Optical absorption in two-dimensional materials with tilted Dirac cones

Abstract

The interband optical absorption of linearly polarized light by two-dimensional (2D) semimetals hosting tilted and anisotropic Dirac cones in the band structure is analysed theoretically. Supercritically tilted (type-II) Dirac cones are characterized by an absorption that is highly dependent on the incident photon polarization and frequency and is tunable by changing the Fermi level with a back-gate voltage. Type-II Dirac cones exhibit open Fermi surfaces and large regions of the Brillouin zone where the valence and conduction bands sit either above or below the Fermi level. As a consequence, unlike their subcritically tilted (type-I) counterparts, type-II Dirac cones have many states that are Pauli blocked even when the Fermi level is tuned to the level crossing point. We analyze the interplay of the tilt parameter with the Fermi velocity anisotropy, demonstrating that the optical response of a Dirac cone cannot be described by its tilt alone. As a special case of our general theory, we discuss the proposed 2D type-I semimetal 8-$Pmmn$ borophene. Guided by our in-depth analytics, we develop an optical recipe to fully characterize the tilt and Fermi velocity anisotropy of any 2D tilted Dirac cone solely from its absorption spectrum. We expect our paper to encourage Dirac cone engineering as a major route to create gate-tunable thin-film polarizers.