  On the basis of the continuum model for long-wavelength charge carriers,
originating in the tight-binding approximation for the nearest-neighbour
interaction of atoms in the crystalline lattice, we consider quantum
ground-state effects of electronic excitations in Dirac materials with
two-dimensional monolayer honeycomb structures warped into nanocones by a
disclination; the nonzero size of the disclination is taken into account, and a
boundary condition at the edge of the disclination is chosen to ensure
self-adjointness of the Dirac-Weyl Hamiltonian operator. We show that the
quantum ground-state effects are independent of the disclination size and find
circumstances when they are independent of a parameter of the boundary
condition. The magnetic flux circulating in the angular direction around the
nanocone apex and the pseudomagnetic flux directed orthogonally to the nanocone
surface are shown to be induced in the ground state.
