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We measure magnetic quantum oscillations in the underdoped cupratesYBa$_2$Cu$_3$O$_{6+x}$ with $x=0.61$, 0.69, using fields of up to 85 T. Thequantum-oscillation frequencies and effective masses obtained suggest that theFermi energy in the cuprates has a maximum at $p\approx 0.11-0.12$. On eitherside, the effective mass may diverge, possibly due to phase transitionsassociated with the T=0 limit of the metal-insulator crossover (low-$p$ side),and the postulated topological transition from small to large Fermi surfaceclose to optimal doping (high $p$ side).

physical review letters

Magnetic quantum oscillations in YBa$_2$Cu$_3$O$_{6.61}$ and  YBa$_2$Cu$_3$O$_{6.69}$ in fields of up to 85 T; patching the hole in the  roof of the superconducting dome