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arXiv · 2109.02135

On the Sector Counting Lemma

Zhituo Wang
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Abstract

In this short note we prove a sector counting lemma for a class of Fermi surface on the plane which are $C^2$-differentiable and strictly convex. This result generalizes the one proved in \cite{FKT} for the class of $C^{2+r}$-differentiable, $r\ge3$, strictly convex and strongly asymmetric Fermi surfaces, and the one proved in \cite{FMRT} and \cite{BGM1}, for the class of $C^2$-differentiable, strictly convex and central symmetric Fermi surfaces. This new sector counting lemma can be used to construct interacting many-fermion models for the doped graphene, in which the Fermi surface is extended and quasi-symmetric.

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Zhituo Wang. 2021-09-17. On the Sector Counting Lemma. https://arxiv.org/abs/2109.02135

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