A local view of quantum mechanics at high magnetic field for the 2D
electron gas

We show how to reformulate the quantum dynamics of 2D electrons submitted to a 
high perpendicular magnetic field in terms of a basis of semi-coherent states [1].
This family of vortex-like wave-functions, strongly localized at the scale of the
magnetic length, provides an intuitive and rigorous quantum analog to the fast
classical cyclotron motion. In the presence of an arbitrary smooth disordered
potential, the theory is controlled by a systematic gradient expansion, and allows 
to compute analytically several experimental observables, such as the local density 
of states [2], which was only recently measured by scanning tunneling spectroscopy
both for semiconducting [3] and graphene [4] devices. We discuss how the disorder
landscape can be reliably extracted from the experimental data, and present 
prospects regarding transport in the quantum Hall regime.

[1] T. Champel and S. Florens, Phys. Rev. B 80, 125322 (2009).

[2] T. Champel and S. Florens, arXiv:1003.3413 (2010).

[3] K. Hashimoto et al., Phys. Rev. Lett. 101, 256802 (2008).

[4] D. Miller et al., Science 324, 924 (2009).