Non-Euclidean Geometry, Nontrivial Topology and Quantum Vacuum Effects

• Main Authors: Yurii A. Sitenko, Volodymyr M. Gorkavenko
• Format: Article
• Language: English
• Published: MDPI AG 2018-01-01
• Series: Universe
• Subjects: nanocones; ground state; quantum effects in monolayer crystals
• Online Access: http://www.mdpi.com/2218-1997/4/2/23

Space out of a topological defect of the Abrikosov–Nielsen–Olesen (ANO) vortex type is locally flat but non-Euclidean. If a spinor field is quantized in such a space, then a variety of quantum effects are induced in the vacuum. On the basis of the continuum model for long-wavelength electronic excitations originating in the tight-binding approximation for the nearest-neighbor interaction of atoms in the crystal lattice, we consider quantum ground-state effects in Dirac materials with two-dimensional monolayer 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 we find circumstances in which they are independent of parameters of the boundary condition.