Abstract

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.

Key words: Dirac materials; nanocones; ground state; quantum effects in monolayer crystals.