Solid State Communications, Vo1.5O,N0.5, pp.405-408, 1984. Printed in Great Britain.

0038-1098/84 $3.00 + .OO Pergamon Press Ltd.

COMMENT ON THE HALL EFFECT IN QUASI-ONE-DIMENSIONAL METAL NbSeg

E.N.Dolgov

L.D.Landau Institute for Theoretical Physics, 117940, Koaygin Str. 2,

Yoacow, U.B.S.R.

(Received 20 February 1984 by V.M.Agranovich)

It is shown in the framework of the model with rusting

quasi-one-dimensional Fermi surfaces that the sliding FrGh-

lioh mode contributes to the Ball voltage and near the tran-

aition temperature may compensate a large .anomaly in the

Hall con&ant. Applicability of the rormulated model to the

description of real NbSe3 ie distxxssed.

At present the properties of the

EbSeg transition metal trichalcogenide

are far from understanding. Its band

structure is still unknown. The nune-

rical calculationa of the band struct-

ure do not provide sufficient informa-

tion (see' and References therein). A

simple quasi-one-dimensional model

"pockets" which have the characteristic

width in the longitudinal direction of

the Brillouin zone tl/Z$r 4 pF . The-

8e "pockets" are the result of neeting

of large almost flat Fermi surfaces (FS)

at low temperaturea. The routine gas

formula (RR(O) N ihee) gives an evi-

dent estimate:

(QlD) has previotaaly been used in ' This simple estimate should be

for describing the peculiarities of elucidated. Due to electroneutrality

the behaviour of the resistance at the the total number of electrona equals

critical temperature. In this way the the total number of holes. The result

well known experimental result --"emea- could lead to a considerable compenea-

ring out" of the resistance anomalies

near the transition by the eliding CDG-

tion of the Hall constant RR(O) for

some simple energy spectra. One can

wa8 reproduced. In this paper I apply hardly expect to obtain such a compen-

the same model for studying the eingu- eation for NbSe3 due to ite complicat-

laritiee of the Hall constant near the ed strpcture. In other words, contribu-

transition temperature. Below I also tions to all the kinetic coefficients

diacuae whether this simple model can coning from the carriers of both aigna

be applied for a description of real are expected to be comparable but not

NbSeg. identical in magnitude.

It should be noted that the large

magnitude 0r RR(O) at low temperatures4

is a natural result of the mode12. Thie

increase is due to formation of emall

I start the analyaie with the aimp-

le expressions for conductivity and the

Hall constant in QlD conductors, which

result from the usual kinetic equation:

406 THE HALL EFFECT IN QUASI-ONE-DIMENSIONAL METAL NbSe 3

Vol. 50, No. 5

(Here n N 102'CUl'3 is given by ete- transition is of a well-defined 3D cha-

chiometry). These formulae make it pos- raeter (see References in '1. My results

sible to eetimate the orders of magni- should be applied, provided

tudes for the high-temperature phase >> $&

IT,- T\/T~

a8 well. In the phase, where the atruc- 9 which ~6118 A .f/&+,.

After tedious calculation8 I get:

tural transition opens a gap in the el-

ectron speotrum, ttt*rm(EFld). There-

fore, at low temperatures:

Near the transition temperature the

physical estimate is more complicated.

In fact, there are no "pocket@, ainae

the "gap" in the electron spectrum is

lees than the temperature: Tp 7) d .

In what follows I u8e the physical as-

sumptions of the model 2 , and, aa befo-

re, I apply the method of analytic oon-

tinuation for calculating the transport

characteristics. The Hall current is

the quadratic in the external field,

i.e., it is a reeponse to the electric

and magnetic fields. Without going in-

to detail, I shall briefly describe the

results.

Aa usual, the structural instabili-

ty is ascribed to the "nesting" effect,

i.e. to an approximate superimposing

of QlD FS, which results in the well

known form of the electron spectrum

in the presence of lattice deformation

( +1 N q (A,' 5 see below) :

According to Ref. ' , soft mode

(Kahn anomaly or the phonon "softening ?I

may provide a large additional relaxa-

tion decreaeing conductivity of QlD con-

ductors. This viewpoint has been rec?n-

tly supported in ' for TaS3. The absen-

ce of diffusive 1D precursor effects in

X-ray scattering study proves that the

I wed d> f/Te,p/, l In e+(5) +O - = - 2 e viEte,,,,k , y = & for a ccnwlete- ly free CDW; the angular bracket8 denote averaging of the correapondlng expres-

sions over one side of the FS:

Thus, the anomaly in the Hall

tant is large, aa compared to the

aly in the resistance. One has:

COW-

anotll-

(6)

As has already been mentioned, the lar-

ge coefficient (fF/TpJ may be conaide-

rably compensated by a small value in

figure brackets for the special form

of I. For instance, this factor

equals xero in the tight binding model.

I a88ume that this compensation ie real-

ly important for NbSe3, since the expe-

rimental anomalies in the Ball con&an ?

are less than that expected from (61, These anomalies could be aleo small for

a natiow electron band (Le., if EF

is small; see below).

It follows from (5) that the motion of the mode doea create the Hall volta-

ge. Thie voltage compensates completely

the Hall contribution of normal carri-

ers for a depinned Fr&lich mode. This

result is somehow unexpected, since in

the experiments the Hall voltage ia

not sensitive to the arising nonlinear

regime lo, though it should be noted

that theee experiment@ were performed

at the temperatures much differing

from the transition temperatures.

Vol. 50, No. 5 THE HALL EFFECT IN QUASI-ONE-DIMENSIONAL METAL NbSej

However, I believe that this res-

ult ie correct rrom the physical point of view. Indeed, at T = 0 there are no excited no-1 carriers, and then

407

QlD bands. An 8nalysi8 of the Shubni- kov- de Gaas oscillations does not con-

tradict these estimates (an anisotropy

is about 1/7)13. The estimate for the

?!b ' can be diminished by assuming

that the effective mass m* for QlD

(niobium) bands is sufficiently large

<map 6~ for d-electrons of nio-

the charge connected with the CDW ia rixed. The motion or CDW in this case is Galilei-invariant and 0r course does not produce the Hall voltage:

j&L P (2TP’

(7)

However, at rinite T a part of elec-

trons is excited and in the relaxation proceeses Qransr0m them into a "con-

densate" and vice versa. Therefore,

the charge cloud connected width the

CDW depends on the fact whether CDW

moves or not. It seems to me that the

errect is to be experimentally obser-

ved. The preliminary data for TaS3 11

support the Validity of these state-

ments. So, the "smearing out" of the

anomaly at T - T& T is caused by

the change or'the charge bounded to

the CDW.

The absen;; of the Hall voltage in

experiments can also be explained

by the fact that at these temperatures

the number of norm81 carrfers is sm8lL

This means that the "pocketan have al-

ready been rormed at the temperatures

corresponding to the resistance maxima

(125 K for Tpi o 145 K and 47 K for

Tp2= 59 K). It would be desirable to

carry out experiments closer to the

transition temperatures in order to

see the CDW contribution to the Hall

voltage.

Other problems connected with the

NbSe3 band structure should also be

discussed. One of the meet serious

difficulties for the Jnterpretation

in terms of the QlD approach is the

low anisotropy of conductivity ('b/6,).

A common estimate for the transverse

P l/10 - l/20 IL. Such a value is not

sufficient for an adequate picture of

bium)g.Measuremsnts of resistsnce

point out in the same direction. Taking

filv 102'cuJ -3 for the number of carri-

ers, and p IV 10-40~*cm for the resis-

tance near T,)f= 145 K I have

-l/10,

-I-

iIre, pk = 2 = j6h ,&.

l set These valuea are comp;tible

with the set of inequalities : 2 (i;r,- yu Tp 5, fi* A h ‘he& .

So, the main problem consists in

the low anisotropy of conductivity.

Let us investigate the alternative pic-

ture of coexisting QlD and 31, carri-

ers proposed in 1 . Thus, if we assume

that there are some small 3D *'pockets"

in addition to large QlD PS, the lar-

ge transverse conductivity could be ae-

cribed to these "pockets". However, at

low temperatures the arbitrarily pla-

ced amall "pocket&* cannot afford the

umklapp processes and this mskes dif-

ficulty with conductivity at low tempe-

ratures. Meanwhile, interpretation of

the data on the Hall effect can be ra-

ther complicated even at high tempera-

tures. Particularly, dominating role

of 31, 'tpocketsV' in the transverse con-

ductivity can "screen" the contributi-

on of the sliding CDW into the Hall

voltage.

The anomaly in the transverse con-

ductivizy calculated under assumption

of Ref. seeme to be zero. In case the

dependence of the relaxation parameter

I&, p h on the transverse momentum is taken into account, and different

tines of relaxation for "backward" and

"forward" scattering are introduced,

the singularity becomes finite. Large

anomalies in the quantity (6~/6,) '*

408 THE HALL EFFECT IN QUASI-ONE-DIMENSIONAL METAL NbSe3 Vol. 50, No. 5

show that the number of phonon modes "smeared out" to the values comparable

contributed to the transveree conducti- with the anomalies of conductivity.

vitg ie likely to be larger than that Beaidea, we neglect the effect of the

contributed to the longitudinal conduc- phonon drag (see 6,7 >. This phenomenon

tivity, as could have been expected. may be violated by some specific umk- It should be noted that the introduc- lapp proce88ee, since the wave vector8 tion of the above dependences (and of of instability are close to the commen-

different phonon modes) are actually aurability 1:4 , or to electron-elec-

the introduction of the parameters of tron interactions.

three-dimenaionality, i.e., our auppo-

sitions are quite self-consistent. Acknowledgements - I would like to

It should be elucidated in conclu- *hank Yu.I.Latyshev and F.Ya.Nad' for

sion that Eq.(5) ia written in the the information on theti papers, not

main (fF/Tp) -parameter approximati- yet published, and for the discussion.

on. Since actually the anomalies in I am also grateful to S.N.Artemenko

the Hall constant are not large,then, and A.N.Kruglov for the information

while the CDW is sliding, they can be 14 on their paper .

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