Non-linear dynamics of charge-density-wave in orthorombic TaS3 at microwaves

(1)

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Non-linear dynamics of charge-density-wave in orthorombic TaS3 at microwaves

I. Vendik, V. Pchelkin, A. Shchepak

To cite this version:

I. Vendik, V. Pchelkin, A. Shchepak. Non-linear dynamics of charge-density-wave in orthorombic TaS3 at microwaves. Journal de Physique I, EDP Sciences, 1992, 2 (7), pp.1497-1505. �10.1051/jp1:1992218�.

�jpa-00246635�

(2)

Classification

Physics

Abstracts

72.15N 71.45L

Non-linear dynamics of charge-density-wave in orthorombic

TaS~ at microwaves

I. B.

Vendik,

V. M. Pchelkin and A. V.

Shchepak

Electrical

Engineering

Institute, 5, Prof.

Popov

street, St.

Petersburg,

197376, Russia

(Received 30 January 1992,

accepted

in

final form

9 March 1992)

Abstract. Non-linear dc and microwave

conductivity

due to collective transport ^of

charge- density-wave

in

TaS3

_was

experimentally investigated

at T

=

78-215 K. The non-linear dc field

dependence

of _a differential

conductivity

dl/dV exhibits _a threshold field

E~j sharply

defined in the temperature range of 140-215 K. As the temperature ^decreases

beyond

140K the field

E~j disappears,

and the second threshold field

E~»E~i originates.

The two fields _are temperature

dependent

and show

decreasing

under _a microwave radiation. A non-linear response V~t to the microwave radiation _was observed at T

= 78-215 K in _a

mixing experiment

(detuned

case, D

= w1 w2 ^* 0). The dc field

dependencies

of the non-linear _response _V~t reveal _no

signs

of the threshold field

singularities.

The

experimental

results have been

satisfactorily

described

by

a classical model of _an overdamped oscillator by

introducing

_an

empirical

distribution function for the threshold field and

by averaging

_V~t _over

E~.

I. Introduction.

The collective transport

phenomena

associated with the

dynamics

of

charge-density-wave (CDW)

in

quasi-one-dimensional

conductors have been of great ^interest ^for many years. The

transport phenomena

_are well established

by

^various

experimental

results. The field and

frequency dependencies

of

conductivity,

the coherent current

oscillations,

the

modelocking phenomena, hysteresis

and

metastability

etc. _are due to the collective transport ^of ^CDW. ^As

follows from the

experimental frequency dependence

of CDW

conductivity [1-3],

the CDW

can be considered as an oscillation system ^with characteristic

frequencies

ⁱⁿ microwave and millimeter _wave _ranges. In

general,

this system ^is

non-linear,

which arises from _a mode

locking experiment

at microwaves

[4].

The non-linear response ^to ^the ^microwave radiation has been observed in _a harmonic

mixing experiment

where _no dc bias

voltage

was used

[5, 6].

The

experimental

results have been accounted for

by

various

phenomenological

models. The most

preferable

is the

Fukuyama-Lee-Rice (FLR) model,

which has been worked out for

explaining

the

frequency dependence

of CDW

conductivity «(w ) [7, 8]

and the harmonic

mixing experiments

_as well

[9, 10].

The novel information can be obtained from

experimental investigations

of non-linear response of CDW to the microwave radiation

superimposed

on

the

steady

electrical field. In this _case the response ^involves ^both ^the field and

frequency

dependencies

of

conductivity.

(3)

1498 JOURNAL DE

PHYSIQUE

I N° 7

In this paper we

report

^the

investigation

results of the non-linear response in orthorombic

TaS3

in the CDW state to the weak microwave

radiation,

_as _a function of dc bias

voltage

under microwave

pumping.

This

experiment corresponds

to the direct

mixing

of two

microwave

signals

with

sufficiently

different

amplitudes

_:

Vi

_m V

~ and V

~ «

V~.

The detuned case, D

= wj w~ #

0,

_was used. The

output altemating voltage

with

frequency

D _was

detected _as the non-linear bias

voltage dependencies

of non-linear response are observed and discussed.

2.

Experiment.

2.I EXPERIMENTAL TECHNIQUE. -All measurements were

performed

_on orthorombic

TaS3 single crystals

ⁱⁿ ^the two-port

configuration

^with

typical

distances between contacts 20-

40~m

and cross-sections in the range of

2-40~m2.

The parameters ^of

TaS~ samples

measured,

_are tabulated

(Tab. I).

The

sample

_was included in the microwave

integrated

circuit. It _was mounted _on the

well-polished

alumina substrate in the gap of _a

gold microstrip

line. A thin In film _was

deposited

on the

crystal

and _on the

microstrip

contact surfaces

(Fig.

I

using

_an

evaporating

and mask

technique.

The

high quality

electrical contacts

yielded

the ohmic resistance of 1-2 fl. The _same

microstrip input

was used for _two microwave

signals

of

frequencies

_wj and _w~.

Owing

_to the

high

value of these

frequencies (w1/2

ar =

2

GHz)

the difference

frequency

of the

output

response

signal

n

= wi- w~ ^was also

big enough

(n/2

_ar =10

MHz)

to indicate the short time response, while any slow processes were

eliminated. The

sample mounting

allowed _us _to _use the _same measurements

technique

to indicate either the differential

conductivity

or the non-linear response to the microwave radiation _as _a function of the bias

voltage.

The bias

voltage

_was _swept

linearly

with time. The output

signal

_was recorded _on _an X-Y-recorder. In the _case of the differential

conductivity

measurements the

output voltage

of a selective

amplifier

_was recorded. The non-linear

response ^to the microwaves was taken from _a

spectrum analyzer

to the recorder. The dc

measurements have been conducted

using

th

epotential

_source with _a low intemal resistance.

2,2 EXPERIMENTAL RESULTS.- The

experimental

field

dependencies

of the differential

conductivity

of

TaS~ sample (N24)

at various temperatures are shown in

figure

2. The _non- linear characteristics with _a well defined threshold field

E~i

have been observed below the

Peierls transition

temperature (Tp=215 +220K),

to mI20K. As _one _can _see in the

figure I,

the threshold

gradually

smoothes off _as the

temperature

decreases, and _at the T<110K

disappears.

^On the other

hand, beginning

with the

temperature Tm140K,

_an

Table I. -Parameters

of

the

experimental samples

_:

f,

_t, S and

RR~

are the

length,

the

thickness,

the cross-section and the _room temperature

respectively.

N

f

_t _s

RAT

~Lm ~Lm ~Lm2 fl

19 42 8 60

24 42 2 25 16

30 20 2 28 8.5

38 30 2 14 31

45 28 3 110

78 45 3 38 12

(4)

3 4 5

j

2 3 4 5

6

j ...

"

,, ,, ', ,' » ,,

" ,, ', " " " "

Fig.

1. The

sample mounting

scheme _:

TaS~ crystal

(1),

organic compound

(2), thin In film (3),

microstrip

(4), substrate (5),

ground plate

of

microstrip configuration

(6).

dt

W

T

= 170K

dt

W

its

orb. units

0 5 V~

(mV)

2

T

= 170

140

50 0 50 100 150

Eo

(V/cm)

Fig.

2. The differential

conductivity

dl/dV of the

sample

N38 _versus electric field at various temperatures. ^The ^inset ^shows ^the ^initial part of

diagram

in details.

(5)

1500 JOURNAL DE PHYSIQUE I N° 7

En (V/cm)

iso

o

°

E~

100

(V/cm)

T

= 78 K

o 400

~

~ /

° o

300 ~%

~~

° ~ ° °

° 200

~

%~

/~

~

100 ^~°

0

50 100 150 200 T(K) 0,1 0.2 0.3 0.4 1.0 _t~ ' (~Lm)

a) b)

Fig.

3.- The temperature

dependence

(a) of the second threshold field

En (sample

N30) the

dependence

of the field

E~

_on the inverse

sample

thickness (b).

other field

E~ originates,

where the

conductivity

increases

sharply.

This field _was called the second threshold field. The field

E~~

^is temperature

dependent (Fig. 3a)

and exhibits the

dependence

on the

sample

thickness

(Fig. 3b).

Under the microwave radiation the field

dependence

of differential

conductivity changes,

and the threshold field decreases

(Figs. 4a, 6a).

No evidence of

modelocking

_was observed up ^to the

amplitude

of microwave pump

signal Vi

=

(10-20) V~.

The non-linear response in the

mixing experiment (Fig. 4b)

reveals _no distinctive

signs

of threshold field. The response V

n

depends

_on the bias

voltage exhibiting

_a

broad maximum. One _can _see _a strong

dependence

of the

amplitude

on the small microwave

signal V~

«

V~.

The non-linear response

disappears

at

Vo

m 0.3

V,

where

peculiarities

on the

dI/dV

characteristics become remarkable

(Fig. 4a).

In

figure

5 the _same

dependencies

_as in the

figure

4b _are shown for another

sample (N19)

at a

lightly

lower

temperature.

The characteristics of the

TaS3 sample (N78)

at the T

= 78 K _are shown in

figure

6. If the second threshold field

E~

is

exceeded,

the differential

conductivity

increases

sharply.

The value of

E~

is

strongly dependent

_on the microwave pump

amplitude.

The relative

change

of the threshold field

AE~/E~~

₌

(E~(O ) E~~(Vi ))/E~(O

is

proportional

to the

amplitude Vi squared (the

inset in

Fig. 6a).

The non-linear response of the

sample

N78 in the

mixing

experiment

is shown in

figure

5b. There is _no maximum _on the _curves in contrast to the results at

higher

temperature

(Figs. 4b, 5).

The response

Vn

increases

non-linearly

as the bias

voltage

rises. The

dependence

exhibits _a

sporadic

nature when the bias

voltage

reaches the value

Vo

m 0.8 V. This

voltage sufficiently

exceeds the second threshold

voltage V~

^for this

sample

in the presence of the microwave radiation.

3. Discussion.

As follows from the

experimental results,

the ID-conductor in the CDW state,

being

under extemal

driving forces,

exhibits

varying

behaviour _as the temperature ^decreases. ^Two different threshold fields have been observed in contrast to the

[I1, 12].

The

results obtained arise from the

experiment

conditions. The

samples

of

TaS~

in these

experiments

_were rather short and thin

(see

Tab.

I),

_so that size effects should be taken into

(6)

dI

W

d/

~ ₌ 128 K

$

~ ~ 14 v

~b units

4 ~ _~

Vi

=0.14

" °

o 5 lo

Vo

(mV)

0.1 0 0.1 0.2 0.3 0.4 Vo (V)

a)

Vn

(~V) ~"

0 ~

; 2

m

4.8

mV

2 ^3.2

~ . l.0

1.0 ⁵

- 0 0,1 0.2 0.3

b)

Fig.

4. The differential

conductivity

dI/dV (a) and non-linear response ^to the microwave radiation

(b) _versus the bias

voltage (sample

N24). The microwave pump

amplitude Vi

= 0.14 V. Solid lines

correspond

to the

experiment,

dashed lines

correspond

to the calculation

by

fomlula (7) with

fitting

parameters tabulated (Tab. II). The insets show the initial part ^of

diagram

in details.

account

[13, 14].

On the other hand the CDW in

TaS~

is

nearly

commensurate and _can be

deformed in _a

high

electric

field,

_so the

pinning

_on the initial lattice should be considered. It

was assumed that the first threshold field _was caused

by

the

impurity pinning,

and the second

one was determined

by

the

predominant pinning

of the commensurate CDW _on the lattice.

The

competition

between the two kinds of the CDW

pinning produces

the

smearing

on the threshold field

(T

=

115-140 K in

Fig. 2).

The contribution of the surface

pinning

of CDW is also

appreciable.

This is demonstrated

by

^the

figure 3a,

where the size effect of the second

threshold field is

presented.

^The

dependence

of

E~~

_on the

sample

thickness is

satisfactorily approximated

as

E~~

_~ t~ ^, that is in agreement ^with ^the ^results ^observed ⁱⁿ

Nbse~ [13].

It is

yet impossible

to

suggest,

^with any assurance that the dc characteristics observed _are due

only

to collective transport ^of ^CDW. ^One can assume the Joule

heating

is

responsible

for the

conductivity increasing

_as well. On the other hand the observation of the

high-frequency

(D/2

_ar

=

10 MHz

)

non-linear response V

a to the microwave radiation is unaffected

by

^Joule

(7)

V~

(~V) ^T = 134 K

80

,

V2

" 17 mV

,

' 13

- ,

'

8.5

/"

^~

~

'

~ .2

Fig.

5. The

experimental

non-linear response to the microwave radiation of the

sample

N19 (solid lines). The microwave pump

amplitude

Vi ₌ 0.2 V. Dashed lines

correspond

to the calculation

by

the

fomlula (7) with

fitting

parameters ^tabulated (Tab. II).

heating.

It _seems safe _to

identify

the bias

voltage dependence

of V

a as a manifestation of

only

the CDW

dynamics.

Let _us discuss the characteristics

Va(Vo) (Figs. 4b, 5, 6b).

The main feature of the

dependence

of non-linear response

Vn

on the bias

voltage

is the absence of _a threshold field.

It is worth

noting

that the

sharply

defined threshold field _on dc characteristics does _not eliminate under the microwave

radiation,

but

changes

^its ^value

(Figs. 4a, 6a).

In order to account for the

experimental

data at

microwaves,

the

following

model _can be devised the CDW is considered _as _a many

panicle

classical system with the statistical nature

[10].

It is believed that the ID-conductor consists of _a number of

weakly-connected non-interacting

chains with CDW, which _are

distinguished by

threshold field

[15].

If the chain consists of

phase

coherent

segments separated

from each other

by impurities

or

incommensuarities,

each

segment

on every chain in the

crystal

cannot be

depinned individually.

But for

weakly

connected chains _a

percolation

_process could

provide

the CDW _movement at the effective field

E~.

So _one _can observe the threshold field _on the dc characteristics. At the _same time the

non-linear response ^to the microwave radiation

involving

the

displacement

current, features the average reaction _to the extemal fields of all pans ^of ^different ^chains ⁱⁿ ^the

sample.

In this

case the threshold field is smeared _out and _can not be revealed.

4. Model

approach.

Let _us consider the CDW _as a

single overdamped

^oscillator ^and use the

equation

^of CDW

motion in the

simplest

classical form

[16].

The

expression

^for ^the ^threshold ^field

E~(V)

ⁱⁿ the presence ^of ^the ^microwave ^radiation was

given

in

[17]

:

E~(V~)

=

E~/(I

₊ _a

), (1)

(8)

d/

Mm

$ _E~ _sample

arb. units

~ ~~

~

l.0 _u 45 T=78K

~/

/

~/~

~ -. »-

2 0 1.0 Vi (V)

Vi = 0.67 V 0.46 ^0.2 ^0.

0 0.25 0.50 0.75 1.00 Vo (V)

a)

Vn V~ ₌ ^o.047 ^V

(mV)

0.2

0.1

_ /

-- 0.020

0 _--

b)

Fig.

6. The differential

conductivity

dI/dV

(a)

under the microwave pump radiation and non-linear response to the microwave radiation (b) _versus the bias

voltage

at the T

= 78 K

(sample N78).

The microwave pump

amplitude (Fig.

5b)

Vi

₌ 0.9 V. Solid lines

correspond

to the

experiment,

dashed lines

correspond

to the calculation

by

the fomlula

(7)

with

fitting

parameters ^tabulated (Tab. U). The inset of

figure

6a shows the

dependence

^of relative

change

of the second threshold field

AE~/E~

_on the

microwave pump

amplitude squared

the dashed lines _are

guides

to the eye.

where

v 2

a "

(~)

(~) f(W),

2

V~

f(W )

=

((W/Wo)~ ^li

+

(wT)-2j)~ ~, (3)

V~

is the threshold

voltage.

wo and _Tare the

pinning frequency

and

damping

_parameter of CDW model

respectively.

(9)

In the _case of _a _«

I, AE~

V), what is in accordance with the

dependences

in the inset of

figure

6a.

The

explicit expression

for _a _current response in the

mixing experiment

under conditions

Vi

_<

V~

and

V~

«

V~

_was derived in

[17].

^Let us introduce the distribution function of the threshold field in the form

[15]

_:

P

(ET )

=

(E

^*

)~

_{x~ exp}

(-

x

)

,

(4)

where E* and _n _are distribution

parameters,

x ₌

E~/E*.

After

averaging

over

E~

with the distribution function

(4)

the _current response looks _as

la ~lii~f~")l'~ ll~i~ ^xl

,

~5)

where V*

=

E*

f,

f is the

sample length,

_a

=

V~V*, R~

is the dc resistance of the

sample

caused

by depinned CDW,

N~

=

j~ ^x~exp(- ^x)

^dx.

⁽⁶⁾

o

If _a load resistance

R~

is connected to the output ^terminals ^of ^the

ID-samples,

the

voltage

response can be found _as

~~~~~~l~na~~~~

^~~~

Here _a~

=

R[/R~

;

R[

= R

~

R~/(R~

₊

R~ ),

and

R~

is the resistance due to normal carriers.

The calculation results _are shown in

figures 4b,

5 and 6b with dashed lines. The

fitting

model parameters are n, V* and

f(w). According

to the

experimental

condition

wT

ml,

and instead of

(3), f(w)

=

(w/w~~)

^with _w~~

=

w(T.

The non-linear

dynamic

response ⁱⁿ

figure

4 is well described

by

formula

(7)

^with the distribution

parameter

n ₌ 2. But for the

sample

N24

(Fig. 3b)

the

good

coincidence with the _same _n

= 2 takes

place only

for

Vow

0.2 V. The

discrepancy

at

Vo~0.2

V is

suggested being

due _to the

sample heating.

One _can _assume that the CDW in this

sample disappears owing

to temperature

increasing,

when the bias

voltage

reaches the value

Vo

_m 0.3 V

(Fig. 4).

The

overheating

is believed to appear as a consequence of the

sample imperfections.

In the _case of the

potential

source used in the

experiment,

the

avalanchi-type

temperature

increasing

_can take

place,

the

imperfections being staning points

of the process.

The non-linear

dynamic

_response to the microwave radiation at T

= 78 K

(Fig. 6b)

_can be described

by

the _same

expression (7).

But the distribution parameter n ₌ 3 _was used. The

change

of parameter n and

respectively

^the

change

^of distribution function with the temperature

decreasing

was

thought

to result from the

change

of the dominant kind of the CDW

pinning. Taking

into account the coexistence of different

types

^of

pinning,

_we assumed that the

impurity pinning

of CDW _was

replaced by

the

commensurability pinning

_as the

predominant

_one. At the _same time the

pinning

on the surface and the _contact

pinning

of CDW remain invariable.

The model parameters ^of ^the

samples investigated

are collected in table II. It is

notewonhy

that the

high

value of

fitting parameter

_w~~ ^for ^all

experimental

data is in _a

good

_agreement

with the two-mode model of CDW

dynamics [19],

(10)

Table II. The model parameters

of

the

samples

_: V * and _n _are the distribution parameters, a~ is the dimensionless load

resistance,

_w~~ is the _crossover

Jkequency

_; T is the

sample

temperature,

V~

is the threshold bias

voltage

in the absence

of

the microwave radiation

(Vi

₌

0).

N T

V~ (Vi

= ~l) ^V* n a~

w~~/2

_ar

K V V GHz

19 134 0.018 0.1 15 2 0.25 0.41

24 128 0.003 0.07 2 0.5 0.82

78 78 0.76 0.88 3 1.0 1.63

5. Conclusion.

We have

presented

^the ^results of the

experimental investigation

of the CDW non-linear response ^to the microwave radiation _versus the bias

voltage

under the microwave pump. ^The stochastic nature of the non-linear response was

emphasized.

The classical model of CDW motion _was used.

Taking

into consideration the distribution of threshold

field,

the non-linear

response was described

by

the

expression (7) using

the distribution function

(4).

The

change

of the distribution

parameter,

n, at

cooling

the

sample,

was attributed to the redistribution of the different kinds of contribution of the CDW

pinning

_:

impurity pinning, pinning

of the

commensurate CDW _on the

pristine lattice, pinning

_on the surface and

pinning

on the

contacts.

Acknowledgements.

This work has been

performed

_on the

TaS3 samples prepared by

the Yu. I.

Latyshev

_group

(Moscow).

We would like to thank Yu. I.

Latyshev,

I. F.

Shchegolev,

Yu. A. Firsov for useful discussions and W.

Wonneberger

for their interest in the

problem.

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Proofs

_not corrected

by

the authors.