A rigorous proof of the Landau-Peierls formula and much more
Philippe Briet (CPT), Horia D. Cornean (Math. Dept., Aalborg, University), Baptiste Savoie (CPT)
TL;DR
This paper provides a rigorous mathematical proof of the Landau-Peierls formula for orbital magnetic susceptibility in non-interacting Bloch electron gases, confirming longstanding conjectures and extending understanding of magnetic properties in various materials.
Contribution
It offers the first rigorous proof of the Landau-Peierls formula and extends the analysis to metals and insulators at fixed temperature and density.
Findings
Confirmed the Landau-Peierls formula in the low temperature and density limit
Established a rigorous mathematical framework for magnetic susceptibility
Extended results to both metals and semiconductors/insulators
Abstract
We present a rigorous mathematical treatment of the zero-field orbital magnetic susceptibility of a non-interacting Bloch electron gas, at fixed temperature and density, for both metals and semiconductors/insulators. In particular, we obtain the Landau-Peierls formula in the low temperature and density limit as conjectured by T. Kjeldaas and W. Kohn in 1957.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Quantum and electron transport phenomena · Advanced Chemical Physics Studies