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 ground state of polyacetylene•approx. 0.08 Å difference between C–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-dimensionBrillouin zone and Fermi surface
Nesting charge
1D
The Brillouin zone and Fermi surface The Brillouin zone and Fermi surface always overlap with each otheralways overlap with each other
2D 3DThe Brillouin zone and Fermi surface are not fully 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 responseof CDW to the applied dc electric field
Single particle model
Washboard potential
220 0
2 * *sin(2 )
2 F xF
d x dx ek x E
dt m dt k m
))2cos(1(
4)(
2
20
*
xkk
mxU F
F
The motion of the single particle
The velocity of the single particle is modulated by a frequency of ω0
Quasi-particle Mattuck’s quasi-horse
Quasi-particle
Entry Free propagation Exit
Collective mode
Collective mode can be measured by optical methodePhase mode is IR activeAmplitude mode is Raman active
),()],(|[|),( txietxtx
Negative resistance
When current is larger than 3.5μA, a negative absolute resistance is observed
The dash line is the average of different segments. It matches with the I-V curve measured in long distance.
The CDW and quasi-particles are driven by different force
Explanations• Phase slipPhase slip and amplitude amplitude
collapsecollapse occur at the strong pinning center.
• The CDW is driven by the electric potentialelectric potential; as well as
the quasi-particle is driven by electrochemical potential electrochemical potential .
• A vortex may occurs at the strong pinning center
Conclusion• Normally, CDW behaves as a semiconductor.
Different samples show diverse dc and ac characteristics. In some samples, we may get hysteresis, switching or negative differential resistance.
• There is some similarity between CDW and BCS superconductivity. CDW has its priority because it is one-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 strong
pinning center.
Acknowledgement
Thanks to my supervisor Prof. P.H.M. van Loosdrecht