Transcript Diapositive 1 - Université Paris-Sud

Preface 1:
STRONGLY CORRELATED ELECTRONIC SYSTEMS AS
UNCONVENTIONAL SEMICONDUCTORS
IN UNCONVENTIONAL CONDITIONS
Comparisons:
Charge Density Waves
Conducting and optically active polymers
Semiconducting and superconducting oxides
Organic conductors with charge ordering and ferroelectricity
After collaborations with :
C. Brun & Z.Z. Wang
Marcoussis
N. Kirova
Orsay
Yu. Latyshev
Moscow
P. Monceau
Grenoble
France
France
Russia
France
Preface 2:
STRONGLY CORRELATED ELECTRONIC SYSTEMS AS
UNCONVENTIONAL SEMICONDUCTORS IN UNCONVENTIONAL CONDITIONS
Fundamental intrigue of many nonstandard conductors:
The energy gap is formed spontaneously by electronic correlations
through various symmetry breakings:
Charge/Spin Density Wave,
Antiferromagnetism,
Charge Ordering
Charge Disproportionation,
Orbital Ordering.
These are volatile states, locally affected by electrons’ injection.
Help from CDWs:
very small electric field deforms the ground state
quite moderate field reaches the microscopic energy scale.
Real time dynamics for reconstruction of a CDW state
under applied field in restricted geometry
Simulations of CDW vortices under increasing voltage – the CDW amplitude
Collaboration:
S. Brazovskii
N. Kirova
Y. Luo
A. Rojo-Bravo
Tianyou Yi
LPTMS, CNRS, Orsay, France
LPS, CNRS, Orsay, France
Université Paris-Sud, France
Boston University, USA
LPTMS, CNRS, Orsay, France
MS
PD
PhD
Outline
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CDW as an electronic crystal and its deformable ground state.
Experiments on nano-junctions.
Dislocations – the CDW vortices.
Time dependent GL approach to numerical modeling.
Results for realistic experimental geometries and parameters.
Stationary and dynamic multi-vortex configurations.
Conclusion
Vortices – the CDW phase
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Zeros of the CDW amplitude at a microscopic scale
identified by the STM as amplitude solitons
C.Brun, Z.Z.Wang, P.Monceau and S.Brazovski 2011
Profiles along the defected chain
vs its nearest neighbor
Defected chain vs theory
 tanh(( x  xs ) /  ) 
sin( 2x /   arctan(( x  xs ) / l ))
Can be viewed also as
branching of stripes at
field-effect dopping.
Topological defects in a CDW.
Solid lines:
maxima of the charge density.
Dashed lines:
chains of the host crystal.
From left to right:
dislocations of opposite signs and
their pairs of opposite polarities.
Embracing only one chain of atoms,
the pairs become a vacancy or an interstitial
or ±2 solitons in CDW language.
Bypassing each of these defects, the phase changes by 2
- far from the defect the lattice is not perturbed.
Dynamic origin of dislocations
v=0
source
Formation of new planes
in the electronic crystal
v~I
drain
Elimination of additional planes
CDW sliding in the applied external electric field – collective motion
of electronic crystal .
To set it in motion at different velocities:
Transfers flow of vortices – thick channels,
Ong and Maki
Coherent phase slip
- thin cannel
Gorkov; Bielis et al.
Direct access to the current conversion via dislocations: Cornell – Grenoble, late1990’s
Another reason for dislocations –
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static equilibrium structures due to applied transverse voltage or current
Dislocation in CDW versus vortex in SC
 SC  C exp( i )
 CDW  A exp( i )
jCDW
e 
 A
 t
2
  A
2
 
2
 2

jSC  C evF
x
2
nCDW
e 
A
 x
2
nSC  C 2
e 
vF t
 [  A] 2  j ext  A 
 2 A  A
2
 [  A] 2  j ext  A
  x  n    n 2scr
  Ax
2
  y   E y  H z    y Ax
Equivalence of given Ey and Hz upon the order parameters.
Dislocations in CDW appear as vortices in SC.
Reverse effect of order parameters upon the fields are opposite:
CDW – electric field is screened via dislocations.
SC - magnetic field enters via vortices
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Intra-plain elasticity (∂x )2 + Coulomb energy  (y)∂x
force to shift the equilibrium CDW charge density ∂ x- (y), i.e.
the CDW wave number  =Qx - (y)x
Breaking of inter-plane correlation.
Resolution : dislocation lines allow to bring new periods in a
smooth way, except in a vortex core.
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Decoupling threshold: arrays of solitons or dislocations.
Discommensurations in a two layers model.
Minimal model: Interlayer decoupling as an incommensurability effect.
Only two layer 1,2 kept at potentials ±V/2

 v
W   dx F

 4
 d1  2  d2  2  V
 
 

 dx   dx   2


 d1 d2 


  J cos1  2 
dx 
 dx


Lattice of discommensurations (solitons in phase difference )
Develops from the isolated discommensuration = the 2π soliton in ∆ .
 x    2 x   1 x   2 Arc cos(tanh( x / l ))
l  J 1/ 2
Critical voltage = the energy necessary to create the first discommensuration: J1/2
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In reality : CDW junction as an array of dislocation lines DLs.
A bulk of many planes, voltage difference monitored at its sides.
Lattice of discommensurations =>
sequence of DLs - vortices of the ICDW phase
Critical voltage - DL entry energy, like Hc1 in superconductors.
(Old theories by Feinberg-Friedel, S.B.-Matveenko)
Recall a parallel topics – plastic flows of ICDW with multiple generation of DLs
within the current conversion area of a junction.
Space-resolved X-ray experiments of Cornell and Grenoble,
theory by N.Kirova and S.B.
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Excitations or stable perturbations
Pair-breaking energy
Eg=2
(to be précised)
One-particle adding energy ∆1
(≠ in general)
In 2D,3D ordered phases, T<Tc<<  :
Dislocation = 2 vortex of
Addatoms/vacancies = particles with charges ±2e =
minimal pairs of dislocations (2D) /dislocation loop (3D) on one chain = 2
solitons
Phase slips:
Microscopically – a self-trapping of electrons into solitons with their subsequent
aggregation
Macroscopically – the edge dislocation line proliferating/expanding across the
sample.
Low T: the energetics of dislocation lines/loops is determined by the Coulomb
forces and by screening facilities of the free carriers.
Electrons  Amplitude solitons 2 phase solitons
Phase slips
D-loops/lines
Motivation for our modeling : Experiment on tunnel junctions
Yurii Latyshev technology of mesa-structures:
fabrication by focused ion beams.
All elements – leads, the junction –
are pieces of the same single crystal whisker NbSe3
Overlap junction forms a tunneling bridge of 200A width -only 20-30 atomic plains of a layered material.
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Direct observation of solitons and their arrays in tunneling on NbSe3
Y. Latyshev, P. Monceau, A. Orlov, S.B., et al, PRLs 2005 and 2006
creation of solitons at ≈2/3 :
Es=2/ !
oscillating fine
structure
peak 2 for intergap
creation of e-h
pairs
absolute
threshold
at low Vt≈0.2
All features scale with the gap (T) !
First degree puzzle:
Why the voltage is not multiplied by N~20-30 - number of layers in the junction
- It seems to be concentrated at just one elementary interval.
In similar devices for superconductors the peak appears at V=2 *N
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Junction reconstruction by entering of dislocations
Fine structure is not a noise !
It is : sequential entering into the junction area of
dislocation lines = CDW vortices = solitons‘ aggregates.
Need a complex modeling for intricate distributions of
the order parameter (amplitude and the phase),
electric potential, normal density and normal current.
Recall a new science: field effect transformations in strongly correlated materials
Their symmetry broken phases will be subject to reconstruction.
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Known from analytic static solutions for an infinite CDW media:
Potential distribution in a DL
vicinity. Notice concentration of
potential Ф(x,y) drop facilitating
the tunneling.
3d and contour plots ±y(x)
for surfaces Ф(x,y)±∆ where
the tunnelling takes place.
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What does tunnel at these low subgap voltages ?
±2π phase solitons stretching/squeezing of a chain by one
period with respect to the surrounding ones: elementary
particles with the charge ±2e and the energy E~Tp 3D
ordering temperature Tp.
Outcome :
pair of 2 solitons can be created by tunneling almost
exclusively within the dislocation core,
The process can be interpreted as a excitation of the
dislocation line as a quantum string.
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Before the reconstruction:
Distribution of potentials (values in colours, equipotential
lines in black) and currents (arrows) for moderate conductivity
anisotropy ( ||/ =100).
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Junction reconstruction with cross-sections of dislocations.
Junction scheme with
crossections of dislocations
The very low sharp threshold voltage Vt ~ 0.2 Δ can be provided only by the low
energy phase channel, and the experiment also indicates that the voltage
applied to the whole stacked junction drops mostly at a single elementary
interlayer spacing.
It can happen when the electric field in this junction exceeds a threshold value
for phase decoupling in neighboring CDW layers.
This decoupling is expected to proceed via the successive development of
dislocation lines entering to the junction area.
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GL – like model
e 
jCDW   A2
 t
H CDW
  A exp( i )
nCDW  A 2
H=HCDW+Hel

3   0 0
  d r
4s


 

 x
2
e 
 x
2

 
0
2
2 

 ln


y  2 0 s
e 


2
2



A


2
3
H el   d r 
 (n( )  n(0)) / d z 
  F (n)
8
 s  x

n( ) 
n0T
F

 F   
ln 1  exp 

 T 

vF
0 
0
Only extrinsic carriers n are taken explicitly.
Intrinsic ones, in the gap region, are hidden
in the CDW amplitude A.
EF
-PF
PF
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Boundary conditions
Equations
00
 2
2 
 A  
A     A
2
x
t
2
CDW stress vanishes at the boundaries:
Natural for sides, for drain/source
boundaries the no-sliding is implied
00 2

A
2

 A  A( ) 2   0 A ln A   A
2
0
t

 2
1  n( )  n0
 

4
s x
dz
n
n
j 
     
0
t
t
Normal electric field is zero at all
boundaries:
total electro neutrality and
confinement of the electric potential
within the sample
No normal current flow at the boundaries
except for the two source/drain boundaries
left for the applied voltage.
There, the chemical potentials are applied:
      V ;
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Simplified rectangular geometry assuming passive role of other parts
Amplitude V=7meV, 9 meV, 11 meV; t~10-8 sec
Phase: wider sample, higher V
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Many vortices appear temporarily in the course of the evolution.
For that run, only two will be left.
Time unit – 10-13 sec given by the inverse CDW conductivity.
Here, t~100ps – 10GHz
Real geometry: initial short time fast dynamics, t=3.4x10-10 sec
Amplitude A
Unexpected result: long
living traces of the amplitude
reduction following fleshes
of vortices.
2
2




2   
2 
 
W ( )  A 
   
 x 
 y  
W( )+W(A)
W( )=0
Phase
1
Composite energy W( )+W(A)
All these 5 flashes are the phase-slip processes
serving to redistribute the CDW collective charge
A
Phase deformations energy cannot relax fast enough
following the
rapidly moving vortex.
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Real geometry: final stationary state at the first threshold voltage
A
V=7-8 meV, t=10-7 sec

z
Strong drop of the
electric potential
(with inversion !)
and of the
current concentration.
Perturbations
are concentrated near the
vortex core –
the location of tunneling
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processes.
Movie for a full multi-vortex evolution to the junction stationary state
with just one remnant vortex
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Distributions of the chemical potential zeta, electric potential phi,
electro-chemical potential zeta+phi; lines of current.
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I(V) and dI/dV,
slits geometry
I(V) and dI/dV,
rectangular geometry
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Conclusions.
Modeling of stationary states and of their transient dynamic for the CDW in
restricted geometries is reachable.
Model takes into account multiple fields in mutual nonlinear interactions:
the complex order parameter Aexp(i ) of the CDW, and distributions of the
electric field, the density and the current of normal carriers.
Vortices are formed in the junction when the voltage across, or the current
through, exceed a threshold; their number increases step-wise in agreement with experiments.
A much greater number appears in transient processes
The vortex core concentrates the total voltage drop, working as a self-tuned
microscopic tunnelling junction, which might give rise to observed peaks of the
inter-layer tunneling .
Parameters need to be adjusted – e.g. the conductivity increased.
The reconstruction in junctions of the CDW can be relevant to modern
efforts of the field-effect transformations in strongly correlated material
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which also show a spontaneous symmetry breaking.
Conclusions II:
Specifics of strongly correlated electronic systems :
inorganic CDW, organic semiconductors,
conjugated polymers, conducting oxides, etc…
Electronic processes, in junctions at least, are governed
by solitons or more complex nonlinear configurations.
As proved by presented experiments and recent ones
on charge ordered states, they can lead to :
• Conversion of a single electron into a spin solitons
• Conversion of electrons pair into the 2 phase slip
• Pair creation of solitons (tunneling and optics)
• Arrays of solitons aggregates
– dislocation lines, stripes, walls of discommensurations –
reconstruct the junction state and provide
self-assembled micro-channels for tunneling;
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