Analysis of causality principle for the conductivity of graphene

A paper by Kazan University and Russian Academy of Sciences appeared in Physical Review D.

Vladimir Mostepanenko, Chief Research Associate of KFU Cosmology Lab and Pulkovo Astronomical Observatory, explains, “Despite graphene layers’ extremely small width, it has proven to be a firm material which conducts electricity even under zero temperatures when density of charge carriers also equals zero. But something absolutely unexpected was that this residual conductivity can be expressed through fundamental physical constants – electron charge and Planck constant. Graphene has been used successfully in dozens of electronic devices and has been found in interstellar matter.”

Graphene's unusual qualities led to speculation that the causality principle may not be observed for it. The authors, Vladimir Mostepanenko and Galina Klimchitskaya, proved that the principle is preserved for graphene. Through the direct analytic calculation it was shown that the real and imaginary parts of graphene conductivity, found recently on the basis of first principles of thermal quantum field theory using the polarization tensor in (2+1)-dimensional space-time, satisfy the Kramers-Kronig relations precisely.

The results are important for further inquiries into reflective and absorptive qualities of graphene.