Non-Drude THz conductivity of graphene due to structural distortions

The remarkable electrical, optical and mechanical properties of graphene make it a desirable material for electronics, optoelectronics and quantum applications. A fundamental understanding of the electrical conductivity of graphene across a wide frequency range is required for the development of such technologies. In this study, we use terahertz (THz) time-domain spectroscopy to measure the complex dynamic conductivity of electrostatically gated graphene, in a broad $\sim$0.1 - 7 THz frequency range. The conductivity of doped graphene follows the conventional Drude model, and is predominantly governed by intraband processes. In contrast, undoped charge-neutral graphene exhibits a THz conductivity that significantly deviates from Drude-type models. Via quantum kinetic equations and density matrix theory, we show that this discrepancy can be explained by additional interband processes, that can be exacerbated by electron backscattering. We propose a mechanism where such backscattering -- which involves flipping of the electron pseudo-spin -- is mediated by the substantial vector scattering potentials that are associated with structural deformations of graphene. Our findings highlight the significant impact that structural distortions and resulting electrostatic vector scattering potentials can have on the THz conductivity of charge-neutral graphene. Our results emphasise the importance of the planar morphology of graphene for its broadband THz electronic response.