Charge-Density-Wave nanowires

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

3. Nb Se II III I multi-chain nanowires NbSe3 wires Ultrasonic cleaving in pyridine Disperse on substrate with predefined markers

4. 1 mm contacting nanowires 2 mm 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 W

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

6. ET -ET sliding pinned sliding 10-3mm2 3 x 10-3mm2 7 x 10-3mm2 22 x 10-3mm2 threshold field increases as cross section decreases T=120 K

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

8. no evidence for single-particle model in IV characteristics ET -ET sliding pinned sliding 10-3mm2 3 x 10-3mm2 7 x 10-3mm2 single-particle expectation 22 x 10-3mm2 T=120 K

9. gradual reduction of transition temperatures as cross section decreases R/L (kW/mm) R/L (kW/mm)

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

11. power-law behavior in I-V(T) R  T-a: a = 2.15 I  Vb : b = 4.2 I/Ta+1 = C sinh(geV/kBT) |G(1+b/2+igeV/pkBT)|2 power-law in both I(V) and R(T), and scaling behavior (bosonic excitations with linear spectrum) are a fingerprint for 1D transport

12. power-law behavior due to uncondensed carriers ! coexistence of power law behavior and sliding threshold in IVs no abrupt decrease of nonzero TP1,TP2 R/L (kW/mm) R/L (kW/mm)

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

14. and NbSe3 MWNT • Both diffusive conductors • Both interaction between chains • Both show power-law behaviour • Both show scaling of I(V)s Xinluo Zhao et al., Phys. Rev. Lett. 90, 187401 (2003) 7 Å 7 Å 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) Coulomb blockade is smeared by quantum fluctuations in the leads ‘Environment’ (Z-transmission line) I(V)  Vb b = 2Z/RQ + 1 V Junction

16. nanowire as transmission line R’ L’ G’ C’ V For NbSe3 nanowire: Kinetic inductance L’ = 17 nH/mm (very high!) Capacitance C’ = 10 aF/mm Z = 41 kW  1.6RQ

17. nanowire with tunnel barrier LC V wL’ > R’  ħ> 0.4 meV measurement I(V)  Vb b = 2Z/RQ + 1 4.2 model b = 4.2 Z = 41 kW  1.6RQ

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

19. ‘Environment’ V Junction low carrier density (1018 cm-3: 30 nm distance between electrons) and low Fermi energy indicate the importance of e-e interactions Environmental Coulomb Blockade But applicability of ECB is not clear: developed for a single junction • Alternative model: Wigner crystal • Coulomb energy larger than Fermi energy • Power-law exponent determined by localization length 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 TP2: NbSe3 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 NbSe3 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 pinning 1D Weak pinning ET independent on size ET (1/A)2/3