Negative static permittivity and violation of Kramers-Kronig relations in quasi-two-dimensional crystals

Abstract

We investigate the wave-vector and frequency-dependent screening of the electric field in atomically thin (quasi-two-dimensional) crystals. For graphene and hexagonal boron nitride we find that, above a critical wave-vector $q_c$, the static permittivity $\epsilon (q>q_c,\omega =0)$ becomes negative and the Kramers-Kronig relations do not hold for $\epsilon (q>q_c,\omega )$. Thus, in quasi-two-dimensional crystals, we reveal the physical confirmation of a proposition put forward decades ago (Kirzhnits, 1976), allowing for the breakdown of Kramers-Kronig relations and for the negative static permittivity. In the vicinity of the critical wave-vector, we find a giant growth of the permittivity. Our results, obtained in the {\it ab initio} calculations using both the random-phase approximation and the adiabatic time-dependent local-density approximation, and further confirmed with a simple slab model, allow us to argue that the above properties, being exceptional in the three-dimensional case, are common to quasi-two-dimensional systems.

9 pages, 13 figures

References in corpus (4)

• The electronic properties of graphene
• Dynamical polarization of graphene at finite doping
• Excitonic Effects on the Optical Response of Graphene and Bilayer Graphene
• Electronic excitations in quasi-2D crystals: What theoretical quantities are relevant to experiment?

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• Broken Symmetries in Quasi-2D Charged Systems via Negative Dielectric Confinement
• Negative superluminal velocity and violation of Kramers-Kronig relations in "causal" optical setups