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We investigate the relation between the Fermi sea (FS) of zero-field carriersin two-dimensional systems and the FS of the corresponding composite fermionswhich emerge in a high magnetic field at filling $\nu = \frac{1}{2}$, as thekinetic energy dispersion is varied. We study cases both with and withoutrotational symmetry, and find that there is generally no straightforwardrelation between the geometric shapes and topologies of the two FSs. Inparticular, we show analytically that the composite Fermi liquid (CFL) iscompletely insensitive to a wide range of changes to the zero-field dispersionwhich preserve rotational symmetry, including ones that break the zero-field FSinto multiple disconnected pieces. In the absence of rotational symmetry, weshow that the notion of `valley pseudospin' in many-valley systems isgenerically not transferred to the CFL, in agreement with experimentalobservations. We also discuss how a rotationally symmetric band structure caninduce a reordering of the Landau levels, opening interesting possibilities ofobserving higher-Landau-level physics in the high-field regime.

Connection between Fermi contours of zero-field electrons and $\nu=\frac12$ composite fermions in two-dimensional systems