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

Vladimir U. Nazarov

Published 2015-06-24Version 1

We investigate the wave-vector and frequency-dependent screening of the electric field in atomically thin (quasi-two-dimensional) crystals of graphene and hexagonal boron nitride. We find that, above a critical wave-vector $q_c$, the static permittivity $\varepsilon(q \! > \!q_c,\omega \! = \!0)$ becomes negative and the Kramers-Kronig relations do not hold for $\varepsilon(q \! > \! q_c,\omega)$. Thus, in quasi-two-dimensional crystals, we reveal a robust physical confirmation of a proposition put forward decades ago (Kirzhnits, 1976), allowing for the breakdown of Kramers-Kronig relations and negative values of the static permittivity. In the vicinity of the critical wave-vector, we find a giant growth of the permittivity. We argue that these properties, being exceptional in the three-dimensional case, are common to quasi-two-dimensional crystals, while their discovery opens new pathways in the two-dimensional superconductivity.