Transcript Z.Z. Wang

CDW PHASE SHIFT STUDY
BY UHV-LT-STM
J.-C. Girard et Z.Z. Wang
Laboratoire de Photonique et de Nanostructures
LPN / CNRS
Route de Nozay – 91460 Marcoussis , France
Outline
1/ Introduction : Quantum Imaging by STM
imaging of ground state of quantum mechanics and of many body
problem
2/ CDW in TTF-TCNQ :
an ideal candidate for local phase shift j(r) studying (unique?)
3/ phase shift ja(x,y) for modulation in “a” direction
(perpendicular to the chain direction): the variation is trivial in real space
(commensurate pining)
4/ phase shift jb(x,y) for modulation in “b”direction (chain
direction):
important variation presented in our measurement, phase shift “map”
5/ Conclusion: CDW complex order parameter Y = D eiF can be
studied by STM
measurement
We soon find ourselves armed with wonderful new tools. The
more we used them, the more applications we find; and the more
applications we find, the more use of quantum theory we make.
In no way do the advances of physics spread more widely to the
community than in new and improved measuring devices.
Is it true that
« no elementary quantum phenomenon is a
phenomenon until it is a recorded phenomenon »?
John Archibald Wheeler
Quantum Theory and Measurement
STM measurement
STM might be a unique technique to study, in real space, local
electronic structure with energy resolution.
- the typical tip-sample resistance (tunneling gap resistance) is of 610 orders higher than the sample resistance, resulting in a less
significant matrix transfer element in tunneling junction.
- only an insignificant electric field built inside the sample.
- tunneling current is of order of 1-100pA, one electron every 1100ns! No question for escaping, recombination , thermalizing…
Both topographic and spectroscopic measurement in nanometer
scale can be performed simultaneously with a least tip-sample
interaction (without destructive).
Ground state in quantum mechanics is robust
against the STM measurement
Quantum Imaging with STM
-A lot of the phenomena that are traditionally encountered
in course in quantum mechanics, such as molecular orbital,
harmonic oscillators, particle in a box, eigen wave function,
impurity Bohr radius, Fermi’s golden rule, chemical
bonding, and the electron spin can be directly visualized
with the STM.
-Recently, some second quantification phenomena that are
introduced in many body problems of condensed matter
physics are studied by STM too.
Kondo effect, Friedel Oscillation, Charge Density Wave,
inhomogeneity of superconducting gap are clearly observed
without ambiguity.
Band structure
Eigenenergy and eigenstate in QD
InAs(P)/nP(001) QD
Height : 5.8 nm
Lateral size : 42 nm
e0
e1
e3
e4
e5
e9
e7
e2
e10
e11
e8
e6
e0
e1
e2
V = 867 mV V = 901 mV V = 936 mV
e3
V = 970
mV
e4
V = 1024
mV
e5
V = 1074 mV
e6
e7
e8
e9
e10
e11
V = 1124 mV V = 1155 mVV = 1182 mVV = 1216 mV V = 1255 mV V = 1297 mV
LPN PRL 2009, APL 2010
Confined electronic states in different nanostructures by STS
Electronics states
steps confinement
Burgi et al,
PRL 81, 24 (1998)
Electronics states
for InAs/GaSb (QW)
Suzuki et al.,
Technical Review NTT
(2008)
Electronics states
in Ag(111) islands
C. Tournier-Colletta et al.,
PRL 104, 016802 (2010)
TTF-TCNQ crystallography
Cleavage plane ab :quadratic cell
Monocrystal: monoclinic cell
a = 1.23 nm
b = 0.38 nm
c = 1.58 nm
b = 104.6 °
-
H
C
C
N
S H
Molecular Resolution at T = 63K on TTF-TCNQ (001) surface
TTF+
TCNQTCNQ-
It= 1nA , Vbias= 50mV
Acquisition time : 210 s
Corrugation:
TCNQ : 2 x 0.6 Å
TTF : 2 x 0.2 Å
hTCNQ-hTTF = 1 Å
CDW at 35.6K
Sequential images of CDW on TTF-TCNQ at T = 35.6 K
100 mV
1nA
Total
time : 50
minutes
Temp.
shift:
0.4K
Time for
take one
Image:
210s
T = 35.6K
dimensions : 14.89 nm x 16.09 nm
a
b x
a=1.22nm
b=0.38nm
41.b
y: chain dir.
analysis on
12 rows X 41columns
12.a
LPN PRB 2003
Fourier Analysis : bi-q modulation
two generating vectors for CDW at 35.6K :
q1= 0.25 a* + 0.295 b* = qa. a* + qb b*
q2= -0.25 a* + 0.295 b* = - qa.a* + qb b*
In real space, the wave vectors are:
l1= la a + lb b
with la = (2p/qa) = 4 (commensurate)
l2= - la a + lb b
lb = (2p/qb) = 3.39 (incommensurate)
(LPN PRL 2009, PRB 2008, PRB 2006, PRB2003)
Phase shift j (r)
CDW is a quantum condensate state of electronic state in lowdimensional materials. It can be presented as a complex order
parameter Y = D eiF
D determines - the size of the electronic energy gap
- the amplitude u1 of the atomic displacements
- the amplitude of the electron density modulation
F(r) determines the position of the CDW relative to the
underlying lattice.
Dr (r) = r0 .cos [F (r) ]
with F (r) = qCDW. r + j (r)
j(r) represents local deformation of CDW which is related to the
elastic energy
Weak / Strong CDW pining and local phase shift
Perfect one-dimensional lattice: f(r) is constant (superconducting state)
j(r)
No impurities
r
CDW pinning : Coulomb interaction between the CDW and impurities
strong pinning: abrupt
variation in f(r) at each
impurity site
f(r)
r
i
i
i
i
i
j(r)
weak pinning (Fukuyama, Lee,
Rice): smooth variation in
j(r)over a distance containing
several impurities
i i i
i
i
i
i i
i
r
-Phase determination is crucial to understand the physics of a complex order parameter
- Importance in the understanding of the static and dynamic properties of the CDW state.
Phase shift in modulation bi-q
r(x,y) = r0 [1+ Dr(x,y) ]
: b unit
Dr(x,y)= A1 cos(q1.r + j1 ) cos(q2.r + j2 )
q1= 0.25 a* + 0.295 b* = qa. a* + qb b*
: a unit
q2= -0.25 a* + 0.295 b* = - qa.a* + qb b*
Dr(x,y) = 2A . cos[(2p/la). x + ja ] . cos[( 2p/lb).y + jb ]
the phase shift ja and jb can be calculated separately:
Perpendicular to chain, in “a” direction (commensurate)
y = const ; Dr(x) = 2A(y) . cos[(2p/la). x + ja ]
For a chain , in “b” direction (incommensurate)
x = const ; Dr(y) = 2A(x) . cos[( 2p/lb).y + jb ] (4)
(3)
(2)
TTF-TCNQ: an ideal candidate to study the local phase shift j(r)
CDW phase transition (TP = 53K)
Semiconductor at low temperature (condensate state)
an ideal candidate to study the local phase shift j(r)
- Quadratic unit cell in the ab plane. (a.b = 0)
- Low temperature CDW phase (T<38K):
Commensurate in the “a” direction
Incommensurate in the “b” direction
bi-q modulation
-the phase shift ja and jb can be treated as
independents parameters
both ja and jb are fonction of x and y
T = 35.6K
dimensions : 14.89 nm x 16.09 nm
a
b x
a=1.22nm
b=0.38nm
41.b
y: chain dir.
analysis on
12 rows X 41columns
12.a
LPN PRB 2003
phase shift ja for modulation in “a” direction
In “a” direction (commensurate), for a TCNQ
molecular row (y = const), CDW modulation
Dr(x,y) = A(y) y cst..cos((2p/la).x + ja )
with (2p/la) = 2p/4 = p/2
(4)
Amplitude (nm)
analysis method:
1st step: cross section profile in “a” direction
(perpendicular to chain )
2nd step: determination of the CDW maxima at the
lattice position
3rd step: best fit from sinusoidal function
A.cos((2p/la).x + ja )
Origin’s non linear regression method : LevenbergMarquardt algorithm (c2 minimization)
ja is the only fitting parameter
(ja average on ~ 3 CDW wavelengths) A = Max(Zi)
– Min(Zi)
0,10
0,05
0,00
-0,05
-0,10
-0,15
-0,20
-0,25
0
2
4
6
Distance (nm)
8
10
12
14
“a” direction phase shift ja
0,10
Amplitude (nm)
0,05
0,00
-0,05
-0,10
-0,15
-0,20
-0,25
0
2
4
6
8
10
12
14
Distance (nm)
ja = - 0.76 p
 - (p/2 + p/4)
Agree with X-ray analysis result reported: p/4 J.P. Pouget
The change of ja is trival in real space, we concentrate on the local variation of jb
Commensurate pining by the lattice
phase shift <jb> for modulation in “b” direction
a single chain analysis
In “b” direction (in commensurate), for a
TCNQ chain (x = constant)
CDW modulation is
Dr(x,y) = A(x) x cst..cos((2p/lb).y + jb )
With (2p/lb) = 2p/3.39
Section on
Column
The fitting function is Dr(x,y) =Cross
A..cos((2p/l
b).y + jb )
We find jb = -258
(nm)
amplitude (nm)
Amplitude
Maxima along cross section
jb is the only fitting parameter (average
onfit~ 12 CDW wavelengths)
Sinusoidal
0,10
0,05
0,00
-0,05
-0,10
-0,15
-0,20
0
2
4
6
8
10
distance (nm)
(nm)
Distance
12
14
16
(nm)
amplitude(nm)
Amplitude
Cross Section on Column
The fitting function is Dr(x,y) = A..cos((2p/l
+ jb ) cross section
b).yalong
Maxima
jb is the only fitting parameter (average
on ~ 12 CDW
Sinusoidal
fit wavelengths)
0,10
0,05
0,00
-0,05
-0,10
-0,15
-0,20
0
2
4
6
8
distance (nm)
10
Distance (nm)
12
14
16
A m p lit u d e ( nA mm )p lit u d e ( nA mm )p lit u d e ( n m )
A m p lit u d e ( n m )
The phase shift <jb> on four adjacent chains
C r o s s S e c t io n o n C o lu m n
M a x im a a lo n g c r o s s s e c t io n
S in u s o id a l f it
0 ,1 0
0 ,0 5
0 ,0 0
-0 ,0 5
-0 ,1 0
1
-0 ,1 5
-0 ,2 0
0
2
4
0 ,1 0
6
8
D is ta n c e
1 0
1 2
1 4
1 2
1 4
1 6
(n m )
0 ,0 5
0 ,0 0
-0 ,0 5
-0 ,1 0
-0 ,1 5
-0 ,2 0
2
0
2
4
6
0 ,1 0
8
1 0
D is ta n c e
0 ,0 5
1 6
(n m )
0 ,0 0
-0 ,0 5
-0 ,1 0
3
-0 ,1 5
-0 ,2 0
0
2
4
6
8
D is t a n c e
0 ,1 0
1 0
1 2
1 4
1 6
(n m )
0 ,0 5
0 ,0 0
-0 ,0 5
-0 ,1 0
-0 ,1 5
-0 ,2 0
4
0
2
4
6
8
D is t a n c e
1 0
(n m )
1 2
1 4
1 6
As we measured ja = p/4 for the CDW commensurate acomponent
First chain:
Dr(y, x = 0) = 2Acos(ja).cos(qb.y + jb )
= 2 A1 cos(qb.y + jb )
Second chain
Dr(y, x = a) = 2Acos(p/2 + ja).cos(qb.y + jb )
= 2 A2 cos(qb.y + jb )
Third chain
Dr(y, x = 2a) = 2Acos(p + ja).cos(qb.y + jb )
= 2 A1 cos(qb.y + jb + p)
Fourth chain
Dr(y, x = 3a) = 2Acos(3p/2 + ja).cos(qb.y + jb )
= 2 A2 cos(qb.y + jb + p)
Variation on each chain of jb(n)
-200
-200
-210
-220
-200
Djb(n) = 0.15
C1
-210
-220
Djb(n) = -0.04
C5
C9
-210
-220
-230
-230
-230
-240
-240
-250
-250
-260
-260
-270
-270
-280
-200
-280
-240
-250
-260
-270
-210
-220
10
15
20
Djb(n) = 0.22
25
30
C2
-210
-220
-230
-240
-250
-260
-270
-280
-200
-210
-220
10
15
20
25
Djb(n) = 0.12
30
C3
-230
-240
-250
-260
-210
-220
15
20
20
25
30
25
Djb(n) = -0.11
30
C4
Djb(n) = 0.73
-250
-260
-260
-270
-270
-280
-200
15
20
25
30
-230
-240
-240
-250
-250
-260
Djb(n) = 0.51
10
15
20
-270
-280
25
30
C8
-210
-240
-250
-250
-260
-260
-270
-270
-280
10
15
20
25
30
C10
Djb(n) = -0.94
10
15
20
25
30
C11
Djb(n) = -0.36
10
15
20
25
30
-200
C12
-210
-220
-220
-230
30
-220
-230
-240
25
-210
-220
-230
20
C7
-210
-280
-200
15
-230
-250
10
10
-220
-240
-280
-200
Djb(n) = -0.77
-210
C6
-240
-270
10
15
-230
-260
-270
-280
-200
10
-200
-280
-200
-230
-240
-250
-260
Djb(n) = -0.38
-270
-280
-280
10
15
20
25
30
Average <Djb(n)>= 0.45/ b unit
Djb(n) = -0.72
10
15
20
25
30
Variation of the phase shift jb in the “a” direction
jb for 12 chains
Phase shift jb (degres)
0
-50
-100
-150
-200
-250
-300
1
2
3
4
5
6
7
8
9
10 11 12
9
10
Column number
With p correction
the phase shift <jb> has a variation of 4
degrees per a unit length in the a
direction.
Phase shift jb (degres)
0
-50
-100
-150
-200
-250
-300
1
2
3
4
5
6
7
8
Column number
11
12
Local phase shift: the variation of jb(n) in the “b” direction
We have previously measured the average phase shift <jb> over 12 CDW for
each TCNQ chain.On a single chain, the local variation of the phase shift jb(n)
can be determinedby selecting only 6 CDW wavelengths centred at y = n.b
jb(10) = -262°
jb(30) = -252°
0,10
Z-deflection (nm)
0,05
0,00
-0,05
-0,10
-0,15
-0,20
0
2
4
6
8
10
12
14
Distance (nm)
-200
Djb(n) in degrees
-210
jb(30)
= -252°
-220
-230
-240
-250
jb(10)
= -262°
We measured a Djb phase shift of
0.15 degrees per b unit length
along a single chain in the b direction
-260
-270
-280
10
15
20
25
30
center position (n) of the fitted data
Local phase shift jb(n) in next image in “b” direction
Experimental cross section BB'
Experimental maxima along BB'
cos(2py/lb + fb) fit
Amplitude (nm)
0.28
0.21
0.14
0.07
0
0
3
6
9
Distance (nm)
12
CDW Domains Size Estimation in TTF-TCNQ
In 1980’s, Fukuyama, Lee, Rice postulated the existence of domain
in the CDW condensate in the weak pinning case. Inside the domain
the variation of phase shift is less than p.
So far, the experimental observations of domains is difficult (Steed
and Fung;? Fleming; ?)
We have measured variations of the phase shift jb for modulation in b
direction
Transverse to the chains (in a direction)
D<jb> = 4 degrees / a unit length
Parallel to the chains (in b direction)
0 < Djb(n) < 0.45 degrees / b unit length
If we defines size domains with L^ and L as the lengths on which the
phase shift varies by 180 degrees:
L^ = ( 180 / 4 )2 . a = 2470 nm  2.5 mm
L = ( 180 / 0.45 )2 . b = 61120 nm  60 mm
Fourier Analysis
Methode d’analyse d’images HR-TEM
M.J. Hyttch (Ultramicriocopy 74 (1998) 131)
2p
0
Selection d’un spot dans le spectre de Fourier
Transformation de Fourier inverse
écart a la périodicité
Phase shift map Dj < p/5
(F. Pailloux, LMP, Univ Poitiers)
Summary
in “a” direction ( commensurate ), CDW is pinned by the lattice with a phase shift ja close
to ~ p/4 relative to the underlying lattice
- in “b” direction ( incommensurate), CDW is weakly pinned by impurities as the phase
shift jb varies smoothly along the chain
-the existence of the jb correlation between chains and the jb vary slowly from chain to
chain., however the change of jb is more important in “a” direction than in “b” direction
the size of the CDW domains in TTF-TCNQ, can be estimated as:
L^ x L = 2.5 mm x 60 mm
STM ability to determine both atomic structure and CDW structure
 resolution of complicated structural details of CDW
CDW complex order parameter Y = D eiF can be studied by STM