Charged two-dimensional quantum gas in a uniform magnetic field at finite temperature

被引:9
|
作者
van Zyl, BP [1 ]
Hutchinson, DAW
机构
[1] McMaster Univ, Dept Phys & Astron, Hamilton, ON L8S 4M1, Canada
[2] Univ Otago, Dept Phys, Dunedin, New Zealand
关键词
D O I
10.1103/PhysRevB.69.024520
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We present closed-form, analytical expressions for the thermodynamic properties of an ideal, two-dimensional (2D) charged Fermi or Bose gas in the presence of a uniform magnetic field of arbitrary strength. We consider both the homogeneous quantum gas (in which case our expressions are exact) and the inhomogeneous gas within the local-density approximation. Our results for the Fermi gas are relevant to the current-density-functional theory of low-dimensional electronic systems in magnetic fields. For a 2D charged Bose gas (CBG) in a homogeneous magnetic field, we show that the uniform system undergoes a sharp transition at a critical temperature T-c(star), below which there is a macroscopic occupation of the lowest Landau level. An examination of the one-body density matrix, however, reveals the absence of long-range order, thereby indicating that the transition cannot be interpreted to a Bose-Einstein condensate. Nevertheless, for T<T-c(star) and weak magnetic fields, the system still exhibits magnetic properties which are practically indistinguishable from those of a condensed, superconducting CBG. We therefore conclude that while a condensate is a sufficient condition for the ideal CBG to exhibit a superconducting state, it may not be a necessary condition.
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页数:13
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