Skip to main content

Transport in Quasi One-Dimensional Systems

  • Chapter
  • First Online:
Advances in Solid State Physics

Part of the book series: Advances in Solid State Physics Volume 41 ((ASSP,volume 41))

Abstract

The interplay of Umklapp scattering from a periodic potential and other scattering processes determine the conductivity of (quasi) one-dimensional metals. We show that the transport at finite temperature is qualitatively and quantitatively strongly influenced by a number of approximate conservation laws. Typically, not the strongest but the second strongest scattering mechanism determines the dc-conductivity. We discuss the optical conductivity both of strongly anisotropic, quasi one-dimensional Fermi liquids and of Luttinger liquids.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Sólyom: The Fermi gas model of one-dimensional conductors, Adv. Phys. 28, 201–303 (1979); V. J. Emery in Highly Conducting One-Dimensional Solids, eds. J. Devreese et al. (Plenum, New York, 1979), p. 247

    Article  Google Scholar 

  2. V. Vescoli et al.: Dimensionality-driven insulator-to-metal transition in the Bechgaard salts, Science, 281, 1188 (1998); A. Schwartz et al.: On-chain electrodynamics of metallic (TMTSF)2X salts: Observation of Tomonaga-Luttinger liquid response, Phys. Rev. B 58, 1261 (1998)

    Article  Google Scholar 

  3. A. Rosch and N. Andrei: Conductivity of a clean one-dimensional wire, Phys. Rev. Lett. 85, 1092–1096 (2000)

    Article  CAS  Google Scholar 

  4. M. Garst and A. Rosch: Transport in a classical model of an one-dimensional Mott insulator: Influence of conservation laws, preprint, cond-mat/0102109

    Google Scholar 

  5. A. Rosch and N. Andrei, to be published

    Google Scholar 

  6. P. Mazur: Non-ergodicity of phase functions in certain systems, Physica 43, 533–545 (1969)

    Article  Google Scholar 

  7. M. Suzuki: Ergodicity, constants of motion and bounds for susceptibilities, Physica 51, 277–289 (1971)

    Article  Google Scholar 

  8. D. Pines and P. Nozières, The Theory of Quantum Liquids: Volume 1, Benjamin (New York 1966)

    Google Scholar 

  9. T. Giamarchi: Umklapp process and resistivity in one-dimensional fermion systems, Phys. Rev. B 44, 2905–2913 (1991)

    Article  Google Scholar 

  10. T. Giamarchi and A. J. Millis: Conductivity of a Luttinger liquid, Phys. Rev. B 46, 9325–9331 (1992)

    Article  Google Scholar 

  11. S. Fujimoto and N. Kawakami: Exact Drude weight for the one-dimensional Hubbard model at finite temperatures J. Phys. A 31, 465–474 (1998)

    Article  Google Scholar 

  12. X. Zotos: Finite temperature Drude weight of the one-dimensional spin-1/2 Heisenberg model, Phys. Rev. Lett. 82, 1764 (1998); H. Castella, X. Zotos, and P. Prelovšek: Integrability and ideal conductance at finite temperature, Phys. Rev. Lett. 74, 972 (1995)

    Article  Google Scholar 

  13. X. Zotos, F. Naef, and P. Prelovšek: Transport and conservation laws, Phys. Rev. B 55, 11029 (1997)

    Article  CAS  Google Scholar 

  14. S. Kirchner et al., Phys. Rev. B 59, 1825 (1999); S. Sachdev and K. Damle, Phys. Rev. Lett. 78, 943 (1997); V. V. Ponomarenko and N. Nagaosa, Phys. Rev. Lett. 79, 1714 (1997); A. A. Odintsov, Y. Tokura, S. Tarucha, Phys. Rev. B 56, 12729 (1997); M. Mori, M. Ogata, H. Fukuyama, J. Phys. Soc. J. 66, 3363 (1997). K. Le Hur, cond-mat/0001439

    Article  CAS  Google Scholar 

  15. D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions, (Benjamin, Massachusetts, 1975)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Rosch, A. (2001). Transport in Quasi One-Dimensional Systems. In: Kramer, B. (eds) Advances in Solid State Physics. Advances in Solid State Physics Volume 41, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44946-9_16

Download citation

  • DOI: https://doi.org/10.1007/3-540-44946-9_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42000-2

  • Online ISBN: 978-3-540-44946-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics