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

TL;DR

This study demonstrates that in atomically thin quasi-two-dimensional crystals like graphene and hBN, the static permittivity can become negative above a critical wave-vector, violating Kramers-Kronig relations, confirmed through ab initio calculations.

Contribution

It provides the first direct confirmation that negative static permittivity and Kramers-Kronig violations occur in quasi-two-dimensional materials, extending previous theoretical propositions.

Findings

Negative static permittivity appears above a critical wave-vector

Kramers-Kronig relations break down for certain wave-vectors

Giant permittivity growth near the critical wave-vector

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 $\varepsilon(q \! > \!q_c,\omega \! = \!0)$ becomes negative and the Kramers-Kronig relations do not hold for $\varepsilon(q \! > \! q_c,\omega)$. Thus, in quasi-two-dimensional crystals, we reveal 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.