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