Landau diamagnetism and the de Haas-van Alphen effect from a single geometric construction

@misc{lee2026landau,
  title = {{Landau diamagnetism and the de Haas-van Alphen effect from a single geometric construction}},
  author = {Sung-Hoon Lee},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20146},
  eprint = {2609.20146},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20146},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Landau diamagnetism and the de Haas-van Alphen effect from a single geometric construction
AU  - Sung-Hoon Lee
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20146
UR  - https://arxiv.org/abs/2609.20146
AB  - Landau diamagnetism is usually derived from the grand canonical potential, a calculation that yields the correct susceptibility but little physical insight, while the rule that extremal cross sections govern the de Haas-van Alphen (dHvA) oscillations is commonly asserted rather than exhibited. We present an elementary zero-temperature construction in which the occupied states of a free-electron gas are grouped, interval by interval along the field direction, into the Landau levels onto which they condense. Within each interval the field-induced energy cost reduces to a transfer of states between two congruent triangles, and center-of-mass arithmetic yields the Landau susceptibility. The construction fails only in a narrow neighborhood of an extremal cross section of the Fermi surface; there the contribution oscillates with the dHvA period, one oscillation for each Landau level that passes through the extremal cross section. Direct zero-temperature state counting locates the oscillation: the residual is concentrated in the few intervals nearest the extremal cross section, the summed contribution of the distant ones being negligible on the scale of the peak oscillation amplitude.
ER  -