Casimir (vacuum) energy in planar QED with strong coupling

Ferromagnetic Phase in Graphene‐Based Planar Heterostructures Induced by Charged Impurity

“…The corresponding values of vacuum energy turn out to be E ren vac = −674.167 and E ren vac = −56518.3, respectively, and lie substantially lower than in absence of magnetic field (E ren vac = −456.759 and E ren vac = −25240.2, see Ref. [3]). Therefore the spontaneous generation of ferromagnetic phase beyond the "Curie point" Z ≥ Z * turns out to be energetically favorable compared to the purely electrostatic polarization in graphene on substrates SiC and h-BN.…”

“…In Refs. [3,14,15] there was shown that in absence of magnetic field this series in m j is linearly divergent. Further on account of model-independent considerations it was argued that the elimination of this divergence should follow the same rules as in the QEDperturbation theory (PT) via regularization the fermionic loop with two external lines.…”

“…For the planar DE there are known only single results, which concern either point-like Coulomb and string-like AB sources or a quite different background of vector and scalar Cornell potentials combined with an external magnetic field [8,12]. This circumstance makes impossible the evaluation of the Casimir (vacuum) energy via representing it as the sum of the integral of the total elastic scattering phase and the contribution of discrete spectrum, which is shown to be very powerful in purely Coulomb problems [3,[13][14][15]. However, elaborated recently in Refs.…”

“…[3,14,15] the behavior of vacuum energy in the strongly coupled planar QED-system similar to graphene in presence of a supercritical extended Coulomb source has been explored. In particular, there was established the fact of rapid decline of the vacuum energy in the over-critical region ∼ (−Z 3 /R 0 ) with Z > Z cr,1 and R 0 being the charge and radius of the Coulomb source, which provides complete screening of the electrostatic repulsive self-energy of the external source for impurity charges Z ∼ 6 for α g ≃ 0.8 [3]. Such behavior of the vacuum energy indicates that in the over-critical region with growing impurity charge the induced polarization effects become essentially non-perturbative.…”

Casimir (vacuum) energy in planar QED with strong coupling

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The essentially non-perturbative vacuum polarization effects, caused by an extended external supercritical Coulomb source, are explored for a planar Dirac-Coulomb (DC) system with strong coupling (similar to graphene and graphene-based heterostructures). Taking account of results, obtained in [1] for the induced charge density ρV P ( r), in the present paper the evaluation of the Casimir (vacuum) energy EV P is presented. The main result is that for a wide range of the system parameters in the overcritical region EV P turns out to be a rapidly decreasing negative function ∼ −Z 3 /R0 with Z , R0 being the charge and the size of the external source.

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