The Casimir effect for fermionic currents in conical rings with applications to graphene ribbons

Abstract

We investigate the combined effects of boundaries and topology on the vacuum expectation values (VEVs) of the charge and current densities for a massive 2D fermionic field confined on a conical ring threaded by a magnetic flux. Different types of boundary conditions on the ring edges are considered for fields realizing two inequivalent irreducible representations of the Clifford algebra. The related bound states and zero energy fermionic modes are discussed. The edge contributions to the VEVs of the charge and azimuthal current densities are explicitly extracted and their behavior in various asymptotic limits is considered. On the ring edges the azimuthal current density is equal to the charge density or has an opposite sign. We show that the absolute values of the charge and current densities increase with increasing planar angle deficit. Depending on the boundary conditions, the VEVs are continuous or discontinuous at half-integer values of the ratio of the effective magnetic flux to the flux quantum. The discontinuity is related to the presence of the zero energy mode. By combining the results for the fields realizing the irreducible representations of the Clifford algebra, the charge and current densities are studied in parity and time-reversal symmetric fermionic models. If the boundary conditions and the phases in quasiperiodicity conditions for separate fields are the same the total charge density vanishes. Applications are given to graphitic cones with edges (conical ribbons).

Casimir effect for fermion condensate in conical rings

“…In addition to an infinite number of modes with γ = γ l , depending on the boundary conditions, one can have a mode with γa = iη, η > 0. As it has been shown in [59], for that mode η ma and, hence, E 0. This means that under the boundary conditions (7) the vacuum state is always stable.…”

“…Similar to the case of the charge and current densities, discussed in [59], it can be shown that the expression ( 28) is valid in the presence of bound states as well. Under the replacements…”

Vacuum fermionic currents in braneworld models on AdS bulk with a cosmic string

“…For a massless field the corresponding boundary-induced contribution vanishes. Note that the fermionic condensate, the charge and current densities in (2+1)-dimensional conical spacetime with a single and two circular boundaries have been investigated in [57,[60][61][62].…”

Fermionic Condensate on Finite Radius Cones

“…The fermionic condensate for the bag boundary condition has been investigated in [21]. The vacuum expectation values of the fermionic charge and current densities in conical rings, with boundary conditions that include also the condition (4), have been investigated recently in [27].…”

“…Graphene cones with these angles have been observed in experiments [17]. The vacuum polarization in graphene with a conical topological defect is investigated in [19]- [27] within the framework of a long-wavelength continuum model. In the main part of those papers for cones with edges the MIT bag boundary condition was imposed on the fermionic field.…”