JUNCTION RECONSTRUCTION AND DYNAMICS OF DISLOCATIONS IN
CHARGE DENSITY WAVESCHARGE DENSITY WAVES.
N. KirovaLPS, CNRS and Université Paris‐Sud, Orsay, France
C ll b tiCollaboration:S. Brazovskii LPTMS, Orsay, FranceT. Yi LPTMS, Orsay, France
Thanks:P. MonceauYu. Latyshev
A. Roho Bravo Boston Uiversity, USAY. Luo Université Paris‐Sud, France
Incommensurate charge density wave
Order parameter: y=Acos(q0x+φ)Order parameter: y=Acos(q0x+φ)
•Periodic lattice distortion : u(x)=u0sin(q0x+φ) –Periodic lattice distortion : u(x) u0sin(q0x φ)observed by diffraction (X-Ray), information in reciprocal space u(q).
•Modulation of the electronic density ρ(x) ~– ∂u(x)/∂xuniaxial crystal of singlet electronic pairs electronic CDW observed by STM – information in direct space
Important feature: CDW sliding in the applied external electric field– collective motion of the electronic crystal (Monceau and Ong)
2
Dislocations in a CDW.
Solid lines: maxima of the charge density. h d li h i f h h lDashed 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 ± 2 solitons in CDWan interstitial 2 solitons in CDW
By passing each of these defects, the phase changes by 2Far from the defect the lattice is not perturbed.
Dynamic origin of dislocations
source drain DW stress is releasedsource drainv=0
v~IDW stress is released
Formation of new planes inElastic DW stress
CDW sliding in the applied external electric field – collective motion of electronic
Formation of new planes in the electronic crystal Elimination of additional planes
g ppcrystal .
Direct access to the current conversion via dislocations: Space resolved X‐ray studies
2
4
6x 10
−4
Sample with a single strong planar defect, almost complete current
−4
−2
0
2
q sh
ift (
b*)
, preconversion → full plasticity(transverse flow of dislocations)
4−2 −1 0 1 2
−6
−4
x (mm)
D. Rideau et al, Europhysics Letters 56 (2001) 289
Static origin of dislocations
V
Static equilibrium structures due to applied transverse voltage or current
FV
Breaking of inter‐chain correlation:
‐V
Intra‐chain elasticity (∂xj)2 + Coulomb energy F(y)∂xjforce to shift the equilibrium CDW charge density ∂jx‐F(y), i.e. the CDW wave number j=Qx ‐F(y)xthe CDW wave number j=Qx F(y)x
Resolution : dislocation lines allow to bring new periods in a smooth way, except in a vortex core.except in a vortex core.
N i fi ld ff t t f ti i t l l t d t i l
5
New science: field effect transformations in strongly correlated materialsTheir symmetry broken phases will be subject to reconstruction.
Yurii Latyshev technology of mesa‐structures (Yu. L. Friday, Sect XV).All elements – leads, the junction – are pieces of the same single crystal whisker NbSNbSe3
Overlap junction forms a tunneling bridge of 200A width ‐‐only 20‐30 atomic plains of a layered material.
Distribution of potentials (values in colours, equipotential lines in black)and currents (arrows) for moderate conductivity anisotropy (s||/s =100)and currents (arrows) for moderate conductivity anisotropy (s||/s^ 100).
6
Direct observation of solitons and their arrays in tunneling on NbSe3Y. Latyshev et al, PRLs 2005 and 2006
All features scale with the gap (T) !
peak 2 for inter‐gap creation of e‐h pairs
Absolute threshold oscillating fine structure
at low Vt≈0.2
Puzzles: 1 Origin of the low threshold at V1. Origin of the low threshold at Vt.2. Why the voltage for the “normal” 2peak is not multiplied by N~20‐30 ‐
number of layers in the junctionI b d j l i l
7
‐ It seems to be concentrated at just one elementary intervalIn similar devices for superconductors the peak appears at V=2D*N
Charge carriers and potentials
Intrinsic carriers : the spectrum is formed by the CDW gap, energies move up and down with changes of the Fermi level vchanges of the Fermi level
Extrinsic carriers in semimetallic DWs (NbSe3 ):
xF
FvE 2
their spectrum is unaffected by the gap, nex, jex, Vex(Dark matter) .Collective variables : =q n = /π; j =‐ ; ρ =1‐ρ
T 01Collective variables : x=q, nc= x/π; jc=‐ t; ρc=1‐ρi
cTT0
Potentials :reciprocal x
Fin
vV 2
exV
inFxF nvvU 22
1
DW stressDW stress contributions: electric elastic nonequilibrium
8
2U – energy per chain paid to distort the CDW elastically by one period
Ginzburg‐Landau – like model )exp( iA
H=HCDW+Helt
eAjCDW
2
xeAn CDW
2
rdH2
202
22
003 ln
CDW el
esyxsrdH CDW
0
ln24
)(8
)( 20
23 nFn
xA
srdH el
0 FvEquation of state for n()
00
Only extrinsic carriers n are taken explicitly.Intrinsic ones in the gap region are hidden
q ()
9
Intrinsic ones, in the gap region, are hidden in the CDW amplitude A.
Boundary conditionsEquations
tAA
xA
2220
2
CDW stress vanishes at the boundaries:Natural for sides, for drain/source bo ndaries the no sliding is implied
AAAAA A
222 ln1)(1
boundaries the no‐sliding is implied
t
AAAA A
2
0
ln)(2
1 s
Normal electric field is zero at all boundaries:
)(14
22
n
xes
total electro neutrality andconfinement of the electric potentialwithin the sample
0
tn
tnj
p
No normal current flow at the boundaries t f th t /d i b d iexcept for the two source/drain boundaries
left for the applied voltage. There, the chemical potentials are applied:
Near the vortex core5ö;V
10
Near the vortex core 5ö,Hence Aö0
Dislocation in CDW vortex in SC
)exp( iA
eAj 2eAnCDW
2 e 2
eCn 2
)exp( iC
tAjCDW
x
AnCDW x
eCjSC
2
tCnSC
2 e
2
2
x
n
n
22
AAce
scrn Aj ext
EE )00()00()00( AAyEE )0,0,()0,0,(),0,0( HyAAHH x
Equivalence of given E and H upon the order parametersEquivalence of given Ey and Hz upon the order parameters.Dislocations in CDW appear as vortices in SC.Reverse effects order parameter upon the fields are different:
i f h l l i fi ld b di l i
11
CDW: screening of the external electric field by dislocationsSC: magnetic field enter via vortices
Simplified geometry
Amplitude V=7meV, 9 meV, 11 meV; t=2x10‐8 sec
Ph id l hi h VPhase: wider sample, higher V
12
Simplified geometry
Many vortices appear temporarily in the course of the evolution.y pp p yFor 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 AUnexpected result: long living traces of the amplitude
d ti f ll i fl h
Amplitude A
reduction following fleshes of vortices.
W(j)+W(A)Phase j
2
22
2)(yx
AW
1
W(j)=0
Ph d f i
1A
Phase deformations energy ‐cannot relax fast enough following thegrapidly moving vortex.
14
Real geometry: final stationary state at the first threshold voltage
V=7meV, t=10‐7 secDetails: T. Yi, Poster P21
Strong drop of the electric potential and
A
pthe current density perturbations
t t dj
are concentrated near the vortex core –the location of tunneling
j
processes.
15
Analytic static solutions for an infinite CDW media:
Potential distribution in a DL vicinity. Concentration of potential Ф(x,y) drop facilitating the tunneling.
3d and contour plots ±y(x) for surfaces Ф(x y) ±∆ wheresurfaces Ф(x,y)=±∆ where the tunnelling takes place. 16
Problems with Ginzburg‐Landau – like model
Well established and works for stationary state . Takes into account the extrinsic carriers (not interacting with the CDW)R i iRestrictions:The intrinsic carriers have been integrated out and come into the model only via order parameter total charge =0model only via order parameter, total charge =0, Rem. boundary conditions En=0 Cannot take into account: Charge conservation for the condensateCannot take into account: Charge conservation for the condensate (Violating of charge conservation)
A 2 A 2only if
jdx
Anc
2
tAjc
2 A = const 0
xj
tn
dtdn cc
In our case A(x y t)0 022 AAdn
17
In our case A(x,y,t)0 0
txtxdt
1D intrinsic carriers are taken explicitly into accountForbidden : scattering in the frame of the host lattice ‐ no impurities Allowed: scattering by CDW phonons; electronic collisions
More general scheme :
Local frame of the floating CDW = chiral transformation 2/exp i
FvEE xkkk
Allowed: scattering by CDW phonons; electronic collisions
Aeevit
i xF
xFF EE 2
200 FFF kkk
tv
xv
cxt
LFF
l
22
vv
Acee
xvi
ti
L
FF
xF
el
tv
xv FF
22
vee
xvee F
2
tvA
ceA
ce F
xx
2
22
2
2
22
2 12 tcxvEFE F Gauge and chiral invariant field
acting upon electrons
Local energy functional )exp( iA
2
22
222
44,,,,
yA
xAvCAvAnnW F
yxF
exin
inx
Fex
xF nveneA
Av
2ln
2
22
20
e 22 0
),,(8
2exin
h nnAs
xi ; ‐ charge density
8
A=
i
i x; g y
Δ=2π = CDW period = 2 electrons
(Δ,nin,nex) free energy of normal carriers2Δ CDW gap (the gap for intrinsic carriers)n n concentrations of intrinsic and extrinsic free carriers
19
nin, nex concentrations of intrinsic and extrinsic free carrierss area per one chain
Good verification of the new scheme: we get the vortices nucleated.Bad news: we cannot launch them from the boundaries to proliferate across – the program crashes at the singularityacross the program crashes at the singularity.The verified results (height – the amplitude, contours – the phase).Parameters were chosen such that A vanishes when the chemical potential of electrons exceeds Z* 0 25Δ T 0 1Δchemical potential of electrons exceeds Z*=0.25Δ. T=0.1Δ
Intermediate states, several nodes try to develop.
Final achieved states: only one vortex develops in full.
Averaged description: distributed current conversion via many unresolved phase slips – sweeps of dislocations.Adapting the model used successfully to describe space 0
2
4
6x 10
−4
ft (b
*)
Adapting the model used successfully to describe space resolved X‐ray studies
−2 −1 0 1 2
−6
−4
−2
0
q sh
ift (
Electric potential – arbitrary units.Expected perturbation – at the slits' tips
−2 −1 0 1 2x (mm)
Expected perturbation at the slits tipsArtifacts – at the slits' bases.Intriguing, of the opposite sign andaccompanied by 2 phase increments :accompanied by 2 phase increments :at the slits' middles on the level of another slit tip.
Plot of the amplitude A withPlot of the amplitude A with streamlines of the normal current.The current jet is formed from far away.Hitting the obstacle the jet burns downHitting the obstacle, the jet burns down the CDW which facilitates the current conversion.
Conclusion.
We have performed a program of modeling of stationary states and of their transient dynamic for the CDW in restricted geometries. lik d l (i d i i i i ) d i f i f iFor GL like model (integrated out intrinsic carriers) dynamic formation of vortices and final reconstruction of mesa junction with formation of vortices has been studied. The results are in agreement with experiments. For more general scheme : we get the vortices nucleated. But till now we cannot launch them from the boundaries to proliferate ‐ calculation problems.
Local and non stationary processes in CDWs under the applied electric fieldLocal and non stationary processes in CDWs under the applied electric field or injecting currents in squeezed geometry suggest a new playground for methods and concepts of the IMPACT meeting
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