Calculated femtosecond optical response for trans-polyacetylene

ELSEVIER

Synthetic

Metals

69 (1995)

655-656

Calculated femtosecond optical response for trans-polyacetylene H. W. Streitwolf

MPG-AG

‘Halbleitertheorie’,

and S. Block

Hausvogteiplatz

5-7,

D-10117

Berlin,

FRG

Abstract Within

the SSH-Hamiltonian

the classical

dynamics

numerically.

Fluctuations

characteristic

peaks

[l] interacting

of the pump

of the monomers

of the current

with an external

induced

current

density

electric

are taken into account

density

are discussed.

Local

field as a model

for optically

as well as the electronic changing

energy

the displacements

field corrections

are included

pumped

eigen

values

at constant

polyacetylene are determined

total

energy.

in the microscopic

The

electric

field.

1. INTRODUCTION (to=2.5 It is generally as charging

that optical

pumping

[3] [4] of trans-polyacetylene

ized distortions within

accepted

of the chain connected

the Peierls

gap which

[2] as well

may produce

local-

with electronic

levels

can be detected

by optical

ab-

[5] a photoinduced

Experimentally (low energy

peak)

below

toinduced

the

gap

Starting

[6] attributed

a model

n* transitions

from

Heeger

(SSH)

within

adiabatic

bleaching

dynamics

oscillates

after

Schrieffer

about

pair with electronic

ing oscillation

of the chain

Here we focus process

the initial

coherent

states in the gap.

to a localized

[7] and optical

our investigation

in the fs range

breath-

phonons.

on the optical

and calculate

[9] found

100 fs a separat-

was transferred

energy

at the on-

pair in the Su-Schrieffer-

[l] Su and

ing soliton-antisoliton abundant

of pho-

for poly(%alkyl

[8].

an electron-hole

Hamiltonian

while

The

excitation

the current

density

regime.

THE

+ HEi

local

P = -e/V external reproduce

We use the SSH-Hamiltonian

The

xn(t)

(ckcn

-

-

Eo3 = chain

I) E(t),

we use the Lorentz-

2P/3&0)/&~.

3 the dielectric

volume

as

pulse

are the ion positions.

polarizable

= (Eext

interacting

approximation

by a laser pump

= 12 a + u”,(t)

the experimental

constant

V is determined

static

Eext

dielectric

the

of the gin order

to

constant

E, =

to classical

Born-

11.0. The ion displacements Oppenheimer MI&

= -

x,

Pnn~&r-C

with the elIc:ronic 11,is the solution

[l] 4.

ul(t)

are subject

dynamics Cpnn Cn

&ulf+eE(t)

density

matrix

p(t)

of the Schrijdinger

h(t)=h’(t)

+ hEe(t))

= $*(t)

equation

with initial

= $(t o ) E and the initial

f = (f(Q)&

-+

f $T(t).

ih?)

= h$

conditions

distribution

function

).

RESULTS We applied

Eext(t) (where

= &(t,

a Gaussian

the power

pump

pulse at t:

t;) = Ep cosq,t G(t - t;)

G(t) = e-t2/tg,

an initially

0379-6779/95/$09.50 6 1995 Elsevier Science S.A. All rights reserved SSDI 0379-6779(94)02603-V

21 eV/A2)

2, (pn,, - 1) is the polarization,

fieldnand

transitions.

=

in dipole

= --e c

field E(t)

c

K

excited

Since the chain is highly Lorenz

(where

MODEL

eV/A,

field E(t)

for polyacetylene

h(toMto) 2.

4.1

electric

HE = HEe(t)

absorption peak some-

to absorption

[7] were found,

a photoinduced

set of the K -

midgap

at 0.45 eV and a high energy

breathers

thienylene)s

during

CY =

(e < 0). Here zra(t)

sorption.

what

eV,

with the local

dimerized spectrum

t, = 30 fs, Ep some

chain of 140 monomers of the current

density

10’ V/m)

to

and calculated

656

H. W. Shdwo&

induced

by pumping.

Our preliminary ferred our

from

classical

pump

dynamics phonons

Furthermore

gap is at 1.35 eV.

was

showed

rule

quickly

near

trans-

over

within

by coher-

was excited.

our that in a chain of 140 monomers

Fluctuations

sensitivity

taken

distortion

was well satisfied.

by the chain sensitively

quency.

that energy

field to the electrons

and no localized

it turned

the k-selection

band

observations

the electric

ent optical

absorbed

The

S. Block / Synthetic Metals 69 (1995) 655-656

Hence

the energy

depends

on the pump

fre-

of the displacements

will reduce

this

the band

gap and are considered

to be of

importance. We therefore each instant the energy The pulse

of time

the displacements

energy

and averaged

absorbed

r)

at

changing

by the chain from

expressed

a Gaussian

pulse

tween

the probe

current

by the induced

Its

on the delay

[8] therefore carrier

time

w>]

-

current

density.

dependence

of the

pump

and

may result from the difference

be-

frequency

T between

and a near peak

At equal

energy

frequency

transferred

of the large influence (2 eV)

of the electron

chain (Fig.

phonon

the peak in [j(w)]

1.) appears

energy

which

nearer the pump

frequency

couat the

to be quite broad.

B, 22 (1981) 2. A. Feldblum, T.-C.

Chung,

(1982)

is to some effective

(1982) 7. A. B.

R.

Friend,

The

peak

at about

w (eV) current

0.35 eV arises from

electronic

energies

reduction

of the mean

difference

of the instantaneous

5

9. W.

J. H. Kaufman,

density.

the shift

after and before

and is displayed

electronic

the pump

pulse

density (Fig.

2.).

of the

with the in the

of states

S. Etemad,

S. Etemad,

Phys.

Rev.

Rev.

A. J. Heeger,

Phys.

Rev.

A. J. Heeger,

Lett.,

Streitwolf,

T. M. Jedju, Phys.

45 (1980)

B, 26

phys.

and A. G.

1209.

stat.

sol.

and

P. D. Townsend,

Rev.

Lett.,

G. L. Baker,

Bishop,

D.

and

K.

S. R.

(b),

150

S. Etemad,

65 (1990)

Phys.

Campbell, Phillpot,

Rev.

100. Lett.,

49

P.

S.

Synthetic

Lomdahl, Metals,

9

223. Samuel, J. Riihe,

K. E. Meyer, and

S. C.

G. Wegner,

Graham,

Phys.

Rev.

R. H. B, 44

9731.

P. Su and J. R. Schrieffer,

USA,

into the gap which is connected dimerization

(1991)

Phys.

1043.

8. I. D. W.

of the induced

the

147.

Horovitz,

(1984)

1. Spectrum

and

resonance.

and A. J. Heeger,

and A. G. MacDiarmid,

M. Ozaki,

6. J. Orenstein

Fig.

transferred

intensity

2099.

and G. L. Baker,

4

pump

815.

5. L. Rothberg,

3

of the pump

REFERENCES

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2 Frequency

density

the frequency

detuning

with growing

at higher

4. H. Puff and H. W.

1

to the chain

It increases

is larger

MacDiarmid,

0

electronic

pulse.

with increasing

and the gap.

3. N. Suzuki,

(DDOS)

the pump

1. W. P. Su, J. R. Schrieffer,

in a one-dimensional frequency

of the instantaneous

after and before

in the

density.

Because

E (eV)

test

T).

b(wt - w) + j(mwt

found nearly periodic

energy

probe

2. Difference

of this peak decreases

The experimentally absorbed

Fig. of states

transform

is immediately

pump

without

Energy

at

over 50 chains.

t, + T is S(7, wt) = S dtj(t)Et(t,

S(w, wt) = $Et&&-wztf/4

pling

stochastically

2.5 x lo-r7s)

(every

of the chain

&(t,

Fourier

changed

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