Advertisement

Dependence of structure factor and correlation energy on the width of electron wires

  • Vinod Ashokan
  • Renu Bala
  • Klaus Morawetz
  • Kare Narain Pathak
Open Access
Regular Article

Abstract

The structure factor and correlation energy of a quantum wire of thickness ba B are studied in random phase approximation (RPA) and for the less investigated region r s < 1. Using the single-loop approximation, analytical expressions of the structure factor are obtained. The exact expressions for the exchange energy are also derived for a cylindrical and harmonic wire. The correlation energy in RPA is found to be represented by ϵ c (br s ) = α(r s )/b + β(r s ) ln(b) + η(r s ), for small b and high densities. For a pragmatic width of the wire, the correlation energy is in agreement with the quantum Monte Carlo simulation data.

Keywords

Solid State and Materials 

References

  1. 1.
    G.F. Giuliani, G. Vignale, Quantum theory of the electron liquid (Cambridge University Press, Cambridge, 2005) Google Scholar
  2. 2.
    R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical properties of carbon nanotubes (Imperial College Press, London, 1998) Google Scholar
  3. 3.
    M. Bockrath, D.H. Cobden, J. Lu, A.G. Rinzler, R.E. Smalley, L. Balents, P.L. McEuen, Nature 397, 598 (1999) ADSCrossRefGoogle Scholar
  4. 4.
    H. Ishii, H. Kataura, H. Shiozawa, H. Yoshioka, H. Otsubo, Y. Takayama, T. Miyahara, S. Suzuki, Y. Achiba, M. Nakatake, T. Narimura, M. Higashiguchi, K. Shimada, H. Namatame, M. Taniguchi, Nature 426, 540 (2003) ADSCrossRefGoogle Scholar
  5. 5.
    M. Shiraishi, M. Ata, Solid State Commun. 127, 215 (2003) ADSCrossRefGoogle Scholar
  6. 6.
    J. Schäfer, C. Blumenstein, S. Meyer, M. Wisniewski, R. Claessen, Phys. Rev. Lett. 101, 236802 (2008) ADSCrossRefGoogle Scholar
  7. 7.
    Y. Huang, X. Duan, Y. Cui, L.J. Lauhon, K.-H. Kim, C.M. Lieber, Science 294, 1313 (2001) ADSCrossRefGoogle Scholar
  8. 8.
    H. Monien, M. Linn, N. Elstner, Phys. Rev. A 58, R3395 (1998) ADSCrossRefGoogle Scholar
  9. 9.
    A. Recati, P.O. Fedichev, W. Zwerger, P. Zoller, J. Opt. B: Quantum Semiclass. Opt. 5, S55 (2003) ADSCrossRefGoogle Scholar
  10. 10.
    H. Moritz, T. Stoferle, K. Guenter, M. Kohl, T. Esslinger, Phys. Rev. Lett. 94, 210401 (2005) ADSCrossRefGoogle Scholar
  11. 11.
    F.P. Milliken, C.P. Umbach, R.A. Webb, Solid State Commun. 97, 309 (1996) ADSCrossRefGoogle Scholar
  12. 12.
    S.S. Mandal, J.K. Jain, Solid State Commun. 118, 503 (2001) ADSCrossRefGoogle Scholar
  13. 13.
    A.M. Chang, Rev. Mod. Phys. 75, 1449 (2003) ADSCrossRefGoogle Scholar
  14. 14.
    A. Nitzan, M.A. Ratner, Science 300, 1384 (2003) ADSCrossRefGoogle Scholar
  15. 15.
    S. Tomonaga, Prog. Theor. Phys. 5, 544 (1950) ADSCrossRefGoogle Scholar
  16. 16.
    J.M. Luttinger, Phys. J. Math. 4, 1154 (1963) CrossRefGoogle Scholar
  17. 17.
    F.D.M. Haldane, J. Phys. C 14, 2585 (1981) ADSCrossRefGoogle Scholar
  18. 18.
    H.J. Schulz, Phys. Rev. Lett. 71, 1864 (1993) ADSCrossRefGoogle Scholar
  19. 19.
    M.M. Fogler, Phys. Rev. Lett. 94, 056405 (2005) ADSCrossRefGoogle Scholar
  20. 20.
    M.M. Fogler, Phys. Rev. B 71, 161304(R) (2005) ADSCrossRefGoogle Scholar
  21. 21.
    M. Fabrizio, A.O. Gogolin, S. Scheidl, Phys. Rev. Lett. 72, 2235 (1994) ADSCrossRefGoogle Scholar
  22. 22.
    S. Capponi, D. Poilblanc, T. Giamarchi, Phys. Rev. B 61, 13410 (2000) ADSCrossRefGoogle Scholar
  23. 23.
    G. Fano, F. Ortolani, A. Parola, L. Ziosi, Phys. Rev. B 60, 15654 (1999) ADSCrossRefGoogle Scholar
  24. 24.
    D. Poilblanc, S. Yunoki, S. Maekawa, E. Dagotto, Phys. Rev. B 56, R1645 (1997) ADSCrossRefGoogle Scholar
  25. 25.
    B. Valenzuela, S. Fratini, D. Baeriswyl, Phys. Rev. B 68, 045112 (2003) ADSCrossRefGoogle Scholar
  26. 26.
    W.I. Friesen, B. Bergersen, J. Phys. C 13, 6627 (1980) ADSCrossRefGoogle Scholar
  27. 27.
    L. Calmels, A. Gold, Phys. Rev. B 56, 1762 (1997) ADSCrossRefGoogle Scholar
  28. 28.
    V. Garg, R.K. Moudgil, K. Kumar, P.K. Ahluwalia, Phys. Rev. B 78, 045406 (2008) ADSCrossRefGoogle Scholar
  29. 29.
    M. Tas, M. Tomak, Phys. Rev. B 67, 235314 (2003) ADSCrossRefGoogle Scholar
  30. 30.
    R. Bala, R.K Moudgil, S. Srivastava, K.N. Pathak, J. Phys.: Condens. Matter 24, 245302 (2012) ADSGoogle Scholar
  31. 31.
    R. Bala, R.K. Moudgil, S. Srivastava, K.N. Pathak, Eur. Phys. J. B 87, 5 (2014) ADSCrossRefGoogle Scholar
  32. 32.
    C.R. de Oliveira, A.A. Verri, Ann. Phys. 324, 251 (2009) ADSCrossRefGoogle Scholar
  33. 33.
    L.O. Wagner, E.M. Stoudenmire, K. Burke, S.R. White, Phys. Chem. Chem. Phys. 14, 8581 (2012) CrossRefGoogle Scholar
  34. 34.
    E.M. Stoudenmire, L.O. Wagner, S.R. White, K. Burke, Phys. Rev. Lett. 109, 056402 (2012) ADSCrossRefGoogle Scholar
  35. 35.
    R.M. Lee, N.D. Drummond, Phys. Rev. B 83, 245114 (2011) ADSCrossRefGoogle Scholar
  36. 36.
    M. Casula, S. Sorella, G. Senatore, Phys. Rev. B 74, 245427 (2006) ADSCrossRefGoogle Scholar
  37. 37.
    A. Malatesta, Quantum Monte Carlo study of a model one-dimensional electron gas, Ph.D. thesis, Universita Degli studi Di Trieste, Departmento di Fisica Teorica, 1999 Google Scholar
  38. 38.
    L. Shulenburger, M. Casula, G. Senatore, R.M. Martin, Phys. Rev. B 78, 165303 (2008) ADSCrossRefGoogle Scholar
  39. 39.
    A. Malatesta, G. Senatore, J. Phys. IV 10, 5 (2000) Google Scholar
  40. 40.
    P.F. Loos, J. Chem. Phys. 138, 064108 (2013) ADSCrossRefGoogle Scholar
  41. 41.
    K. Morawetz, V. Ashokan, R. Bala, K.N. Pathak, to be published Google Scholar
  42. 42.
    D. Pines, P. Nozieres, The theory of quantum liquids (W.A. Benjamin, Inc., New York, 1966) Google Scholar
  43. 43.
    V. Ashokan, N.D. Drummond, K.N. Pathak, to be published Google Scholar
  44. 44.
    R.J. Needs, M.D. Towler, N.D. Drummond, P.L. Ríos, J. Phys.: Condens. Matter 22, 023201 (2010) ADSGoogle Scholar
  45. 45.
    Handbook of mathematical functions, edited by M. Abramowitz, I. Stegun (Dover Publications, Inc., New York, 1972), pp. 498 and 260 Google Scholar
  46. 46.
    H. Bateman, A. Erdélyi, Higher transcendental functions (McGrawHill, New York, 1953), Vol. I, p. 206 (see 5.3, Definition of the G-Function) Google Scholar

Copyright information

© The Author(s) 2018. This article is published with open access at Springerlink.com 2018

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Vinod Ashokan
    • 1
  • Renu Bala
    • 2
  • Klaus Morawetz
    • 3
    • 4
    • 5
  • Kare Narain Pathak
    • 1
  1. 1.Centre for Advanced Study in Physics, Panjab UniversityChandigarhIndia
  2. 2.Department of PhysicsMCM DAV College for WomenChandigarhIndia
  3. 3.Muenster University of Applied PhysicsSteinfurtGermany
  4. 4.International Institute of Physics – UFRN, Campus Universitário Lagoa novaNatalBrazil
  5. 5.Max-Planck-Institute for the Physics of Complex SystemsDresdenGermany

Personalised recommendations