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We study the influence of a magnetic flux tube on the possibility toelectrostatically confine electrons in a graphene quantum dot. Without magneticflux tube, the graphene pseudospin is responsible for a quantization of thetotal angular momentum to half-integer values. On the other hand, with a fluxtube containing half a flux quantum, the Aharonov-Bohm phase and Berry phaseprecisely cancel, and we find a state at zero angular momentum that cannot beconfined electrostatically. In this case, true bound states only exist inregular geometries for which states without zero-angular-momentum componentexist, while non-integrable geometries lack confinement. We support thesearguments with a calculation of the two-terminal conductance of a gate-definedgraphene quantum dot, which shows resonances for a disc-shaped geometry and fora stadium-shaped geometry without flux tube, but no resonances for astadium-shaped quantum dot with a $\pi$-flux tube.

Interplay of Aharonov-Bohm and Berry phases in gate-defined graphene quantum dots