Mesoscopics and interlayer tunneling spectroscopy of charge density waves Yu.I. Latyshev Institute of Radio-Egineering and Electronics RAS, Mokhovaya 11-7, 125009 Moscow, Russia In collaboration with A.P. Orlov, V.N. Pavlenko, A.M. Nikitina IREE RAS, Moscow A.A. Sinchenko MEPhI, Moscow P. Monceau, O. Laborde, Th. Fournier CRTBT-CNRS, Grenoble B. Pannatier S.A. Brazovskii LPTMS-CNRS, Orsay L.N. Bulaevskii LANL, Los Alamos, USA At the early stage T. Yamashita, T. Kawae, T. Hatano NIMS, Tsukuba, Japan
Transcript
Mesoscopics and interlayer tunneling spectroscopy of charge density waves
Yu.I. LatyshevInstitute of Radio-Egineering and Electronics RAS, Mokhovaya 11-7,
P. Monceau, O. Laborde, Th. Fournier CRTBT-CNRS, Grenoble
B. Pannatier
S.A. Brazovskii LPTMS-CNRS, Orsay
L.N. Bulaevskii LANL, Los Alamos, USA
At the early stage
T. Yamashita, T. Kawae, T. Hatano NIMS, Tsukuba, Japan
OUTLINE
1. Introduction to the CDW state.
2. Introduction to the CDW mesoscopics: (a) Aharonov-Bohm effect on columnur defects, (b) reflection at the N-CDW boundary, (c) coherent phase slippage on CDW nanowires.
3. Introduction to the interlayer tunneling.
4. Spectroscopy of CDW energy gap and intragapstates. Coherent interlayer tunneling.
5. CDW Phase dislocation lines. Analogy with HTS.
6. Conclusions.
Introduction
Peierls transition. CDW state.The gap is opened at the Fermi-surface due to the pairing of electrons and holes at the opposite parts of the FS with total momentum 2pF. As a result, correlated electron density is spatially modulated with the wave vector 2kF
The order parameter in the ground state is Δ0 =A cos (Qx + ϕ) with Q the CDW wave vector Q = 2kF and ϕ the arbitrary phase in the incommensurate (ICDW) state. CDW conductors are usually chain conductors with flat parts of FS providing nesting condition.
3 4 5 6 7 8 9 10 11 121m
10m
100m
12
S2 S3 S4
o-TaS3 I =1uA
R/R
(90K
)
1000/T0 50 100 150 200 250 300 350
0.0
0.2
0.4
0.6
0.8
1.0 NbSe3 #4-3
Rb
Ra*
norm
aliz
ed re
sist
ance
(Ω)
temperature (K)
NbSe3 Tp1=145K, Tp2=59K, still ungapped pockets at low temp.
o-TaS3, Tp=215K, fully gapped
CDW collective transport along the chains. Phenomenology.
Schematic chain structure of MX3 compounds
Threshold for CDW depinning
Froelich model of superconductivity
Froelich 1954
Incommensurate CDW sliding along the chains can provide superconductivity since the phase of the OP is not coupled with the lattice.
Experiment showed that there is significant CDW pinning on charged impurities. However, collective CDW transport was found above threshold for CDW depinning. P. Monceau et al. 1976, NbSe3
o-TaS3
NbSe3
A.Zettl and G.Gruener 1982
Narrow band noise and Shapiro steps
Fleming and Grimes 1979
two-fluid model
Itot = In + Icdw
f ∝ ICDW P. Monceau 1980
ICDW /f ∝ N, the number of condensed electrons
Jcdw/f =2e per chain
A. Zettl and G.Gruener 1984
Yu.I. Latyshev et al.1987
Shapiro steps II. Mode locking regime
Complete mode locking
Hall and Zettl, 1984
R. Thorne et al. 1988
CDW can slide phase coherently over the whole sample length of about 1mm
The differential resistance in the mode-locking regime is an indicative of coherency of CDW motion. Under complete mode locking CDW moves coherently between potential probes
Classical versus quantum description of the CDW transport
CDW as classical object (rigid or deformable) in periodic potential
G.Gruener, A.Zawadowski and P.Chaikin 1981
L.Sneddon, M.Cross and D. Fisher 1982
P. Pee and H. Fukuyama 1978CDW as a quantum object, possessing quantum coherence.
Quantum tunneling ransport: J. Bardeen 1979, 1980, 1985
Aharonov-Bohm effect on CDW rings: E.N. Bogachek et al. 1990
Andreev-type reflection on the N-CDW interface: A. Kasatkin and E.Pashitskii 1984
CDW/N/CDW, N/CDW/N coherent transport M Wissher and G.E.W Bauer 1996
Until recently there were no clear evidence of quantum CDW transport on macroscopic samples. That stimulated the searching of quantum coherence on mesoscopic scale.
Searching for Aharonov-Bohm effect of sliding CDW
Aharonov-Bohm effect of sliding CDW on columnar defects with trapped magnetic flux
Theoretical prediction: E.N. Bogachek, I.V. Krive, I.O. Kulik, A.S. Rozhavsky PR B 1990 small ring of CDW conductor with diameter of the order of CDW coherence length should provide A-B flux quantization with “superconducting” flux Φ0=hc/2e
Experimental idea: To use a thin sample containing massive of columnur defects. Diameter of each columnur defect D ≈ 10 nm ≈ ξCDW. All CDs are absolutely identical, since each one is produced by identical heavy ion. The phases of the all local CDWs can be synchronized in the complete mode locking regime. In magnetic field, oriented along the CD axis, CD traps flux and works as a local solenoid.
Columnur defects in NbSe3
CD – is a long (~ 10μm)uniform cylinder of amorphous (non conducting) matter.
c=3109def/cm2
TEM, bright field HREM
First experiment
Threshold current is ≈ 100 μA, T=50K
A-B effect is observed only in sliding CDW state and corresponds to flux quantization Φ0=hc/2e , i.e.
ΔHπD2/4 = Φ0
Yu.I. Latyshev, O. Laborde, P. Monceau and S Klaumuenzer 1997
averaged picture
Further experiments
Yu.I.Latyshev, O.Laborde, Th. Fournier and P.Monceau PR B1999
Effect was reproduced on 4 samples
Is well reproduced for low CD concentration c< 1010def/cm2 on freshly irradiated thin samples d< 1μm. For those samples complete mode locking is achieved
The effect was observed only in field orientation along the CD axis and not in a perpendicular orientation
A-B experiment. Conclusion and remarks.
The A-B effect is a result of quantum interference of the CDW coherently moving through the massive of CDs with trapped magnetic flux.
We found that the A-B effect was not observed under conditions when phase coherence of moving CDW was not available: thick crystals, high defect concentration (that can be controlled by the absence of complete mode locking regime). The effect observed only on freshly irradiated samples and disappeared after about a month of keeping at room temperature, because the recrystallization destroys theidentity of CDs.
Searching for Andreev-type reflection at the N-CDW interface
Andreev reflection at the N-S interface
Andreev reflection at the N-S boundary. A.F. Andreev, Sov. Phys. JETP, 19, 1228 (1964).
A particle incident from the normal metal changes its charge and all momentum components upon reflection. In this case a charge of 2e is carried through the interface as a Cooper pair, whereas the reflected particle moves back along the incident trajectory. AR is a result of the interaction of incident particle with the whole condensate.
How to observe that?
Van Kempen method P.C van Son, H. van Kempen and P. Wyder, 1987
Andreev-type reflection at the N-CDW interface
A.Kasatkin and E.Pashitskii 1984 stated that at the N-CDW interface the reflected particle should not change charge, but all momentum components as in AR.
In that case in van Kempen geometry on N-CDW boundary one could expect to observe mirror reflected picture to compare with N-S boundary
Experiment N-N-CDW
A.A. Sinchenko, Yu.I. Latyshev, S.G. Zybtsev and I. Gorlova, Sov. JETP 1986
The value of the gap found 2Δ≈100 mV is consistent with optics and thermo-activation of conductivity data in K0.3MoO3 : C. Schlenker and J. Dumas, Phil. Mag. 1985
Experiment on N-CDW reflection II.
However, reflected signal was small(two orders less then expected) and was proportional to a2/d2, where a is the contact diameter, d is the thickness of the normal-metall film.
That is consistent with a conclusion that only carriers incident along the chain direction can be reflected by Andreev-type way. That implies that in this case the momentum 2pF can be transferred through the boundary into the CDW condensate.
Charge-momentum duality in S-N-S and CDW-N-CDW transport has been considered by M.I. Vissher and A.F.G. Bauer PR B 54, 2798 (1996)
S CDW
Cooper pair e-h pair
Q=2e, P=0 P=2pF, Q=0
N-S interface: N-CDW interface:
Q is transferred P is transferred
Coherent CDW phase slippage on submicron scale
CDW motion and phase slips
Normally, CDW transport in bulk samples is characterized by a transformation of the normal current into the CDW current nearby the current contacts. That transformation occurs via the strain induced phase slippage. That results in the CDW stress and periodic suppression of the CDW amplitude while the CDW phase is increased by 2π :L.P. Gor’kov 1983, N.P. Ong and G. Verma, 1984.
How to measure?
The energy, necessary for formation of phase slip, eVps, can be found by the Gill method J.C. Gill, 1986. That was found that Vps does not dependent on sample length down to 20 μm M.P. Maher et al 1995.
Correlated phase slippage for CDW transport in nanowires
We found that the energy Vps is significantly (by several times) reduced for specimens of submicron scale.
First it was shown oh the arrays of nanowires of local length below 0.5 μm Yu.I.Latyshev, B.Pannetier and P.Monceau Eur. Phys.B 1998
and then has been approved on the individual wires of various lengths down to ½ micron O.C. Mantel et al.PRL 2000.
Vps reduction with the distance between current leads
We suggested that with a decrease of the distance two phase slips become time correlated (coherent) and that reduces the energy for their formation. That points out that at submicron scale CDW acquires quantum coherence.
The experiment has been supported by microscopic calculations by S.N. Artemenko, PR B, 2003
Introduction to interlayer tunneling in layered
superconductors
The amplitude of the OP is vertically modulated, while phases are coupled. One can expect both phase interference effect and quasiparticle tunneling.
Introduction to intrinsic Josephson effects (IJE) and Josephson flux-flow (JFF) in layered HTS materials
IJE - Josephson effects on naturally layered crystalline structure of layered superconductors
Early ideas in 70-s: W.E.Lawrence, S.Doniach1971L.N. Bulaevskii 1973
Further development in 90-s, after discovery of HTS
L.Bulaevskii, J.Clem, L.Glazman 1992
stationary IJE for short stacks L< 2λJ,
λJ, = s λc /λab~ 1μm in Bi-2212
ehc
sLH
sLH
IHI cc 2|
)sin(|)( 0
0
00 =Φ
Φ
Φ= π
π
sLLL
I. Phase effects
Yu.I.Latyshev, N. Pavlenko, S-J.Kim, T.Yamashita ISS-99, Morioka, Physica C 2001
Bi-2212 stack: L=1.4 μm, s=1.5 nm, ΔH=1.01 T
First experimental evidence of IJE: R.Kleiner, P.Mueller et al. PRL 1992
R. Kleiner and P.Mueller PR 1994
They had junctions of big lateral size ~ 30 μm and Fraunhoffer oscillations of critical current were not so clear
Phase interference. Intrinsic DC Josephson effect
Long stack, L>>λJJosephson vortex (phase topological defect). No normal core.
J. Clem and M.Coffey, PR 1990
Josephson-vortex lattice (JVL)L. Bulaevskii and J. Clem, PR
1991
Dense lattice can move as a whole being driven by DC current across the layers
200
ssBB
Jcr πγλπ
Φ=
Φ=>
Dense Josephson-vortex lattice
L. Bulaevskii, D.Dominguez et al. PR 1996
γ~103 Bcr~0.3T
H
V
I
λJ
λab
Josephson vortices
Phase coherence is locally broken with appearance of JV at H>Hc1
Linear ff, low fields J.U Lee et al. 1995------------------------------------------------------------------
ff-step B≤1T Yu. Latyshev, P. Monceau et al. Physica C 1997------------------------------------------------------------------
ff-step B<0.3T G. Hechtfischer et al. PR 1997------------------------------------------------------------------
ff-step 0.5<B<3.5T G. Hechtfischer et al. PRL 1997
Experiments
~0.1% c
Josephson flux-flow regime
ehfNVst 2
1 = with N=57Yu.Latyshev, M.Gaifullin et al. PRL 2001
Experimental ways to identify JVL
(1) Shapiro step response in JFF regime to subterahertz external radiation. Coherent response of 60 elementary junctions
II. Quasiparticle tunneling over a gap: multibranched IVs, gap/pseudogap spectroscopy
Yu.I. Latyshev et al.ISS Conf. 1999, Physica C, 2001; V.M. Krasnov et al. PRL, 2000, 2001
Interlayer tunneling
in layered CDW materials
CDW interlayer tunneling spectroscopy: NbSe3
The elementary prisms are assembled in elementary conducting layers with higher density of conducting chains (shaded layers in a figure) separated by a double barrier of insulating prism bases. That results in a very high interlayer conductivity anisotropy σa*/σb ~ 10-3 at low temperatures compared with intralayer anisotropy σc/σb ~ 10-1.
That provides a ground for interlayer tunneling spectroscopy of CDW layered materials..
FIB microetching methodYu.I. Latyshev, S.-J. Kim, T. Yamashita, IEEE Trans. on Appl. Sup. 9 (1999) 4312.S.-J. Kim, Yu.I.Latyshev, T. Yamashita, Supercond. Sci. Technol. 12 (1999) 729.
TaS3 mesa fabricated by lateral FIB etching method
NbSe3 mesa
Typical mesa sizes 1μm x 1μm x 0.05-0.2μm
CDW gap spectroscopy. Zero bias conductance peak (ZBCP)
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.150.0
0.2
0.4
#4-3 4.2K
dyna
mic
con
tuct
unce
( O
hm-1)
voltage (V)
(a)
2Δ1
2Δ2
NbSe3: low temperature interlayer tunneling spectra
Yu.I. Latyshev, P. Monceau, A.A.Sinchenko, L.N. Bulaevskii, S.A. Brazovskii, T. Kawae, T Yamashita,. J.Phys. A, 2003
Coexisting of both CDW gaps, zero bias conductance peak (ZBCP)
2Δ2 ≈ 50-60 mV,
2Δ1 ≈ 130-150 mV
Consistent with STM, optics and low temperature ARPES data
Temperature evolution of the spectra
-0.2 -0.1 0.0 0.1 0.2
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
61.3595652.6
48.342363025K
dyna
mic
con
duct
ance
(1/O
hm)
-0.2 -0.1 0.0 0.1 0.2-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4NbSe3 stack #4-3
20
15
8
6K
dyna
mic
con
duct
ance
(1/O
hm)
(a) 2Δ2 2Δ1
Point contact spectra NbSe3-NbSe3 along the a*-axis A.A. Sinchenko et al., 2003
Stacked junction behaves as a single junction. We consider that as the weakest junction in the stack.
Integral density of states
In spite of very sharp variation of dI/dV within CDW gap the integral
density of states S= V0= 200 mV does not change at both
Peierls transitions similarly as in superconductors∫
−
0
0
)(/V
V
dVVdVdI
Interaction of both CDWs in NbSe3
0 20 40 60 80 100 120 140 1600
50
100
150
200
250
300
350
40 50 60 700.0
0.2
0.4
0.6
0.8
1.0
1.2
δΔ1, Δ
2 , Δ2 2, n
orm
. uni
ts
T (K)
α∗δΔ1
Δ2
(Δ 2)2
V (m
V)
T(K)
Vg1
Vg2
NbSe3 N1
BCS
δΔ1
A.P. Orlov, Yu.I. Latyshev, A.M. Smolovich, P. Monceau, JETP Lett. 2006
)(2cos)( 2122
21
422
222112 ϕϕ +ΔΔ+Δ+Δ+Δ= +BBAFF
2
2122
2)||(
BBA Δ−
=Δ +
q1 = (0, 0.241, 0), q2 = (0.5, 0.260, 05)Joint commensurability effect with reciprocal lattice:2(q1+q2) ≅ (1,1,1)R.Bruinsma and S.Trullinger PRB,1980found an additional term in the GL energy due to this commensurability effect and predicted some enhancement of Δ1 in the presence of Δ2
However, this effect has not been observed until recently. Instead, it was found the effect of dynamical decoupling of two CDWs in sliding state A.Ayary et al. PRL 2004
Using interlayer tunneling technique we found the effect of enhancement of Δ1 in the presence of Δ2: δΔ1 ≈ 0.1 Δ.1
101
10
theory
NbSe3 stack #4-3no
rmal
ized
ZB
CP
am
plitu
de
temperature (K)
-0.02 -0.01 0.00 0.01 0.020.0
0.2
0.4
0.6
0.8
1.0
1.2
experiment
theory
NbSe3 stack # 4-3 @ T=4,2 K
norm
aliz
ed d
ynam
ic c
ondu
ctan
ce
voltage (V)
Zero bias conductance peak Bulaevskii theory of coherent tunneling of the ungappedcarriers L.N. Bulaevskii, JETP Lett. 2002.
Coherent tunneling implies the conservation of particle in-plane momentum in the process of tunneling. This is necessary because the pockets represent some localized small parts of the Fermi surface and electron momentum should not be scattered beyond the pockets by tunneling from one layer to another. The width of ZBCP characterizes the energy uncertainty for the state characterized by momentum p.
)( 11 −− += insc ττγ h
1]*)(/[/1),0( −+=∝ incmTeT γμγσ h
2222
2222
)4(44
)0()(
γγγ
σσ
+−
=Ve
VeVFitting parameters: γeff = 0.25 mV, γsc= 0.13 mV, N=30, m*=0.24 me, μ(T) was taken from the paper of N.P.Ong PRB 1978
)4(2||)0()( 2223
2
γπγ+
=Ve
eVtNVI
for dI/dV
Intragap states: NbSe3
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.522
24
26
282Δ1
2Δ1/3dI
/dV
(kO
hm-1)
V/2Δ1
T=100 K
Vt
There are two new features inside the CDW gap with characteristic energies Vs ~2Δ/3 and Vt ~ 2Δ/10
Yu.I. Latyshev, P. Monceau, S. Brazovskii, A.P. Orlov, Th. Fournier, 2005
Intragap CDW states I.CDW anplitude solitons
Amplitude solitons in the incommensurate CDW (ICDW)
The order parameter in the uniform ground state is Δ0 =A cos (Qx + ϕ) with Q the CDW wave vector Q = 2kF and ϕ the arbitrary phase in the ICDW state and A=const. That means that the ground state is degenerated with respect to A ↔ -A.
That leads to the possibility of non-uniform ground state with local phase change by π and simultaneous acceptance of one electron from free bandcalled amplitude soliton (AS). In this case A=tanh (x/ξ0)
AS is a self-localized state with an energy Es= 2Δ0 /π. S.A. Brazovskii, Sov. Phys.-JETP, 1980
This state is more preferable since its energy is smaller than the lowest energy Δ0 of the free band electron by ≈Δ0/3.
The existence of ASs has been well documented for in dimeric CDW materials (polyacetilene or CuGeO3). However , for ICDW materials of higher order incommensurability as MX3 existence of ASs has not been reliably demonstrated yet.
Intragap CDW spectroscopy in NbSe3. (I) ZBCP is suppressed by temperature
Temperature dependence at high temperatures T > Tp/2
CDW 1
CDW 2
Peak at Vs ≈ 2Δ/3 for both CDWs,
Scaling Vs and 2Δ is temperature independent!!!
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.520
22
24
26
28
30 T=80K 90K 100K 107K 114K 121K
2Δ1
2Δ1/3dI
/dV
(kO
hm-1)
V/2Δ1
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
0
10
20
30
40
502Δ2
25K
48K42K36K30KdI
/dV
(kO
hm-1)
V/2Δ2
x0.3
20K
2Δ2/3
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.51
10
502Δ2/3
2Δ2
H=0T 5T 10 T 15 T 20 T 25 T 27 T
dI/d
V (k
Ohm
-1)
V/2Δ2
Soliton peak at low temperatures
At high magnetic fields parallel to the layers, H//c
Parallel magnetic field narrows ZBCP and soliton peak becomes clear
Perpendicular magnetic field to the contrast broadens ZBCP
T=4.2K
(II) ZBCP narrowed by magnetic field
Yu.I. Latyshev, P. Monceau, S. Brazovskii, A.P. Orlov, Th. Fournier, PRL, 2005
CDW gap spectroscopy: o-TaS3
-0.2 -0.1 0.0 0.1 0.23.5
4.0
4.5
5.0
5.5
6.0
6.5TaS3 S4 T=230K
dI/d
V (k
Ohm
-1)
V (V)
-0.5 0.0 0.520
100
300
140K 135K 130K 125K 120K 115K 110K 105K
dI/d
V (M
Ohm
-1)
V (V)
TaS3 S4
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
150
200
250
300
350
400
dI/d
V (M
Ohm
-1)
TaS3 S4 T=140K
V (V)
100 150 200 2500
20406080
100120140160180200220 #2
#42Δ
NCDW
ICDWCCDW4Δ/3
2Δtu
nn (m
V)
T (K)
TaS3
Parabolic background substraction at high temperatures
ICDW-CCDW transition at T ≈ 130 K
Yu.I. Latyshev, P. Monceau, S. Brazovskii, A.P. Orlov,
Th. Fournier, J.Phys.IV France 2005
Schematic view of tunneling spectra
Δ0
-Δ0
EF
ES
-ES
2Δ 2Δ/3
-Δ0
EF
ES
-ES
Δ0
ICDW
4Δ/3
-Δ0
EF
Δ0
CCDW
2Δ
NbSe3
o-TaS3
at CCDW amplitude solitons with accepting of one electron are forbidden
Intragap CDW states II.CDW dislocation lines
Threshold for interlayer tunneling
1 μm
a* b
c
stacked junction
b
1 μm
c
Specially designed mesa oriented across the chain direction to avoid contribution of CDW sliding in connecting electrodes
Set up
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.63.55
3.60
3.65
3.70
dI/d
V (k
Ohm
-1)
V/2Δ1
NbS3 N1 T=130K
V+ I+
V−I−
stack
a*
c
b
Threshold behaviour is very clear
Threshold voltage scaling with CDW gap
-1.0 -0.5 0.0 0.5 1.04.0
4.5
5.0
5.5
6.0
6.5
7.0
-Vt Vt
40K 45K 50K 55K 60K
dI/d
V (k
Ohm
-1)
V/2Δ2
NbSe3 N1
-3 -2 -1 0 1 2 320
100
300
Vt 140K 135K 130K 125K 120K 115K 110K 105K
dI/d
V (M
Ohm
-1)
V/2Δ
TaS3 S4 -Vt
eVt ≈ 0.2 Δ
NbSe3
o-TaS3
CDW 1
Scaling with ΔYu.I. Latyshev, P. Monceau, S. Brazovskii, A.P. Orlov, Th. Fournier, 2005
Threshold voltage scaling with Tp
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
1.2 o-TaS3
NbSe3 low NbSe3 high
BCS
norm
aliz
ed th
resh
old
T/Tp
0 50 100 150 200 2500
5
10
15
20
25
30
o-TaS3
NbSe3 (upper CDW)
NbSe3 (lower CDW)
tresh
old
ener
gy (m
eV)
Tp (K)
eVth ≈ 1.3 kTp
CDW dislocation lines (DLs)The energy ~ Tp is known as an energy of 3D CDW ordering. As known from structural measurements, above Tp transversal phase coherence of the CDW becomes lost.
Therefore, Vt may be interpreted as phase decoupling between neighbour elementary layers.
S. Brazovskii suggested that this decoupling occurs via successive entering in the “weakest” junction the set of CDW dislocation lines.
DLs appear as a result of share stress induced by electric field across the layers. Each DL is oriented across the chains in elementary junction and corresponds to the charge 2e per chain or entering of one unit of CDW period. DL can be considered as phase CDW vortex. There is also some similarity between Vtand Hc1 in superconductors.
p
pdzLτω
≈
dz
Electric field concentrates within dislocation core: dz~ 10Å i.e. that drops within one junction,
ωp/Tp ~ 20. L~ 200 Å. For 1 μm size junction one needs 5-10 DLs to overlap all the junction area and to have complete decoupling of neigbour layers.
So one can expect multiple threshold for successive entering of a of DLs.
Threshold and staircase structure
0.0
0.1
0.2
0.3
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.63.55
3.60
3.65
3.70
dI/d
V (k
Ohm
-1)
V/2Δ1
NbS3 N1 T=130K
d2 I/d
V2 , arb
. uni
ts
n I2n .
0.5 0 0.5
5
5.5
6Unn1 Unn2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
2 .105
0
2 .105
4 .105
6 .105
lefti h
U/2Delta2
d2I/d
U^2
T 50 .
1
2 34 5 76
CDW 1CDW 2
Yu.I. Latyshev, P. Monceau, S.Brazovskii, A.P. Orlov, Th.Fournier, PRL, 2006
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
50
100
150
5432T=130K
NbSe3 N1 neg. pos.
d2 I/dV
2 , arb
. uni
ts
1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-200
0
200T=50K
V/2Δ1
V/2Δ2
Staircase structure scaling with gap
0.0 0.1 0.2 0.3 0.4 0.5 0.6-200
-100
0
100
200
300 neg. pos.
NbSe3 #1 T=130K
d2 I/dV
2 , arb
. uni
ts
V/2Δ1
4321
When dislocation cores start to overlap at high voltage bias all the voltage drops on a single elementary junction. That can explain puzzling equivalence of the behaviour of the stacked junction and point contact containing one junction.
Schematic picture of DLs entering in the junction
Duality of phase topological defects in layered HTS and CDW systems
HTS CDW
flux charge
Φ0 = hc/2e Q0 = 2e
H // layers E ⊥ layers
Hc1 Eth
SUMMARY
1. We studied CDW dynamics at various mesoscopic structures and found some evidence of CDW quantum coherence at the nanometer length scale.
2. The method of interlayer tunneling spectroscopy has been adapted for studies of layered CDW materials of MX3 type. Using this technique we identified CDW energy gaps and zero bias conductance peak, we found an interaction between two CDWs in NbSe3 in the temperature range of their coexistence. We also found intragap states with an energy of 2Δ/3 and ≈ 0.1Δ that have been attributed to the amplitude and phase excitations of CDW.
