Abstract
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.
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References
J.H. Davies, The Physics of Low Dimensional Semiconductors: An Introduction (Cambridge University Press, Cambridge, 1998)
S. Das Sarma, A. Pinczuk (eds.), Perspectives in Quantum Hall Effects: Novel Quantum Liquids in Low-dimensional Semiconductor Structures (Wiley, New York, 1997)
M.A. Wilde, M.P. Schwarz, Ch. Heyn, D. Heitmann, D. Grundler, D. Reuter, A.D. Wieck, Phys. Rev. B 73, 125325 (2006)
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)
Z. Wang, W. Zhang, P. Zhang, Phys. Rev. B 79, 235327 (2009)
J.P. Eisenstein, H.L. Störmer, V. Narayanamurti, A.Y. Cho, A.C. Gossard, C.W. Tu, Phys. Rev. Lett. 55, 875 (1985)
T. Ando, A.B. Fowler, F. Stern, Rev. Mod. Phys. 54, 437 (1982)
A.C.A. Ramos, T.F.A. Alves, G.A. Farias, R.N. Costa Filho, N.S. Almeida, Physica E 41, 1267 (2009)
X.C. Xie, Q.P. Li, S. Das Sarma, Phys. Rev. B 42, 7132 (1990)
I. Meinel, D. Grundler, D. Heitmann, A. Manolescu, V. Gudmundsson, W. Wegscheider, M. Bichler, Phys. Rev. B 64, 121306(R) (2001)
T.P. Smith, B.B. Goldberg, P.J. Stiles, M. Heiblum, Phys. Rev. B 32, 2696 (1985)
E. Gornik, R. Lassnig, G. Strasser, H.L. Störmer, A.C. Gossard, W. Wiegmann, Phys. Rev. Lett. 54, 1820 (1985)
W. Zawadzki, R. Lassnig, Solid State Commun. 50, 537 (1984)
W. Zawadzki, R. Lassnig, Surf. Sci. 142, 225 (1984)
R.P. Gammag, C. Villagonzalo, Solid State Commun. 146, 487 (2008)
T. Chakraborty, P. Pietiläinen, Phys. Rev. B 55, R1954 (1997)
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)
J.K. Jain, P.W. Anderson, Proc. Natl. Acad. Sci. 106, 9131 (2009)
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)
I.S. Gradshteyn, I.M. Ryzhik, in Table of Integrals, Series and Products, 7th edn., ed. by A. Jeffrey, D. Zwillinger (Elsevier, Amsterdam, 2007)
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Villagonzalo, C., Gammag, R. The Intrinsic Features of the Specific Heat at Half-Filled Landau Levels of Two-Dimensional Electron Systems. J Low Temp Phys 163, 43–52 (2011). https://doi.org/10.1007/s10909-010-0259-3
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DOI: https://doi.org/10.1007/s10909-010-0259-3