1. Charge-Density-Wave nanowires Erwin Slot Mark Holst Herre van der Zant Sergei Zaitsev-Zotov Sergei Artemenko Robert Thorne Molecular Electronics and Devices group http://med.tn.tudelft.nl/

2. submicron CDW devices 3  m 5  m 1  m 5m5m thin films junctions/constrictions nanowires etched wires in crystals submicron probes bulk CDW properties studied in detail; much less in known about the microscopic details

3. multi-chain nanowires NbSe 3 wires Ultrasonic cleaving in pyridine Disperse on substrate with predefined markers Nb Se   

4. contacting nanowires 1  m 2  m E-beam lithography Buffered Hydrofluoric acid (4 sec) Deposition of Ti and Au width: 30-300 nm, thickness: 10-50 nm Lowest contact resistance  100 

5. linear resistance measurements 1D CDW dynamics E. Slot et al., Phys. Rev. B 69 (2004) power-law behavior E. Slot et al. Phys. Rev. Lett. 93 (2004) 176602 reducing cross section

6. threshold field increases as cross section decreases T=120 K pinnedsliding ETET -E T 10 -3  m 2 3 x 10 -3  m 2 7 x 10 -3  m 2 22 x 10 -3  m 2

7. 1D collective pinning: single phase coherent domain surface and 2D pinning with E T  (1/A) 1/2 can be excluded slope 2/3 slope 1/2 evidence of 1D weak collective CDW pinning: E T  (1/A) 2/3 2D1D E. Slot et al., Phys. Rev. B 69 (2004)

8. no evidence for single-particle model in IV characteristics T=120 K pinnedsliding ETET -E T 10 -3  m 2 3 x 10 -3  m 2 7 x 10 -3  m 2 22 x 10 -3  m 2 single-particle expectation

9. gradual reduction of transition temperatures as cross section decreases R/L (k  /  m)

10. R  T  power-law behavior in R(T)

11. power-law behavior in I-V(T) I/T  +1 = C sinh(  eV/k B T) |  (1+  /2+i  eV/  k B T)| 2 power-law in both I(V) and R(T), and scaling behavior ( bosonic excitations with linear spectrum) are a fingerprint for 1D transport R  T -  :  = 2.15 I  V  :  = 4.2

12. power-law behavior due to uncondensed carriers ! coexistence of power law behavior and sliding threshold in IVs no abrupt decrease of nonzero T P1,T P2 R/L (k  /  m)

13. multiwall carbon nanotubes Bachtold et al., Phys. Rev. Lett. 87, 166801 (2001)

14. and 7 Å Xinluo Zhao et al., Phys. Rev. Lett. 90, 187401 (2003) MWNTNbSe 3 Both diffusive conductors Both interaction between chains Both show power-law behaviour Both show scaling of I(V)s LL and ECBT have the same dependencies on energy

15. Environmental Coulomb Blockade Ingold & Nazarov, Single charge tunneling Matveev & Glazman, Phys. Rev. Lett. 70, 990 (1993) ‘Environment’ (Z-transmission line) V Junction Coulomb blockade is smeared by quantum fluctuations in the leads I(V)  V   = 2Z/R Q + 1

16. nanowire as transmission line R’L’ G’C’ For NbSe 3 nanowire: Kinetic inductance L’ = 17 nH/  m (very high!) Capacitance C’ = 10 aF/  m Z = 41 k  R Q V

17. nanowire with tunnel barrier  L’ > R’  ħ  > 0.4 meV V LC  = 4.2 I(V)  V   = 2Z/R Q + 1  4.2 Z = 41 k  R Q model measurement

18. model reproduces dependence of exponents of R(T) on cross section

19. Alternative model: Wigner crystal Coulomb energy larger than Fermi energy Power-law exponent determined by localization length But applicability of ECB is not clear: developed for a single junction ‘Environment’ V Junction Environmental Coulomb Blockade low carrier density (10 18 cm -3 : 30 nm distance between electrons) and low Fermi energy indicate the importance of e-e interactions Data in agreement with general concepts describing 1D conductors. At present no full theory describing our system with many channels and disorder.

20. gate effect: periodic features are NOT observed switches occur with pulses on the gate IVs are switchy when the gate is not grounded

21. Conclusions As the cross-section of CDW nanowires becomes smaller, the Peierls temperature gradually decreases and the threshold field increases (1D collective pinning) Below T P2 : NbSe 3 nanowires with less than 1000 chains in total show power-law behavior typical for 1D transport Data in agreement with general concepts describing 1D conductors. At present no full theory describing our system with many channels and disorder Role of impurities: discussed by Artemenko on Monday

22. conclusions Current conversion occurs through strain-induced phase-slip processes (changes on the micron scale) Importance of strain: change in the chemical potential (negative resistance) Energy spectroscopy in CDW junctions and weak links: evidence for solitons A single phase coherent CDW domain can not be described with the single particle model Thin NbSe 3 nanowires show the characteristics of one- dimensional transport (power-law behavior; low electron density) A full microscopic CDW model needed

23. gradual reduction of transition temperatures as cross section decreases bulk sample

24. 1D collective pinning Fukuyama-Lee-Rice Hamiltonian: 3D Weak pinning1D Weak pinning E T independent on size E T  (1/A) 2/3