Charge-Density-WaveCharge-Density-Wave
LU MINGTAOLU MINGTAO
Outline
1. Peierls Transition
2. DC Characteristics
quasi-particle
collective excitation
3. Negative Resistance
4. Explanations
5. Conclusion
Peierls Transition
•The two degenerate groundstate of polyacetylene
•approx. 0.08 Å difference betweenC–C and C=C bond lengths
Examples of electronic phase transition:
3D Superconductivity
2D Quantum Hall effect
1D Charge-Density-Wave
•n(x,t)=n0+Δncos(2kFx+φ(x,t)), kF=πNe/a
Peierls Transition
Why one-dimension
Brillouin zone and Fermi surface
Nesting charge
1D
The Brillouin zone and Fermi surfacealways overlap with each otherThe Brillouin zone and Fermi surfacealways overlap with each other
2D
3D
The Brillouin zone and Fermi surface are notfully match with each in 2D and 3D
NbSe3
One-dimensional materials
K0.3MoO3
DC characteristics
1) Nonlinear dc response
2) Narrow band noise
DC characteristics describe the response
of CDW to the applied dc electric field
Single particle model
Washboard potential
The motion of the single particle
The velocity of the singleparticle is modulated by afrequency of ω0
Quasi-particle Mattuck’s quasi-horse
Quasi-particle
Entry
Free propagation
Exit
Collective mode
Collective mode can be measured byoptical methode
Phase mode is IR active
Amplitude mode is Raman active
Negative resistance
When current is larger than 3.5μA, anegative absolute resistance is observed
The dash line is the average of differentsegments. It matches with the I-V curvemeasured in long distance.
The CDW and quasi-particlesare driven by different force
Explanations
•Phase slipamplitudecollapse•Phase slip and amplitudecollapse occur at the strongpinning center.
electric potential•The CDW is driven by theelectric potential; as well as
electrochemical potential the quasi-particle is driven byelectrochemical potential .
•A vortex may occurs at thestrong pinning center
Conclusion
•Normally, CDW behaves as a semiconductor.Different samples show diverse dc and accharacteristics. In some samples, we may gethysteresis, switching or negative differentialresistance.
•There is some similarity between CDW and BCSsuperconductivity. CDW has its priority because it isone-dimensional.
•The NR could be gotten in a length scale less than
1μm. The origin of NR is still not clear.
•The quasi-particle and CDW are driven by different force.
•The macroscopic defect gives a vortex of the CDW motion around the strongpinning center.
Acknowledgement
Thanks to my supervisor
Prof. P.H.M. van Loosdrecht