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We study the Fermi surface of metallic, non-magnetic \textit{ortho}-IIYBa$_2$Cu$_3$O$_{6.5}$ using three different density-functional-basedband-structure techniques (GGA, GGA+U, PSIC). The calculated Fermi surfaceexhibits no pockets in GGA+U and PSIC, a minor one in GGA. Upon shifting theFermi level in the vicinity of the calculated value, we instead observe severalpocket structures. We calculate their cross-sectional areas and cyclotronmasses. Overall, our calculations show no solid evidence of the existence ofelectron-like --nor, in fact, of any-- Fermi surface pockets in this phase.This suggests that the origin of the pockets should be sought for in other,different phases.

Fermi-surface pockets in $YBa_2Cu_3O_{6.5}$ : A comparison of ab initio techniques