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

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


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.

Acceptance Date Aug 7, 2008
Publication Date Aug 7, 2008
Publicly Available Date Mar 29, 2024
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

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