Journal of Low Temperature Physics

, Volume 163, Issue 1–2, pp 43–52 | Cite as

The Intrinsic Features of the Specific Heat at Half-Filled Landau Levels of Two-Dimensional Electron Systems

  • Cristine Villagonzalo
  • Rayda Gammag


The specific heat capacity of a two-dimensional electron gas is derived for two types of the density of states, namely, the Dirac delta function spectrum and that based on a Gaussian function. For the first time, a closed form expression of the specific heat for each case is obtained at half-filling. When the chemical potential is temperature-independent, the temperature is calculated at which the specific heat is a maximum. Here the effects of the broadening of the Landau levels are distinguished from those of the different filling factors. In general, the results derived herein hold for any thermodynamic system having similar resonant states.


Two-dimensional electron gas Density of states Landau levels Specific heat 


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  1. 1.
    J.H. Davies, The Physics of Low Dimensional Semiconductors: An Introduction (Cambridge University Press, Cambridge, 1998) Google Scholar
  2. 2.
    S. Das Sarma, A. Pinczuk (eds.), Perspectives in Quantum Hall Effects: Novel Quantum Liquids in Low-dimensional Semiconductor Structures (Wiley, New York, 1997) Google Scholar
  3. 3.
    M.A. Wilde, M.P. Schwarz, Ch. Heyn, D. Heitmann, D. Grundler, D. Reuter, A.D. Wieck, Phys. Rev. B 73, 125325 (2006) ADSCrossRefGoogle Scholar
  4. 4.
    M. Zhu, A. Usher, A.J. Matthews, A. Potts, M. Elliott, W.G. Herrenden-Harker, D.A. Ritchie, M.Y. Simmons, Phys. Rev. B 67, 155329 (2003) ADSCrossRefGoogle Scholar
  5. 5.
    Z. Wang, W. Zhang, P. Zhang, Phys. Rev. B 79, 235327 (2009) ADSCrossRefGoogle Scholar
  6. 6.
    J.P. Eisenstein, H.L. Störmer, V. Narayanamurti, A.Y. Cho, A.C. Gossard, C.W. Tu, Phys. Rev. Lett. 55, 875 (1985) ADSCrossRefGoogle Scholar
  7. 7.
    T. Ando, A.B. Fowler, F. Stern, Rev. Mod. Phys. 54, 437 (1982) ADSCrossRefGoogle Scholar
  8. 8.
    A.C.A. Ramos, T.F.A. Alves, G.A. Farias, R.N. Costa Filho, N.S. Almeida, Physica E 41, 1267 (2009) ADSCrossRefGoogle Scholar
  9. 9.
    X.C. Xie, Q.P. Li, S. Das Sarma, Phys. Rev. B 42, 7132 (1990) ADSCrossRefGoogle Scholar
  10. 10.
    I. Meinel, D. Grundler, D. Heitmann, A. Manolescu, V. Gudmundsson, W. Wegscheider, M. Bichler, Phys. Rev. B 64, 121306(R) (2001) ADSCrossRefGoogle Scholar
  11. 11.
    T.P. Smith, B.B. Goldberg, P.J. Stiles, M. Heiblum, Phys. Rev. B 32, 2696 (1985) ADSCrossRefGoogle Scholar
  12. 12.
    E. Gornik, R. Lassnig, G. Strasser, H.L. Störmer, A.C. Gossard, W. Wiegmann, Phys. Rev. Lett. 54, 1820 (1985) ADSCrossRefGoogle Scholar
  13. 13.
    W. Zawadzki, R. Lassnig, Solid State Commun. 50, 537 (1984) ADSCrossRefGoogle Scholar
  14. 14.
    W. Zawadzki, R. Lassnig, Surf. Sci. 142, 225 (1984) ADSCrossRefGoogle Scholar
  15. 15.
    R.P. Gammag, C. Villagonzalo, Solid State Commun. 146, 487 (2008) ADSCrossRefGoogle Scholar
  16. 16.
    T. Chakraborty, P. Pietiläinen, Phys. Rev. B 55, R1954 (1997) ADSCrossRefGoogle Scholar
  17. 17.
    H.L. Stormer, D.C. Tsui, in Perspectives in Quantum Hall Effects: Novel Quantum Liquids in Low-dimensional Semiconductor Structures, Chap. 10, ed. by S. Das Sarma, A. Pinczuk (Wiley, New York, 1997) Google Scholar
  18. 18.
    J.K. Jain, P.W. Anderson, Proc. Natl. Acad. Sci. 106, 9131 (2009) ADSCrossRefGoogle Scholar
  19. 19.
    F. Schulze-Wischeler, U. Zeitler, C. von Zobeltitz, F. Hohls, D. Reuter, A.D. Wieck, H. Frahm, R.J. Haug, Phys. Rev. B 76, 153311 (2007) ADSCrossRefGoogle Scholar
  20. 20.
    I.S. Gradshteyn, I.M. Ryzhik, in Table of Integrals, Series and Products, 7th edn., ed. by A. Jeffrey, D. Zwillinger (Elsevier, Amsterdam, 2007) Google Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Structure and Dynamics Group, National Institute of PhysicsUniversity of the PhilippinesQuezon CityPhilippines

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