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Insulator, conductor and commensurability: a topological approach

Masaki Oshikawa
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Abstract

I discuss a topological relation of the conduction property of a many-particle system on a periodic lattice at zero temperature to the energy spectrum. When the particle number per unit cell is an irreducible fraction $p/q$, an insulator must have $q$ low-lying states of energy $o(1/L)$ in one dimension and of energy $o(1)$ in two dimensions, where $L$ is the linear system size.

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Masaki Oshikawa. 2003-06-04. Insulator, conductor and commensurability: a topological approach. https://doi.org/10.1103/physrevlett.90.236401%2010.1103%2Fphysrevlett.91.109901

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