Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

Abstract

We derive a closed analytical expression for the exchange energy of the three-dimensional interacting electron gas in strong magnetic fields, which goes beyond the quantum limit (L=0) by explicitly including the effect of the second, L=1, Landau level and arbitrary spin polarization. The inclusion of the L=1 level brings the fields to which the formula applies closer to the laboratory range, as compared to previous expressions, valid only for L=0 and complete spin polarization. We identify and explain two distinct regimes separated by a critical density nc. Below nc, the per particle exchange energy is lowered by the contribution of L=1 , whereas above nc it is increased. As special cases of our general equation we recover various known more limited results for higher fields, and we identify and correct a few inconsistencies in some of these earlier expressions.

Citation

(2008). Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field. Physical review B: Condensed matter and materials physics, https://doi.org/10.1103/PhysRevB.78.085107

• Acceptance Date: Aug 7, 2008
• Publication Date: Aug 7, 2008
• Journal: Physical Review B
• Print ISSN: 1098-0121
• Publisher: American Physical Society
• DOI: https://doi.org/10.1103/PhysRevB.78.085107
• Publisher URL: https://doi.org/10.1103/PhysRevB.78.085107