On Energy References when a Magnetic Field is Applied. A Practical Guide to Reference Energies with and without a Magnetic Field
Abstract
We present a simple analysis of the energy references and of the magnetic-field-dependent and system-dependent features of the Landau energy levels. The energy reference used in describing Landau quantization is usually taken as given, with the Fermi levels of the electron system and the coupled reservoir aligned in thermal equilibrium. Nevertheless, the dependence of the Landau-level spectrum on magnetic field can make the relation between these energy references less transparent. In this work, we show that when a magnetic field is applied and the confined Landau levels En are established, both the Fermi level EF and the bottom energy E0 remain fixed when the magnetic field varies. We show that the bottom energy E0 is independent of B, and determined by a system-dependent field B1, defined by the condition that the first Landau level equals the Fermi energy. In contrast, the minimum of the parabolic well depends explicitly on the magnetic field. The resulting picture provides a simple way of displaying the relative motion of the Landau levels and the fixed Fermi level without introducing a magnetic-field-dependent energy zero.
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BibTeX
@misc{pereyra2026energy,
title = {{On Energy References when a Magnetic Field is Applied. A Practical Guide to Reference Energies with and without a Magnetic Field}},
author = {Pedro Pereyra},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25473},
eprint = {2609.25473},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25473},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On Energy References when a Magnetic Field is Applied. A Practical Guide to Reference Energies with and without a Magnetic Field
AU - Pedro Pereyra
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25473
UR - https://arxiv.org/abs/2609.25473
AB - We present a simple analysis of the energy references and of the magnetic-field-dependent and system-dependent features of the Landau energy levels. The energy reference used in describing Landau quantization is usually taken as given, with the Fermi levels of the electron system and the coupled reservoir aligned in thermal equilibrium. Nevertheless, the dependence of the Landau-level spectrum on magnetic field can make the relation between these energy references less transparent. In this work, we show that when a magnetic field is applied and the confined Landau levels E_n are established, both the Fermi level E_F and the bottom energy E_0 remain fixed when the magnetic field varies. We show that the bottom energy E_0 is independent of B, and determined by a system-dependent field B_1, defined by the condition that the first Landau level equals the Fermi energy. In contrast, the minimum of the parabolic well depends explicitly on the magnetic field. The resulting picture provides a simple way of displaying the relative motion of the Landau levels and the fixed Fermi level without introducing a magnetic-field-dependent energy zero.
ER -