1. Charge-Density-Wave LU MINGTAO

2. Outline  1. Peierls Transition  2. DC Characteristics quasi-particle collective excitation  3. Negative Resistance  4. Explanations  5. Conclusion

3. 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

4. n(x,t)=n 0 +Δncos(2k F x+φ(x,t)), k F =πN e /a Peierls Transition

5. Why one-dimension Brillouin zone and Fermi surface Nesting charge 1D The Brillouin zone and Fermi surface always overlap with each other 2D3D The Brillouin zone and Fermi surface are not fully match with each in 2D and 3D

6. NbSe 3 One-dimensional materials K 0.3 MoO 3

7. DC characteristics 1) Nonlinear dc response2) Narrow band noise DC characteristics describe the response of CDW to the applied dc electric field

8. Single particle model Washboard potentialThe motion of the single particle The velocity of the single particle is modulated by a frequency of ω 0

9. Quasi-particle Mattuck’s quasi-horse

10. Quasi-particle EntryFree propagationExit

11. Collective mode Collective mode can be measured by optical methode Phase mode is IR active Amplitude mode is Raman active

12. 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

13. Explanations Phase slipamplitude collapsePhase slip and amplitude collapse occur at the strong pinning center. electric potentialThe CDW is driven by the electric potential; as well as electrochemical potential the quasi-particle is driven by electrochemical potential. A vortex may occurs at the strong pinning center

14. 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 1 μm. 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.

15. Acknowledgement Thanks to my supervisor Prof. P.H.M. van Loosdrecht