# Uniqueness of Landau levels and their analogs with higher Chern numbers

## Authors

Bruno Mera, Tomoki Ozawa

## Abstract

Lowest Landau level wavefunctions are eigenstates of the Hamiltonian of a charged particle in two dimensions under a uniform magnetic field. They are known to be holomorphic both in real and momentum spaces, and also exhibit uniform, translationally invariant, geometrical properties in momentum space. In this paper, using the Stone-von Neumann theorem, we show that lowest Landau level wavefunctions are indeed the only possible states with unit Chern number satisfying these conditions. We also prove the uniqueness of their direct analogs with higher Chern numbers and provide their expressions.

#### 2 comments

###### scicastboard

Dear Dr Mera -- Thank you for posting an interesting summary. Question: In the presence of the gap, the Chern number is a topological invariant, which means that a small perturbation can not change its quantized value. Suppose we start with a perfect lowest Landau level in a homogenous field and introduce ANY small perturbation. The Chern number must remain the same, but the functions will change. Is there a statement that they become non-analytic?

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