IR Hall Effect for reconstructed Fermi surfaces

The IR Hall Effect in the presence of Fermi surface reconstruction is considered within a density wave model for a 2D metal. Reconstruction of a hole like Fermi surface can produce reconstructed electron-like or hole-like Fermi surfaces. For hole-like reconstruction the inverse Hall frequency (1/$\omega_{\mathrm{H}})$ remains positive. For an electron like reconstruction 1/$\omega_{\mathrm{H}}$ remains hole-like for small density wave gaps and passes continuously through zero as the gap become larger and the electron-like pockets becomes convex. These considerations are applied to IR Hall data on under doped YBCO. It is concluded that the reconstructed Fermi surface in under doped YBCO is hole-like.