Fluctuating conductivity above the charge density wave transition in K0.3MoO3

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Fluctuating conductivity above the charge density wave transition in K0.3MoO3

L. Degiorgi, G. Grüner

To cite this version:

L. Degiorgi, G. Grüner. Fluctuating conductivity above the charge density wave transition in K0.3MoO3. Journal de Physique I, EDP Sciences, 1992, 2 (5), pp.523-528. �10.1051/jp1:1992163�.

�jpa-00246515�

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Classification Physics Abstracts 71.45L 78.20

Short Communication

Fluctuating conductivity above the charge density

_wave

transition

_in

Ko~3Mo03

L.

Degiorgi

and G. Griiner

Department of Physics and Solid State Science Center, University of California at Los Angeles, Los Angeles CA 90024, U-S-A-

(Received

5 February 1992, accepted 28

February1992)

Abstract. We have measured the optical conductivity of Ko.3Mo03 both above and below the charge density _wave transition. We find clear evidence for _a collective mode contribution to the optical conductivity

a(w)

and for

a gradual opening ^of a pseudogap at temperatures above the charge density _wave transition, but below the _mean field transition temperature. We also discuss the parameters which characterize the electrodynamic _response in the fluctuation

regime.

One of the central aspects of the

phase

transition which _occurs in low dimensional solids is the appearance of fluctuation efTects _at temperatures ^above T3D, ^where ^the ^three dimensional

order

develops,

but below the _mean field transition temperature

TMF.

While fluctuation efTects have been examined in various

organic

linear chain

compounds,

the most detailed

analysis

has been

performed

_on the material

Ko.3Mo03,

which

develops

_a

charge density

_wave

ground

state at T3D _" 180 K. Besides

X-ray

and neutron

scattering investigations [I],

various studies

on the

magnetic susceptibility x(T) [2,3]

and _on the

thermodynamic properties (e.g.,

heat

capacity C(T),

elastic

properties

and thermal

expansion)

_[2-4] have demonstrated the _presence of CDW fluctuations in this

quasi

ID conductor. The

magnetic susceptibility,

which decreases with

decreasing

temperature between 300 K and T3D, ^has ^been

interpreted

in terms of _one

dimensional fluctuations [2]. ^In ^contrast

experiments

_on the structural and

thermodynamical properties

_near T3D were

analysed

in _terms of 3D fluctuations

arising

_as the consequence of _a short coherence

length [1,3,4].

The

question

of whether collective transport efTects

(e.g. fluctuating

or

paraconductivity)

associated with ID fluctuations

play

an

important

role for T3D < T < TMF have remained

an elusive

problem.

The clear manifestation of such _an efTect would be evident in

optical experiments through

the observation of deviations from

simple

Drude behaviour above T3D.

While such efTects have been searched for

extensively

in various

materials,

the issue remains controversial

[5-9].

The main _reason for the controversy lies in the

difficulty

in

performing

(3)

524 JOURNAL DE PHYSIQUE I N°5

reliable

reflectivity

measurements in

highly conducting specimens,

which

are also often

plagued by

less than

perfect

surface

quality (I,e.,

like in the _case of mosaic

arrangements).

We have

performed

_a series of detailed

optical experiments

_on

Ko.3Mo03

both above and below T3D in order to search for

fludtuating conductivity

above the 3D

ordering

temperature.

The

superior

characteristics of _our

large single crystals (3x2x1 mm)

allows the

precise

de- termination of the

optical properties

_over _a broad

spectral

_range. Our

experiments provide (to

_our

knowledge

the

first)

clear evidence for both the

opening

^{of the}

pseudogap

and for _a

significant

contribution to the

conductivity

_a

coming

from the collective mode fluctuations.

Ko.3MoO3 specimens

^used ⁱⁿ ^this

study

have been _grown

by electrolytic

reduction of the

starting

materials

(I.e.

K2Mo04 and

Mo03)

and have excellent surface characteristics. _Re-

flectivity

measurements _were

performed

in

a broad

photon

_energy _range from 10~ down to 14 cm~~. In the far infrared energy range

(FIR)

_we have used _a Bruker IFS l13v Fast Fourier

Tiausform Interferometer with _a

Hg

_arc

light

_source and _a He-cooled silicon bolometer detec- tor. In all

experiments,

the

light

_was

linearly polarized along

the chain direction and _a

freshly evaporated gold

mirror _was used _as reference

[10].

^We ^have

performed

measurements at 300

K,

between 200 and 160 K at each 5 K

interval,

and from 160 K down to 100 K in steps ^of10 1<.

Finally,

_a low temperature measurement at 3 K _was also carried out. In this communication

we discuss however

only

_our results at three temperatures, at T

= 300 K, well above T3D and where fluctuation efTects _are

expected

to be

small;

at T

= 200 K

just

above T3D, and at T = 170 K

just

^below the

charge density

_wave transition.

Figure

I shows the

reflectivity

spectrum

R(w)

in the whole

investigated

_energy _range at three temperatures

(T

₌

300,

200 and 170

K),

while the inset

displays

the lowest energy

spectral

_range _on _an

expanded

scale. As

expected,

we,find _no temperature

dependence

at

high frequencies (I,e.,

above 700

cm~~)

and all the FIR spectra

presented

here matched _very well

(I,e.

^within a mismatch of about

3~)

with _our

spectral

_range _[10]. In the

FIR, however,

_our

R(w)

data

display

a

significant

temperature

dependence.

We note that the relative _error in

R(w)

is of the order of 0.2~ and

consequently

the temperature

dependent

features discussed below _are not due to artificial

changes

in the

reflectivity

spectrum. It is evident from

figure

I that the

reflectivity

at 300 K is

higher

than at 200 K in the

spectral

_range above

approximately

30

cm~~,

where

a

crossing

^{of the} two spectra _occurs

(see inset).

The measurement at 170 K shows _some weak mode structures and is

clearly

lower than

R(w)

for the other _two temperatures.

Moreover,

it is worth

noting

that _at low

frequencies R(w)

_merges

perfectly

with the low

frequency Hagen-

Rubens

extrapolation

at all temperatures

[Ill.

We obtained the

optical conductivity a(w) (I.e.

_al

(w)

+

ia2(w)) through

_a

Kramers-Kronig

transformation of the

reflectivity

spectra, and its real part _al

(w)

^is

presented

in

figure

2. Several factors underline the internal

consistency

of _our

analysis. First,

the dc limit of the

optical conductivity

_agrees with the

directly

measured dc

conductivity [10,

12] a clear

signature

for the correctness of the low

frequency

part of the spectrum.

Second,

the full

spectral weight

of the

conductivity (integrated

_over the entire

frequency range)

is temperature

independent

within _our _accuracy of

+2~,

_as

expected. Third,

at T ₌ 300

K,

I.e. well above T3D and at _a

temperature, where fluctuation efTects _are

expected

to be

small,

our results _are

fully

consistent with _a low

frequency

conventional Drude _response

(with

an additional contribution around 3000 cm~~ _which _most

probably

arises from _an interband transition and has been observed before

[13]).

^The most

interesting

feature of

figure

2 is. the formation of _a _narrow _resonance at

w = 0, which

develops

at 200 K, somewhat above the three dimensional

ordering

temperature, but

completely disappears

at 170

K,

I.e. below T3D. This _narrow _resonance is the consequence of the

crossing

at

~w 30-40 cm~~ of the

R(w)

spectra ^taken at 200 and 300 K.

Thus,

this remarkable feature has

already developed

well above _our lowest

experimental frequency

and is

(4)

Ko.3M°°3

[

ii

O 300K

. 200K

~ 170K

p

o .

~~~. .

>~ ~ °

o ..

t ~

n o ..

> no

W ^~ o . .

~ ^~ ^.

oo ~°u

-

~At

~o ~~

~hZ~

,p J°

102

lo° lo~ io~ io~ fo~ ios

frequency ^(cm")

Fig. 1. Reflectivity spectra of Ko.3Mo03 at 300, 200 and 170 K for fight polarized along the chain direction. The inset shows the _same spectra ⁱⁿ ^the ^lowest frequency _range _on _an expended scale.

not _an artifact introduced

by

the choice of the low

frequency extrapolation.

We argue that the low

frequency

_narrow _resonance observed _at 200 K at the temperature where lD fluctuations _are

important

but 3D fluctuation effects do not

play

_a

significant

role

corresponds

to the one-dimensional

unpinned

CDW collective

mode,

and is _a

fingerprint

of the fluctuation

regime.

In

evaluating

the parameters ^which characterize this

feature,

_we first

analyze

the

optical conductivity

in terms of its

spectral weight.

The latter is

generally

defined

by

the _sum rule:

f«i(W)dW ^~

⁼

))

^~

_(i)

As mentioned

above,

_we find that the total

spectral weight

is temperature

independent.

This

means that the _narrow _resonance is due to _a transfer of _a fraction of

spectral weight

from the

high

to the low

frequency

part of the spectrum. In

calculating

the

spectral weight

associated

with the _narrow _resonance _we _must consider that

only

_a fraction of the total number of

charge

carriers condense into the

"fluctuating"

CDW collective mode. This _can be monitored

by measuring

the

magnetic susceptibility

which reflects the

density

of states within _an _energy

interval

kBT

around the Fermi level [2, 3].

Assuming

that

x(300 K)

represents ^the

unperturbed

Pauli value of the

spin susceptibility

of the total uncondensed

electrons,

we can then evaluate the fraction of the Fermi surface removed

by

the

pseudogap formation, by using x(T).

We

estimate that about 25~ of the total number of

charges

condense in the CDW collective mode at 200 K. The

remaining

^75$l of the free uncondensed

charge

carriers

(n~°rr~~')

^contribute to the dc

conductivity, corresponding

to _a

a](rr~~

^of ^about ¹⁰⁰⁰

(Qcm)~~ (i.e.,

0.75 _x

ado(300 K)).

We have assumed that the decrease of

a](~°~~

^is

^totally

^determined

^by

^the ^decrease ^of ^n~°rr~~

[14].

(5)

~0.3~°~3

j ^I

II

j

° 300K

. 200K

° A 170K

~

f

j

°

# ^.

8 _#

~ ..

~ )

~J~

io°

requency

lcm~~l

Fig. 2. Optical conductivity of Ko.3Mo03, evaluated from the Kramers-Kronig transformation of the reflectivity spectra of figure 1.

Defining

the

spectral weight

of

equation (I)

in terms of the

plasma frequency

_wp

(I.e.

xne~/2m

=

w(/8),

_we _can write:

~J300

^K

~ ~300 K g~*200 ^K

P

(~)

~J*200 K ~*200 K ~300 K

P

where

w(

^and ^n*

^represent

^the

plasma frequency (or spectral weight)

^and ^the ^carrier _concen-

tration of the _narrow _resonance,

respectively.

With n*~°° ^~

= 0.25 n~°° ^~

as established

above,

and with m~°° ~

= mb the band _mass, and

hw(~°°

^~ = 0.075 eV

(I.e.

which is obtained

by

integrating

the _area between the _curve at 200 and 170 K in

Fig. 2),

and with the normal

plasma frequency

unscreened from the various interband transitions

hw(°°

^~ = 2 eV

[lo] (I.e.

the total

spectral weight)

we obtain m*~°°

~/mb

" 178. This is the _mass enhancement related _to the

electrons in the

fluctuating

CDW collective

mode,

which contributes to the dc

conductivity.

It is also instructive to compare

w(~°°

^~ ^with ^the

corresponding plasma frequency _w(~

^~ of the

CDW

pinned

mode _at low temperature

[lo].

With n*~°° ^~

=

0.25n~°°

~ and n*~ ~

=

n~°° ~

(as

^all ^the ^electrons are condensed in the CDW mode for T <

T3D)

^and

hw(~

^~ = 74 mev

[lo],

_we ^obtain

(using Eq. (2) properly

reformulated for the ratio between

w(~

^~ ^and

w(~°° ~)

m*~ ~

= 4.lm*~°° ^~

= 730 _mb, which is in fair agreement ^with the

previous experimental

find-

ings (I.e.,

m*

=

400mb) [lo]

and is _very close to the _mean field estimation m* ₌

800mb [15].

Also,

it has been shown earlier that the ratio

m*(T)/n(T)

normalized _to the

corresponding

ratio at T

= 0 K is at T3D 50$l ^{of its} ^initial ^value

[16].

^If _we ^consider

m*(T

₌ 0

K)

ru 800

(I.e.,

the _mean field

estimation),

_we would obtain _a value for m* of100

(I.e.

0.25 _x

400)

at the transition temperature T3D,

again

in

good _agreement

with

our result for T > T3D.

(6)

Assuming

_a renormalized Drude form for the

fluctuating conductivity

'~ i~

_I

wr*

~~~

at 200 K _we obtain

I/r*

_ru 5 cm~~ _for _the renormalized

scattering

rate.

Consequently,

r* h enhanced

along

with the enhancement of the effective _mass, and furthermore

T/m

_ru

r/mb (I.e.,

the ratio of the unrenormalized relaxation time and

mass).

This has been

predicted by

various models

[17, 18],

^and ^has ^been ^shown

experimentally

_[16] below T3D. ^Our

experiments suggest

^that ^this ^{is also} ^the case in the

fluctuating regime.

An

important

manifestation of the

fluctuating regime

is also the

gradual opening

of the _sc- called

pseudogap,

and the temperature

dependence

of the

magnetic susceptibility x(T)

has been accounted for

by

such

picture

_[2]. From _a

semiphenomenological description,

based _on the

theory developed by

Lee et al. [19], an effective _gap of about 500

cm~~

is

extrapolated

[2]. ^The ^value ^of ^the

pseudc- (or effective)

_gap is

essentially

temperature

independent

and

below the 3D transition temperature the true gap ^at the _same _energy

develops.

We believe that the

depression

of _al

(w)

at the

spectral

_range around 10~ cm~~ _at 200 K

(when _compared

with _a at 300

K)

followed

by

_a _very broad

hump

at

approximately

500 cm~~ is due to the

development

of the

pseudogap.

The latter feature

subsequently

_merges in the _even broader

structure at about 3000 cm~~.

By lowering

the temperature ^below

T3D,

the

hump

at 500 cm~~

is

completely removed,

and _a

sharper

and _more intense structure

gradually develops

at the

frequency

of the CDW _gap

(I.e.

at 1600 cm~~

[lo]),

which is furthermore

superimposed

to

higher frequency

interband transition

(like,

_e-g-, that at 3000

cm~~).

In

conclusion,

_we have established the first clear

optical

evidence of the

fluctuating

conduc-

tivity

^associated ^with the

development

of the CDW

ground

state. Based _on

spectral weight

sum rule considerations _we have ascribed the low

frequency

_narrow _resonance at 200 K to the

unpinned

CDW collective

mode,

a

fingerprint

of the _precursor effects of the CDW

ground

state.

The evaluation of the relevant parameters, ^like the _mass enhancement m* and the renormalized relaxation time T*, supports _our conclusions. The

dimensionality

of the fluctuations

remains, however,

_an

interesting question.

Even

though

lD fluctuations _appear to be

solely responsible

for the strong temperature

dependence

of

x(T)

above T3D [2], the issue

regarding

fluctuation effects in the immediate

vicinity

of T3D is somehow controversial and is

beyond

the present

optical investigations.

Acknowledgements.

The authors thank S-E-

Brown,

S. Donovan, K.

Maki,

T-M- Rice and A. Zawadowski for

helpful

discussions. The

samples

used in this research _were _grown

by

B. Alavi. One of _us

(L.D.)

wishes to

acknowledge

the financial support ^{of the} Swiss National Science Foundation. The research at UCLA _was

supported by NSF-grant.

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Refs

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