Geometry of compressible and incompressible quantum Hall states: Application to anisotropic composite-fermion liquids

Haldane's geometrical description of fractional quantum Hall states is generalized to compressible states. It is shown that anisotropy in the composite fermion Fermi surface is a direct reflection of this intrinsic geometry. A simple model is introduced in which the geometric parameter can be obtained exactly from other parameters including electron mass anisotropy. Our results compare favorably with recent measurements of anisotropy in composite fermion Fermi surface [Kamburov, Liu, Shayegan, Pfeiffer, West, and Baldwin, Phys. Rev. Lett. 110, 206801 (2013)]. Broader implications of our results are discussed.