theseexperimental results suggest tha t t he hydrost atic press ure enh ance s t he
CDW transition at Te l, wher eas it suppr ess es t he on e at Te 2 , wh ic h i n tur nmeans that the pressure induces some deforma t ion of t he Fermi surfaces andthus the change in the degree of their nestings , as well as a phonon
stiffening effect. 7 • S )As is well known, in an id eal ized on e- dim ensional

system, the gap energy at T=O,

.1(0),

is given by .1(0) =3.5kBTc ,1 6) wh er e

the CDW transition temperature Tc is proportional to the el ectron - phonon
coupling constant and the lattice distortion associated with th e CDW
transition.

Thus the observed increase in Tc 1 and .11 (T) by pressure

indicates that the electron-phonon coupling constant and/or the lattice
distortion are enhanced by the applied pressure and vice versa for Tc 2 .
In our case, however, it is impossible to obtain the value s of gap
energies at absolute zero .11 (0) and .12 (0) and their pressure depe nd ence,since our empirical method of analysis is made only near Te l and Tc 2 .

Inview of these circumstances, here we have att empted to replot t he .1 i (T) - T
curves at various pressures in terms of their normalized quantities,.1i (T)/k BTc i[rather than .1i (T)/.1i (0)] versus reduced temperatur e T/Te i(i=l and 2) as shown in Fig. 8.

Surprisingly it turns out that al l theexperimental points lie on a universal curve regardless of pr ess ur e .
Corresponding to Fig. 7(b), the behavior of .12 (T)/k BTe2 near T/Te2 ~1 iscontinuous, as shown in Fig. 8(b).

This is because we have tak en th evalue of Tc2 as the temperature at which the p-T curve shows a r esistiv i ty
minimum.

Therefore, in order to fit the experimental data to theuniversal curve of Fig 8(a) [shown in Fig. 8(b) by the da shed curve ], wemus t red e fin e the val ue 0 fT c 2 as Tc 2 '(=0 . 85 Tc 2 ) •Fi gu r e 9 s hows thenor ma liz e d gap en erg i e s a=.1 I (T) / kB Te l 0 r .12 (T) / kBTe 2il plot te d a s a fun c t i on

9

of the reduced temperature t=l-T/T c l or 1-T/Tc 2· for our sample inlogarithmic scales, where the normalized satellite intensities of X-ray
diffractions, 1/ Ie, for T/-M0.1 011 4 ) and (NbSe4 h 1 17 ) are also included forcomparison.

It is clear that our experimental data lie on a straight linewith the slopes a=0.5 to 0.7 for t>O.l and a=1.0 for t<0.08, in
qualitative agreement with the X-ray diffraction data.

Moreover, we seethat the extrapolated value of the normalized gap energy ~ to absolute
zero (t=l) is ~"'3.5, which is in good agreement with the universal value
predicted by BCS theory.

At any rate, it turns out that our redefinitionof Tc2 by Tc 2· is regarded as the "precursor" of the second CDW
transition, where some CDW fluctuations occur.
Such a universal curve can be reasonably understood by conventional
mean-field theory (a=0.5 for OstSl) and more generally by the Landau
theory which predicts a=0.5 for t"'1 and a=l for t«I.

We have tried tocompare our experimental data with the temperature dependence of the orderparameter of the Landau theory defined by the following equation,- A + (A2 + Bt) e . 5 ,(5 )where A and B are some constants.

The calculated curve with the best-

fitted values A=0.19 and B=14.2 is indicated by the dashed line in Fig. 9.
In our case the experimental points derive from the curve at lower reduced
temperature t<0.05; more detailed measurements near the transition temperatures will be required to confirm the validity of Eq. (5).

3.3Quantum Oscillations in the DC Transport Quantities

In the low temperature CDW state (T<T c 2), it has been reported thattwo periodicities in the de Haas-van Alphen oscillations under magnetic

10

field are observed,4.5) which arise from the conduction carriers of sma]lelectron and/or hole pockets that are remained after nesting of theirFermi surfaces.

In Fig. 10, the transverse magnetoresistance dp/pe at 4.2

K is shown with increasing (solid lines) and decreasing (dashed lines)
magnetic field up to 6 T at constant pressures P.

As can be seen, dp/pe

increases with H attaining a value as large as about 12 at H=6 T, and the
dp/po-H curve shows an oscillatory behavior (Shubnikov-de Jlaas oscilla-tions); in addition, we see a noticeable hysteresis near each maximum of
the dp/pe-H curves.

As the pressure is increased, the magnitude of the

dp/po-H curves is decreased and the maximum positions (indicated by arrows

in Fig. 10) are also shifted.

It should be also noted that the hysteresis

at P=I.0 GPa is reversed compared to that at P=O.
On the other hand, the magnetic field dependence of the Jlall vo]tages
VH at 4.2 K under ambient pressure P=O and P=I.0 GPa is shown in Fig. 11.

We see that the Hall voltages are positive and also exhibit oscillatory
and small hysteresis behavior with varying magnetic field.
We have analyzed the oscillatory components in the dp/pe- and VH-H
curves in a semiempirical way, as given below.

The observed resistive orHall voltage V(H) is regarded as the sum of an oscillatory component
Vase (H) and a background VBG (H),
V(H)

Va s e (H)

+

(6 )

VB G (H) ,where the background component VBG (H) is calculated by a successjve
smoothing (or averaging) procedure, with a magnetic field interval dH,
from i=-n to n, as expressed in the following form:n
VB G (H)(2n + 1)-1 .~ V(H+it1}{).

l=-n

11

(7 )

Figure 12 shows one of the results for the oscillatory component of theHall voltage Vose (H) for sample b4 at ambient pressure plotted against thereciprocal magnetic field.
~H=0.04

Here we have taken the magnetic field interval

T and n=5 for the data analysis.

We can see two types ofoscillatory characteristic of the Shubnikov-de Haas (SdIl) phenomena.
In order to obtain the fundamental frequency components

fi

(i=l,

2, .. . ) of the SdH oscillations, we have further analyzed these Vose (H)-I/11
curves using a fast Fourier transform method.

The results are shown in

Fig. 13 for the Hall voltages of sample b4 at different pressures; eachpeak in these profiles shifts toward higher frequency with increasingpressure P.

Figure 14 illustrates some of the most probable components

thus obtained from the magnetoresistance (solid symbols) and JIall data
(open symbols) plotted against applied pressure P.

It is to be noted thatat low pressures P<0.5 GPa three types of frequencies (solid lines) are
observed, the middle of which is undetectable at higher pressure above 0.7
GPa, and an additional frequency component (dashed line) begins to appear
above 0.5 GPa; of the three fundamental frequencies observed at P=O, theonly one of f=16 T is in close agreement with f=17.5 or 17 T obtained fromthe de Haas-van Alphen oscillations by other workers. A • S )The effect ofpressure on fi is appreciable at high pressures P>0.7 GPa.
The above result and the pressure dependence of Te2 [Fig. 6(b)] may
suggest that this material undergoes some pressure-induced structuralchange or phase transition at the characteristic pressure Pe=0.5-0.7 CPa,thus leading to an appreciable change in the shape of Fermi surfaces.
Even though we cannot assign each frequency fi to a respective origin fromthese data alone, we may evaluate the magnitude of cross section SF forthe extrema of electron and/or hole Fermi surfaces perpendicular to themagnetic field (or b"c"-plane) using SFi =(2rr)2 e fi/h (h: Plank constant);

12

at p=o the value of SFi are of the order of (5 - 15) x 10 1 6 m- 2 that
corresponds to only 0.05-0.15 % of the areas of the first Brillouin zone
SBZ(=1.1 x 10 2B m- 2 ).

Such small cross-sectional areas are the result of

the successive nesting of the Fermi surfaces caused by two CDW transitions, and Fig. 14 shows that the resultant Fermi surfaces are strongly
pressure-sensitive.

3.4

Magnetic Field Dependence of the Hall Coefficient

Finally, we shall show the magnetic field dependence of Hall
coefficient RH up to 6 T; a typical result for sample b4 at 4.2 K is shownin Fig . 15, where quantum (SdII) oscillations are clearly observed.

Wenote that RH is increased steeply with increasing magnetic field attaining
a constant value at high field region at least up to 6 T.

Such a magnetjc

field dependence of the Hall coefficient RH except for SdJ[ oscillations,can be understood in terms of classical transport expressions for multiple
conduction carriers (electrons and holes) as given below.
Based on the band model developed by Canadell et al. ,IB) various dc
transport by Inoue et al,7) and dynamic measurements by Sasaki et al. 9 )for ~-M0401 1, a possible nesting model and band scheme of ~-M0401 1 havebeen proposed. 7 )The basic idea is that the dc transport properties of

the quasi-two-dimensional conductor ~-M0401 1 below the second CDW transition temperature Tc2 (=35 K) are primarily due to the "electrons" and"holes" in the respective bands that have remained after the CDW
transitions.

We have attempted to carry out numerical calculations of themagnetic field dependence of the Hall coefficients using a classicalexpression; here we have neglected a quantum effect such as SdH oscillations.

Corresponding to the three frequencies

13

fiof the SdH oscillations

(Fig.13), we have used a simplified three-carrier model, in which twoelectron bands and one hole band are taken into account, with a carrier
concentration ni and carrier mobility ~i for the i-th band; i=l and 2 forelectron bands (hereafter denoted by e3- and e4-bands,

andrespectivE~ly)

i=3 for hole band (h3-band).
Then the Hall coefficient RH is given by
RH (H) = N ( H ) / (A ( H ) 2 + N ( H ) 2 f!2 ) ,

(8 )

with
3
N(H) =.~ nie~i2/(I+~i2f!2),

1=1

(9)

3

A(H)

.~ ni lel~i/(I+~i2f!2),

1=1

with the electronic charge e (e<O for electron and e>O for hole).

(10)

The

calculated RH-H curve for sample b4 is indicated by solid line in Fig. 15
with the best-fit values of nt =1.7xl0t8, n2= 2.8xl0t7, n3=6 .1x10 t 8 cm- 3 ,~t =4.2xl04,~2=1.7xl05,

experimental curve.

and ~3= 5.9x104 cm 2/Vs, in good agreement with theCorresponding to the observed carrier concentration

PH determined from the Hall coefficient at 2.0 T (PH=l/eRH) shown in Fig.
2, the evaluated hole concentration n3 of the hole h3-band has the higher
value compared with those of electrons (nt and n2 ), which indicates thatthe main contribution of carrier transport is due to conduction holes.
The conduction electrons of the e3- and e4-bands are also responsible forthe transport, since their evaluated electron mobilities ~t and ~2 arecomparatively high, even though their concentrations are lower than thehole one.

Thus one may conclude that there are at least two types ofelectron bands and one hole band contributing to dc transport in the CDW

14

state; furthermore we have found two types of hol e bands and two types ofelectron bands, as found by Sasaki et al. 9 )4. Band Scheme and Nesting Model

From the experimental results and discussions described above, weshall now propose a tentative band scheme for ~-Mo401 I with quasi -twodimensional layered structures.

In this material system, both electrons

and holes are degenerate and contribute to the various anisotropictransport phenomena.

Furthermore, these carrier systems undergo thenorrnal-to-CDW transitions through nestings of the Fermi surfaces, at which
the pressure effect is appreciable and the transport anisotropy isenhanced.
As shown schematically in Fig. 16(a), in the normal state (T>Tc l)electrons in the electron band (abbreviated bye-band) are filled up to
EFl e and holes in the hole band (h-band) up to EFth, just like asemimetal.

These carriers are mobile in each band having differ ent

effective masses and drift mobilities.
(Tc 2 <T<Tc t)

After the first CDW transition

due to nesting of each Fermi surface by an amount of 2kF (kF:

the Fermi wave vector), each band is split into two bands [Fig. 16(b)];for electrons, a "vanishing" or "nested" band (e\ -band) with a gap energy~Ie,which does not contribute to the conduction at absolute zero

(insulating), and a "remaining" band (e2-band) with the Fermi energy EF2 e«<EFl e ), which contribute to the conduction with a drift mobility andeffective mass that may be different from those of the original e-band.
Similarly the h-band for holes will be split by nesting jnto a vanishinghI -band with a gap ~Ih and a remaining h2-band with the hole Fermi energy
EF2h; the values of EFt hand EF2h, however, are not obtainable from the15

measurements done so far.

According to our analysis of the RH-/I curve(Fig. 15), the simplified remaining band scheme for n-M0401 I at the CDW
states (T<Te2) can be represented schematically as Fig. 16(c), which
consist of the h3-band for holes and the e3- and e4-bands for electrons.
Such changes in both electron and hole bands upon the CDW transitions
are responsible for the appearance of anomalies near Te l in the temperature dependence of various physical quantities, such as transport properties as shown in this work, together with the specific heats 3 ) andparamagnetic susceptibilities (which indicate the decrease in the densityof states at the Fermi energies, toO).4)

Moreover, the second CDW

transition occurs probably through nesting of the Fermi surface of the"h2-band" of holes, resulting in the splitting of the h2-band into
vanishing and remaining hole bands with the relevant band parameters,
which are inferred from the drastic change in the positive Hall co efficient (Fig. 2) and the sign reversal of the thermoelectric power
observed below Tc2 (Fig. 4).
On the basis of the above band model, we propose a tentative pictureof the variations of the Fermi surfaces of the electron and ho]e bands
associated with the normal-to-CDW transitions with appropriate nesting
vectors for n-M04 01 I , as shown schematically in Fig. 17 for by the fi rst
Brillouin zone in the b'c'-plane; only the nesting vector along the b'axis Qb=O.23b· is experimentally known. 4 )Here we assume, for simplicity,that the e-band lies at the zone center [shaded region] and the h-band at
the zone edges [open region], and that their nesting vectors are equal andpoint towards b'-axis; we denote the nesting vector by Qbl be]ow Tel andQb2

below Te2, as indicated by arrows.

Below the first CDW transition

temperature Tel, through an intraband nesting of the electron and/or holeFermi surface by Qbl (indicated by solid arrows) or an interhand nesting16

(broken arrows), each band splits into two bands; only the Fermi surfacesof the remaining bands are shown in Fig. 17.

The second CDW transition

takes place below Te2 by nesting the separat ed hole Fermi surfaces by anamount of Qb 2, resulting in further splitting into hole bands.

We should

note that the hole Fermi surfaces in the temperatur e range T e 2<T<Te l are
strongly anisotropic (see inset of Fig 1).

5. Conclusion

Present studies on the CDW related transport phenomena in the quasitwo-dimentional n-M0401 I can be summarized as follows:
1) The temperature dependences of the resistivity, Hall coefficient, ITal 1
mobility, and thermoelectric power of n-M04011 have shown that theseelectronic properties are strongly anisotropic in the be-plane,
indicating the anisotropic Fermi surfaces of the conduction carriers.
2) The Hall coefficient RH is positive over the entire temperature range
studied, while the thermoelectric power S is almost negative, except
at low temperatures.

These results indicate that the conduction

carriers in this material system are both "electrons" and "holes".
3) The effect of hydrostatic pressure on the electrical resistivity has
shown that the first CDW transition temperature Te l is increased withpressure, which is considered as due to enhanced electron-ph onon
interactions.

On the other hand, the second CDW transition tempera-ture Te2 is decreased by applied pressure, which indicates that thepressure suppresses the CDW nesting of the Fermi surfaces.
4) From the analysis of the observed p(P)-T curves, we have estimated the
CDW gap energies ~I (T) and ~2 (T).

The temperature dep endence of thesegap energies can be fitted to a universal curve, in good agreement

17with other experimental and theoretical results.
5) Below Tc2, we have found Shubnikov-de Haas oscillations in both themagnetoresistance and Hall voltage.

The fast Fourier transform

analysis of these oscillations gives the three main frequencies atambient pressure (f =4.5, 7.5, 16 T), which are also found to bepressure dependent, suggesting that the Fermi surfaces of electron
and/or holes are very much pressure sensitive.

The extremal crosssections of the Fermi surfaces are estimated to be about 0.05-0.15 %of the first Brillouin zone area.
6) Computer simulations of the magnetic field dependence of the Hall
coefficient have shown that the carrier systems can be represented bythree-carrier model consisting of two types of electron bands (withcarrier concentrations nt =1.7xl0tS, n2=2.8xl0 t7 cm- 3 , and carrier
mobilities ~I =4.2xl04,~2=1.7xl05

cm2/Vs), and one type of hole band

(n3=6.1 xl0 Is cm- 3 and ~3=5.9xl04 cm 2/Vs).
7) Based on these experimental data, we have proposed a possible nestingmodel and a band scheme of this unique material of quasi-twodimensional system.

In order to clarify such a picture, more detailed

experimental and theoretical works will be needed.

Acknowledgements

The author would like to express his sincere thanks to Professor
Masasi Inoue for helpful instruction and stimulating discussions during
the course of the present work.

He is also grateful to Associate

Professor Minoru Sasaki, Drs. Hiroshi Negishi and Mikio Koyano forfruitful discussions and useful advice.
his laboratory for their assistance.

18

He also thanks the all members ofReferences

1 ) A. Magneli, Acta Chern. Scand. 2, 861 (1948) .
2) L. Kihlborg, Acta Chern. Scand. 13, 954 (1959).
3) H. Guyot, C. Escribe-Filippini, G. Fourcaudot, K. Konate, and
C. Schlenker, J. Phys. C 16, L1227 (1983).
4) H. Guyot, C. Schlenker, J. P. Pouget, R. Ayroles, and C. Roucau,
J. Phys. C 18, 4427 (1985).
5) C. Schlenker, J. Dumas, C. Escribe-Filippini, H. Guyot, J. Marcus, andG. Fourcaudot, Philos. Mag. B 52, 643 (1985).
6) C. Schlenker ed., Low-Dimensional Electronic Properties of Molybdenum
Bronzes and Oxides (Kluwer Academic Pub., Dordrecht, Boston, Lonon,1989) p. 159.
7) M. Inoue, S. Ohara, S. Horisaka, M. Koyano, and H. Negishi,
phys. stat. sol. (b) 148,659 (1988).
8) S. Ohara, M. Koyano, H. Negishi, M. Sasaki, and M.lnoue, phys. stat.
sol. (b) 164, 243 (1991).
9) M. Sasaki, G. X. Tai, and M. Inoue, phys. stat. sol. (b) 162, 553(1990).
10) E. Canadell, M. H. Whangbo, C. Schlenker, and C. Escribe-Filippini,
J. Inorg . Chern. 28, 1466 (1989).

11) R. D. Barnard, Thermoelectricity in Metals and Alloys, (Taylor &Francis, London, 1972) P. 58.
12) N. Ogasawara, K. Nakamura, and S. Tanaka, Solid State Commun., 31,
873 (1979).
13) A. Briggs, P. Monceau, M. Nunez-Regueiro, J. Peyrard, M. Ribault, andJ. Richard, J. Phys. C 13, 2117 (1980).

1914) M. Ido, K. Tsutsumi, T. Sambongi, and N. Mori, Solid State Commun.,29, 399 (1979).

15) H. Fujishita, C. Murayama, N. Mori, and M. Sato, J. Phys. 2, 8751
(1990).
16) P. A. Lee, T. M. Rice, and P. W. Anderson, Phys. Rev. Lett.

~ll,

462

(1973).
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Solid State Commun., 51, 191 (1984).

20

Figure Captions

Fig. 1.

Temperature dependence of the electrical resistivity Pb and pc
along (a) b-axis (sample No. b1 with PbR (0)=80 pO cm; squares)and (b) c-axis (sample No. c1 with PeR (0)=140 pO cm; circles)of monoclinic T/-MOA 01 I.
Pc/Pb.

The inset shows the resistivi ty ratio

The arrows indicate the CDW transition temperatures Te l

and Te2.
Fig. 2.

Temperature dependence of the Hall coefficient RH at 2.0 T forthe samples shown in Fig. 1

Fig. 3.

Temperature dependence of the Hall mobilities ~H (=RH/p) for the
samples shown in Fig. 1.

Fig. 4.

Temperature dependence of the thermoelectric power S for
T/-MOAOI I(open circle: No. c2, open square: No. b2, solid

square: No. b3); the value of PR (0) for each sample is listed
in Table 1.
Fig. 5.

Temperature dependence of the electrical resistivity Pb forsample b4 [PbR (0)=90 pO cm] at ambient pressure (opencircles) and different pressures (solid circle: P=0.4, open
square: 0.8, solid square: 1.2 GPa); arrows indicate the CDW
transition transition temperatures Te I and Tc2.

Fig. 6.

Transition temperatures (a) Tel and (b) Tc2 plotted against
hydrostatic pressure P.

Fig. 7.

Temperature dependence of the best-fit values of gap energies,(a) .11 (T) and (b) .12 (T) in Eq. (3) at various pressures P shownin Fig. 6.

21

Fig. 8.

Nor mal i zed plot s for (a) .11 (T) I kBTel and (b) .12 (T) I kBTe 2 0f theexperimental data shown in Fig. 7 at various pressures as afunction of the reduced temperature TITel or TITc2.

The dashedcurve in Fig. 8(b) is the universal curve shown in Fig. 8(a).
Fig. 9 .

Normalized gap energies 0 (=.11 (T) Iks Tc 1, indicated by closed
circles or .12 (T)lkBTc2, indicated by open circles) plottedagainst reduced temperature t (=l-TIT e l or 1-TITe2 ") in logarithmic scales; for comparison, the normalized satellite
indicates IIIe of X-ray diffrations for n-M0401 1 (open square)4l
and(~bSe4bI(solid square)17l are also included.

The dashedcurve is the theoretical one according to the Landau theory
expressed by Eq.
Fig . 10.

(5).

Variation of the transverse magnetoresistance .1plpe for sample
b4 at 4.2 K with increasing (solid lines) and decreasing(dashed lines) magnetic field at constant pressures P; arrows
indicate the peaks of oscillations.

Fig. 11.

Variation of the Hall voltage ~ for sample b4 at 4.2 K withincreasing (solid lines) and decreasing (dashed lines) magnetic
field at P=O and 1.0 GPa; arrows indicate the peaks of oscilJations .

Fig . 12.

The oscillation component of the Hall voltage for sample b4
at 4.2 K and ambient pressure plotted against the reciprocalmagnetic field obtained by a successive averaging procedureusing Eqs.

Fig. 13.

(6)

and

(7).

The fast Fourier transformed components of the Shubnjkov-de
Haas oscillations in the Hall voltages at various pressures P;
arrows indicate the most probable frequencies

22

fi •

Fig. 14.

Fundamental oscillation frequenciesfi

vs. applied pressure p,

obtained from the analysis of the oscillatory components of the~p/PB-H

Fig. 15.

(solid symbols) and VH-H (open symbols) curves at 4.2 K.

Magnetic field dependence of the Hall coefficient RH (H) for
sample b4 at 4.2 K.

The solid line indicates thetheoretical one calculated using Eqs. (8)-(10) with thebest-fit parameters described in the text.

The arrows show the

maxima due to quantum oscillations.
Fig. 16.

Schematic electron and hole bands for (a) normal state (T>Tc l),(b) the first CDW state (Tc2<T<T c t), and (c) the second CDW
state (T<Tc2) (see text).

Fig. 17.

Schematic variation of the Fermi surfaces of electron band(shaded region) and hole band (open region) due to CDWtransitions for n-Mo401 I with the nesting vectors along the b'axis, as indicated by arrows (see text).

23

Table 1 .

Sample characteristics; PbR (0) resistivity along the b-axis, P e R (0)that along the c-axis of ~-M04011 crystals at ambient pressure androom temperature, EFtS and EF2 s electron Fermi energies (see text).

Sample No.

Pc R (0)EF 1 S(/10 cm)

(eV)

(eV)

b1

80

b2

160

4.5

0.90

b3

110

2.6

0.32

b4

90

4.1

0.18

c1

140

c2

190

(a )
~

E

u

C

40

~

""-"

Tc2

~

...0

~

,

O~--~----~--~----~---~

0

50

100

150

T (K)
Fig _

1

2C)0

250

T ( K)
100 5030
20
15100~~~~~~--~----~-----~

10

1

Tc2
~

u

"E

o

(Y)

u

"--"'"

~0

-2
10

:r:
0::

-4

10 0~~--~2--~~4--~~6--~---8~~
100/T (K- 1 )

£.

~L

g; _

2

Tc2

~

100~~~~~~~~~-~~

10 0

10 1

10 2
T (K)

Fig _

3

10 3

· 0

~

-5

~

"=L

>

~

If)-10-15-20~~~--~~~-~

o

100

200

T (K)

FJg_4-

300 ·

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I

I

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1

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1

T

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0)

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0
0

-

0

- 1O

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0

•
0

0

-

- '-!
ro-

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.0

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.

• •
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-

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.

•

O.
•
0

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r-

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rY

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0

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0
0

- r-

0

'~:<3
• [J . 0
• [J

-

«J

0
- CO

it1'~
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.&
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.°io

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.

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.CD

a«J

a~

'00 ~ 0.

o

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•

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[J

.o~~.

N
U

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~~

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0

LD

I

0

~

I

I

0
(Y)

I

I

0

N

(WJU rf ) qd

- 0'-!

I

I

0
or-

- 0N
0

~

~
'-'"

bD
1M

f-

~

116 ~------~------~--·----~

(a )

114
112
~

110

106
104~------~------~------~

(b) .

34

32
~
N

30

U

I-

28

26
24~------~------~------~

o

0.5

1.0
P (GPa)

Fig _

6

1.5

25------~----~------~----~-----~(a)........-..

20

><lJ

E 15

'-'"

~10
<J
5

6~------~-------~---------.---------.

(b)
o
o

•

o
•

0

o

•

•

••

o

•

o

•

o

•

o
o

••

o

o

o
•

0

•
o 0

0

•

OL-------~------~~----~

15

20

25
T (K)

30

35

o•

N
U

COr-

d"

Ir--

to

lJ1 8 >1 I( 1

~V

0

0

00
I

bn
1M

~

0

o;¢~

•

~

1

1

o

102~~~~~~~~~~-~162

1 62. 10 1
t

Fig_

9

1

10

1.0
5

4

2
H (T)
Fig.

10

6

1OOOI-r----r-----r--~---.----P (GPa) ~

750

>

~

500

I

>

250

4

H(T)

Fig.

11

6

~

____~__~~___________ o

•

co•

o

<.0

•

~

o .-I

I-

~

M

"'-'"

~

0

•

N

o•

~----~----~----~----~o
N
N
~

o

I

:r:

"

.--

bD
1M

~

P (GPa)

o
0.4

.

~

::J

,

m

'--'

0.5

<lJ

'"0
::J

eof-J

-0.

0.7

E

«

0.8

1.0

1.2

o

10

20

30

40

Frequency (T )
Fig_

13

- - - - -- -25------~----~-------

20

I

0'
,

o

I

I

I

I
I

,,

"

I

I

,,

.,
,,

.

p.'~

,

Jj
/

~'

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5

0.5

1.0
P (GPa)

Fig_

14

1.5

2.0 r----.----

1.5

u
"-

(V')

E

u 10
""'-'"
.
I

a:

0.5

.o01----L--;-2-~--L-L
4

H(T)
F 1
- 9-

15

6

e-band( a)h-band
( b)

(c)

I-

N
J-U

:4<
U

*..0

1) M. Inoue, S. Ohara, S. Horisaka, M. Koyano, and H. Negishi,
Transport Properties of Quasi-Two-Dimentional M0401 I Crystals,
phys. stat. sol. (b) 148 (1988) 659.
2) S. 5hara, M. Koyano, H. Negishi, M. Sasaki, and M. Inoue,
Effect of Pressure on the Charge Density Wave Transitions in n-M0401 I
Crystal,phys. stat. sol. (b) 164 (1991) 243.

1) M. Inoue, S. Ohara, M. Marushita, M. Koyano, H. Negishi, and ~1. Sasaki,
Charge Density Wave Instabilities in Orthorhombic y-M0401 I ,Jpn. J. Appl. Phys. 26 (1987) Suppl. 26-3, p. 629.

2) M. Koyano, S. Ohara, H. Negishi, M. Sasaki, M. Inoue, M. Nomura, andH. Fujiwara,
Effect of Pressure on Electrical Resistivity and Crystal Structure ofQuas i -Two-Dimentional M04 01 t ,phys. s tat. sol. (b) 147 (1988) 559.

3) H. Negishi, S. Ohara, M. Koyano, M. Inoue, T. Sakakibara, and T. Goto,
Anisotropic Spin-Glass and Cluster-Glass of Layered Fe xTiS2 Crystals,
J. Phys. Soc. Jpn. 57 (1988) 4083.
4) H. Negishi, S. Ohara, and M. Inoue,
Effect of Pressure on Lattice Parameters of Intercalation Compounds
MxTiS2 (M=Fe and Ni),phys. stat. sol. (b) 151 (1989) 441.

5) M. Koyano, S. Ohara, S. Ilorisaka, H. Negishi, M. Inoue, S. Takeyama,
and N. Miura,
Charge-Density-Wave Related Quantum Transport in Monoclinic n-M0401 1
Crystal,Solid State Commun. 71 (1989) 317.

6) H. Negishi, K. Sadahiro, S. Ohara, M. Koyano, M. Sasaki, and M. Inoue,
Spin-Glass Behavior in Itinerant Magnetic Material of Fe xTiS2 ,J. Magn. Magn. Mat. 90 & 91 (1990) 345.
7) H. Negishi, S. Ohara, Y. Takata, T. Yokoyama, M. Taniguchi, and
M. Inoue,
EXAFS Study of Local Structures in Intercalation Compounds MxTiS2(M=Mn, Fe, Co, Ni),
Proc. 6th International Symposium on Intercalation Compounds,
May 27-31, 1991, Orleans, France (in press).