Non-Euclidean Geometry, Nontrivial Topology and Quantum Vacuum Effects

• Published in: Universe (Basel) 2018-02, Vol.4 (2), p.23
• Main Authors: Sitenko, Yurii, Gorkavenko, Volodymyr
• Format: Article
• Language: English
• Subjects: Boundary conditions; Conflicts of interest; Defects; Geometry; ground state; nanocones; Phase transitions; Physics; quantum effects in monolayer crystals; Topology; Vortices
• ISSN: 2218-1997; 2218-1997
• DOI: 10.3390/universe4020023

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.