2015

Geometry of Landau orbits in the absence of rotational symmetry

Haldane, F. D. M., Shen, Yu

Understand

The integer quantum Hall effect (IQHE) is usually modeled using Galilean-invariant or rotationally-invariant Landau levels.

However, these are not generic symmetries of electrons moving in a crystalline background, even in the low-density continuum limit.
We present a treatment of the IQHE which abandons the Galilean dispersion relation while keeping inversion symmetry.
We define an emergent metric $g^n_{ab}$ for each Landau level with a reformulation of the Hall viscosity.

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