Geometric orbital susceptibility: Quantum metric without Berry curvature

@article{Piechon2016GeometricOS,
  title={Geometric orbital susceptibility: Quantum metric without Berry curvature},
  author={Fr'ed'eric Pi'echon and Arnaud Raoux and J N Fuchs and G. Montambaux},
  journal={Physical Review B},
  year={2016},
  volume={94},
  pages={134423}
}
The orbital magnetic susceptibility of an electron gas in a periodic potential depends not only on the zero field energy spectrum but also on the geometric structure of cell-periodic Bloch states which encodes interband effects. In addition to the Berry curvature, we explicitly relate the orbital susceptibility of two-band models to a quantum metric tensor defining a distance in Hilbert space. Within a simple tight-binding model allowing for a tunable Bloch geometry, we show that interband… 
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