Fermi surfaces and quantum oscillations in the underdoped high-T _c superconductors YBa₂Cu₃O_6.5 and YBa₂Cu₄O₈

We study underdoped high-T_c superconductors YBa ₂Cu₃O_6.5 and YBa₂Cu ₄O₈ using first-principles pseudopotential methods with additional Coulomb interactions at the Cu atoms and obtain Fermi-surface pocket areas in close agreement with measured Shubnikov-de Haas and de Haas-van Alphen oscillations. With antiferromagnetic order in CuO₂ planes, stable in the calculations, small hole pockets are formed near the so-called Fermi-arc positions in the Brillouin zone, which reproduce the low-frequency oscillations. A large electron pocket, necessary for the negative Hall coefficient, is also formed in YBa₂Cu₃O_6.5, giving rise to the high-frequency oscillations as well. Effective masses and specific heats are also calculated. Our results highlight the important role of magnetic order in the electronic structure of underdoped high-T_c superconductors.