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

V. U. Nazarov*

*Corresponding author for this work

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6 Scopus citations


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 qc, the static permittivity (q>qc,ω=0) becomes negative and the Kramers-Kronig relations do not hold for (q>qc,ω). Thus, in quasi-two-dimensional crystals, we reveal the physical confirmation of a proposition put forward decades ago [D. A. Kirzhnits, Sov. Phys. Usp. 19, 530 (1976)SOPUAP0038-567010.1070/PU1976v019n06ABEH005268], allowing for the breakdown of Kramers-Kronig relations and for negative static permittivity. In the vicinity of the critical wave vector, we find a giant growth of the permittivity. Our results, obtained in the 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.

Original languageAmerican English
Article number161402
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number16
StatePublished - 6 Oct 2015
Externally publishedYes

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© 2015 American Physical Society.


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