Solitons, experimental manifestations

basketontarioElectronics - Devices

Nov 2, 2013 (3 years and 10 months ago)

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Serguei

Brazovskii

and Natasha
Kirova


Natal 2012


Physics of synthetic conductors as low dimensional correlated
electronic systems.


Lecture 5, part 2

Solitons,

experimental manifestations

We

measure

We obtain

Conductivity

Metal, semiconductor, activation
energy for charge carriers

Magnetic

susceptibility

Collective spins (Pauli
law
) versus
isolated

spins (Curie
law
)

ESR, NMR

Origin of spins (g
-
factor), spin
excitations

Optical absorption

Energy
levels
,
bands,
band states

Non
-
linear optics,
photoinduced absoption,
stimulated emission

Properties of excited states

Time resolved
femto
-
second
optics

Dynamics and evolution of
excited states

Polyacetylene

Ethylene

-

Traditional plastic :
Polyethylene

-

Conjugated polymer :
Trans
-
polyacetylene

Acetylene

Line of milestones:

S.
Shirakawa
; A. Mac
Diarmid
, A.
Heeger
,
Y
.W
.

Park, S.
Etemad
, V.
Vardeny
,

Films of
undoped

PA:

Spaghetti of fibrils D~50nm.

Can be oriented by stretching.


What is inside?

Polycrystals

of chains,

Structure is known for the

pristine material.

Trans
-
PA : the stable form.

But:

The PA is always obtained

in the
metastable

Cis

form.

Transformed under

heat or doping.

Under doping,

the structure is modified

into a high
-
symmetry

hexagonal form.

Columns of ions intercalate

thi

zig
-
zags

of chains.

5

C

H

C

C

C

H

H

C

H

H

Dream

Reality

E

-
k
F

k
F

E

k
F


-
k
F


F


Peierls effect

-

one dimentional chain of equidistant atoms is

unstable
with respect to the dimerisation:

Spontaneus
symmetry braking results in the dielectric state, the gap is
open.


Wexp(
-


Holes doping

gives conduction

6

Topological

defects

on the
polyacethylene

chains

W



Ideal chain

Charge solitons

q=

e, s=0

Spin
soliton
,

q=0, s=1/2


0
tanh

[x/

0
],
W
tot

= (2/

)

0

E
el

=0

Δ
0

-
Δ
0

0

Δ
0

-
Δ
0

0

Q
=
-
e

Q=+e

Δ
0

-
Δ
0

0

7

Solitons and polarons at an isolated (CH)
x

chain

E
b

=0





-




Split
-
off intra
-
gap bound states at levels
±
E
b

Spinless solitons would be favorite charge carries for an unperturbed chain.


The higher energy Polarons (charge e, spin ½) enter the game

thanks to Coulomb attraction from charged dopants.

Only they bring the spin and the magnetoresistance

Spontaneous symmetry breaking gives rise to solitons


kinks between
domains of opposite dimerizations. In PA
-

identified by spectroscopy and
ESR.

specific

Non
-
specific

8

Measurements of the

magnetic susceptibility
χ


χ
through the "Knight shift of the
NMR
-

Nuclear Magnetic Resonance

-

an important test for homogeneity


and directly (Faraday balance)

A major puzzle:

spins appear at much higher doping

than the metallic conductivity:

the whole interval of conduction by

spinless



unlike electrons
--

particles

conductivity

s

Metallization under doping

Low doping:

gap is preserved,

Mid
-
Gap and
IR

activity


appear

Larger doping:

No more gap seen,

all absorption goes to
IR


Metallization in (CH)x
starts at x=1% of
dopping
, end up at
10%
-

enormous concentration,
distance 10
1/3

~2
-
3 units,

effect of one
-
dimensionality!

Only the impurity along the chain is seen for hopping.

Metallization in Si
, etc.:

n=10
18
/cm
3



x=10
-
6
/per Si,

distance 100 units


Linear and non linear optics

10

Linear optics (LO):

Pump: change
the light energy, observe the
absorption/emission
spectra

Nonlinear optics (NLO):
pumpe



probe experiment.

Photoinduced

absorption (PA)

Pump
-

Light 1 : fixed energy through the gap E>
Eg
,
creation of the excited states

Probe


Light 2: test excitations of the earlier excited
states by changing the probe light energy


Stimulated emission (SE)

Pumpe

-

Light 1 : fixed energy through the gap E>
Eg
,
creation of the excited states

Probe


Light 2: provoke recombination of the excited
states with the emission of the optical photons.


Time resolved NLO:

Measurements as a function of time delay between
pump and probe.

SE

PA

Pump

PL

Pump

Optics

and Electron
-
Phonon
Coupling
:

Adiabatical

principle

(Frank
-
Condon
, Born
-
Oppengeimer
)

Relaxation


effects

Emission

LES

E

q

Absorption

GS

Excitation

Figure: energy of an electronic excitation
as a function of a lattice deformation q.


Light is absorbed in a time ~
ћ
/E
g
~10
-
15
sec

Compare with relaxation time of a heavy
lattice ~
ћ
/
ω
ph
~10
-
13
sec :

--

Absorption goes from the relaxed
ground state GS the
unrelaxed

excited
one.

--

Emission


luminescence goes from

the relaxed excited sate to

the
unrelaxed

ground state.

--

Indirect (minimum to minimum )
transitions require the quantum overlap
of the lattice zero
-
point vibrations, hence
the reduced probability ~exp(
-
Δ
E
min
/
ћ
ω
p
)

12

Optical absorption spectra of (CH)x

Δ
0

-
Δ
0

0

Δ
0

-
Δ
0

0

Doping

Photo
-
current, hence the photo
-
conductivity, comes only from excited unbound pairs at E>
E
g


Absorption


also from bound
excitons
, hence expect a lower threshold at
E
ex
<
E
g

as it is normally observed.

Figure shows the photocurrent
I
ph

offset

which starts below the absorption !


Resolution:
I
ph

is much more sensitive,

it recovers adiabatically forbidden creation

of relaxed configurations


here pares of solitons.


Their threshold is, theoretically, 30% lower.

In favor of that: exponential growth of
I
ph
.

Confinement of kinks pair into
2e
charged (
bipolaron
) or neutral (
exciton
)
compex
.

Symmetry determined picture of optical differences for

trans
-

and
cis
-

isomers


S
. B. and N.
K.,
1981

Photoconductivity trans
-
(CH)
x

versus
photoluminescence
cis
-
(CH)
x

also new
optical features due to hybridization of mid
-
gap states

Nature present
--

cis
-
isomer of (CH)
x

:

build
-
in slight
inequivalence

of bonds

hence lifting of ground state degeneracy,

hence confinement of solitons

Effect
upon kinks:
global lifting of symmetry
-

confinement
.

Cis
-
(CH)
x

:

Nonsymmetric

dependence

of GS energy on
dimerisation

Ideal chain

Bipolaron

-
two

confined

solitons

Confinement


the linear growth of the attraction energy
while the particle diverge.

Energy difference per unit length

is a constant confinement force F.

The confinement energy is
F|x
|.

Cis
-
(CH)c


photoluminescence, no photoconductivity,

Trans
-
(CH)x


free solitons, no photoluminescence, but the photoconductivity

Neglecting Coulomb repulsion (suppose two donors sit nearby as counter
-
ions)

the two bound
solitons

are always more favorable than two electrons and even two
polarons
.

It can be:


exciton



in case of light pumping (bound e
-
h pair, two charged
solitons

with
opposite charges)

Bipolaron

(BP)


in case of doping (bound pair of two
solitons

with the same charge)


N.B. taking the
bipolarons

away from the donors (attempt to make conduction by
BPs) turns on the Coulomb repulsion between the two electrons.


Confinement scenario :

the BP is a string between the two kinks at a distance x:

the BP energy, with respect to two bare electrons is



d
W
bp
=
W
bp
(x)
-
2

=
-
(2

-
2W
s
)+
F|x
|+e
2
/(

|x
|)


-
-

always an optimal x:

d
W
bp
=
-
0.6
+2(
Fe
2
/

)
1/2





favorable for small enough confinement force F.

Luminescence of
cis
-
(CH)x and trans
-

(CH)x

Left


a broad line covered by multiple phonons repetitions

-

vibrations of the lattice dressing of the
selft
-
traped

state

-

additional proof of the
selftrapping
.

Right: same
--


cleaned from phonons

trans
-
PA, T=7K, pumping at 2.54eV

Remnant luminescence is 50 times

less then that of
cis
-
PA

Time resolved photoconductivity from the old
pico
-
second epoch:

After a short pump, the photocurrent decays with a characteristic time ~100ps

-

result of recombination of carriers.

Resolving the shorter time, one finds a fast initial recombination of geminate carriers


the e
-
h pairs created by the same photon.

This is why in applications we need a fast capturing of one kind of carriers.

In optics
by specific lines appearing under doping or even (?) pumping.

Doing
ESR

under low
-
to
-
moderate doping to detect no spins

-

especially clear in
polytheophene
.


Clear evidences

that
BPs

function as the main reservoir for charge storage

-

generalize to junctions, to field
-
effect transistor! (
N.K

and
S.B.

for theory)


No clear proof

that
BPs

can conduct as individual 2e particles



would be a step towards the superconductivity


activation into
polarons

may be necessary.

How do we identify
bipolarons
?

Energy schemes for

a) 2
-
holes bi
-
polaron



2 transitions

b) 1
-
hole
polaron




3 transitions.


Both split inside the gap a symmetric pair of levels

-

viewed as splitting of the zero
-
energy state in PA

Experimental identification of
bipolarons

by the double
-
shape structure of the absorption.

--

proved to be WRONG !

One of transitions is optically forbidden,

hence expect 1 transition for
BPs

and 2 transitions for Ps

In optics

by specific lines appearing under doping and pumping


proving their similarity.

Doing
ESR

under low
-
to
-
moderate doping to detect the spins.

Doing combined experiments for
ESR

under optical pumping (
V.
Vardeny

et al
).

In kinetics
,

beyond the internal optical transitions, the
polarons

are like electrons or holes,

just ~10
0

times more heavy, hence reduced mobility, enhanced binding to
dopants
,
impurities.


Why they may not exist?


Theoretically, the
polaron

energy is 0.9
Δ



only 10% gain with respect to a free
electron :

In spite of strongly split
-
off
intarband

levels (E
0
=
±

0.7
Δ
),


the energy gain 0.3
Δ
is almost compensated

by the cost to form the self
-
consistent potential well.

Perturbation like the
interchain

coupling can level out the small net gain 0.1
Δ

to
leave electrons free from
selftraping

How do we identify
polarons
?

Photo
-
absorption spectra of (a) regular and (b)
improved
Polytheophene

films.

Inset: schematic diagrams of negative

(a)
polarons

and

(b)
bipolarons


and their optical transitions.

Two spin 1/2
polarons

will produce pairs with spins either parallel (s
p) or
antiparallel

(s
ap).

For non
-
geminate e
-
h pairs, both sp and sap
pairs will form initially,

but the recombination rate of s
ap pairs is higher, leading to
steady state populations with
sp.
MW
-
induced
spin flips convert s
p pairs into sap pairs,

increasing
the recombination rate of
oppositely charged pairs to
the ground state and
reducing
polaron

populations


to be detected by the
photoinduced

absorption .

Magnetic resonance
will also enhance
bipolaron

formation

from
like
-
charged pairs.

Combination of the techniques of the
photoinduced

absorption (PA)

and of the PA
-
detected magnetic resonance (PADMR).

Single fiber: l



m㬠


<100nm

Inside:



3

chains of the (CH)x

New helicoidal polyacethelene PA (
K. Akagi
)
-

multi
-
scale material
:


cells
-
> spirals
-
> threads
-
> crystalline fibers
-
> polymer chains

-
>

-
敬散tons
-
㸠敩敲ls
-
䠠dim敲iztion
-
㸠solitons
-
㸠confin敭敮t