The free electron gas in a uniform magnetic field at low temperature is restudied. The grand partition function previously obtained by Landau＇s quantitative calculation contains three parts, which are all approximate...The free electron gas in a uniform magnetic field at low temperature is restudied. The grand partition function previously obtained by Landau＇s quantitative calculation contains three parts, which are all approximate. An improved calculation is presented, in which two of the three parts are obtained in exact forms. A simple remedy for Landau and Lifshitz＇s qualitative calculation in the textbook is also given, which turns the qualitative result into the same one as obtained by the improved quantitative calculation. The chemical potential is solved approximately and the thermodynamic quantities are caiculated explicitly in both a weak field and a strong field. The thermodynamic quantities in a strong field obtained here contain both non-oscillating and oscillating corrections to the corresponding results derived from Landau＇s grand partition function. In particular, Landau＇s grand partition function is not sufficiently accurate to yield our nonzero results for the specific heat and the entropy. An error in the Laplace-transform method for the problem is corrected. The results previously obtained by this method are also improved.展开更多
The de Haas-van Alphen oscillations in two-dimensional QED at finite temperature and density are investigated. It is shown that for a given particle density, besides the oscillation of magnetization, the chemical pote...The de Haas-van Alphen oscillations in two-dimensional QED at finite temperature and density are investigated. It is shown that for a given particle density, besides the oscillation of magnetization, the chemical potential is also oscillating with the same period. Different from the earlier work (J.O. Andersen and T. Haugset, Phys. Rev.D51 (1995) 3073), the magnetization oscillations we studied have a correct nonrelativistic limit at zero temperature.展开更多
The magnetisation of heavy holes in III-V semiconductor quantum wells with Rashba spin-orbit coupling （SOC） in an external perpendicular magnetic field is studied theoretically. We concentrate on the effects on the ...The magnetisation of heavy holes in III-V semiconductor quantum wells with Rashba spin-orbit coupling （SOC） in an external perpendicular magnetic field is studied theoretically. We concentrate on the effects on the magnetisation induced by the system boundary, the l^ashba SOC and the temperature. It is found that the sawtooth-like de Haas- van Alphen （dHvA） oscillations of the magnetisation will change dramatically in the presence of such three factors. Especially, the effects of the edge states and Rashba SOC on the magnetisation are more evident when the magnetic field is smaller. The oscillation center will shift when the boundary effect is considered and the Rashba SOC will bring beating patterns to the dHvA oscillations. These effects on the dHvA oscillations are preferably observed at low temperatures. With increasing temperature, the dHvA oscillations turn to be blurred and eventually disappear.展开更多
The orbital magnetization of the electron gas on a two-dimensional kagome' lattice under a perpendicular magnetic field is theoretically investigated.The interplay between the lattice geometry and magnetic field i...The orbital magnetization of the electron gas on a two-dimensional kagome' lattice under a perpendicular magnetic field is theoretically investigated.The interplay between the lattice geometry and magnetic field induces nontrivial k-space Chern invariant in the magnetic Brillouin zone,which turns to result in profound effects on the magnetization properties.We show that the Berry-phase term in the magnetization gives a paramagnetic contribution,while the conventional term brought about by the magnetic response of the magnetic Bloch bands produces a diamagnetic contribution.As a result,the superposition of these two components gives rise to a delicate oscillatory structure in the magnetization curve when varying the electron filling factor.The relationship between this oscillatory behavior and the Hofstadter energy spectrum is revealed by selectively discussing the magnetization and its two components at the commensurate fluxes of f = 1/4,1/3,and 1/6,respectively.In particular,we reveal as a typical example the fractal structure in the magnetic oscillations by tuning the commensurate flux around f = 1/4.The finite-temperature effect on the magnetization is also discussed.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10675174
文摘The free electron gas in a uniform magnetic field at low temperature is restudied. The grand partition function previously obtained by Landau＇s quantitative calculation contains three parts, which are all approximate. An improved calculation is presented, in which two of the three parts are obtained in exact forms. A simple remedy for Landau and Lifshitz＇s qualitative calculation in the textbook is also given, which turns the qualitative result into the same one as obtained by the improved quantitative calculation. The chemical potential is solved approximately and the thermodynamic quantities are caiculated explicitly in both a weak field and a strong field. The thermodynamic quantities in a strong field obtained here contain both non-oscillating and oscillating corrections to the corresponding results derived from Landau＇s grand partition function. In particular, Landau＇s grand partition function is not sufficiently accurate to yield our nonzero results for the specific heat and the entropy. An error in the Laplace-transform method for the problem is corrected. The results previously obtained by this method are also improved.
文摘The de Haas-van Alphen oscillations in two-dimensional QED at finite temperature and density are investigated. It is shown that for a given particle density, besides the oscillation of magnetization, the chemical potential is also oscillating with the same period. Different from the earlier work (J.O. Andersen and T. Haugset, Phys. Rev.D51 (1995) 3073), the magnetization oscillations we studied have a correct nonrelativistic limit at zero temperature.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60821061, 60776061, 10604010 and 60776063)
文摘The magnetisation of heavy holes in III-V semiconductor quantum wells with Rashba spin-orbit coupling （SOC） in an external perpendicular magnetic field is studied theoretically. We concentrate on the effects on the magnetisation induced by the system boundary, the l^ashba SOC and the temperature. It is found that the sawtooth-like de Haas- van Alphen （dHvA） oscillations of the magnetisation will change dramatically in the presence of such three factors. Especially, the effects of the edge states and Rashba SOC on the magnetisation are more evident when the magnetic field is smaller. The oscillation center will shift when the boundary effect is considered and the Rashba SOC will bring beating patterns to the dHvA oscillations. These effects on the dHvA oscillations are preferably observed at low temperatures. With increasing temperature, the dHvA oscillations turn to be blurred and eventually disappear.
基金supported by the National Natural Science Foundation of China(Grant Nos.90921003,10904005,60776061 and 60776063)the National Basic Research Program of China(Grant Nos.2009CB929103 and 2009CB929300)
文摘The orbital magnetization of the electron gas on a two-dimensional kagome' lattice under a perpendicular magnetic field is theoretically investigated.The interplay between the lattice geometry and magnetic field induces nontrivial k-space Chern invariant in the magnetic Brillouin zone,which turns to result in profound effects on the magnetization properties.We show that the Berry-phase term in the magnetization gives a paramagnetic contribution,while the conventional term brought about by the magnetic response of the magnetic Bloch bands produces a diamagnetic contribution.As a result,the superposition of these two components gives rise to a delicate oscillatory structure in the magnetization curve when varying the electron filling factor.The relationship between this oscillatory behavior and the Hofstadter energy spectrum is revealed by selectively discussing the magnetization and its two components at the commensurate fluxes of f = 1/4,1/3,and 1/6,respectively.In particular,we reveal as a typical example the fractal structure in the magnetic oscillations by tuning the commensurate flux around f = 1/4.The finite-temperature effect on the magnetization is also discussed.
