Tunning the tilt of the Dirac cone by atomic manipulations in 8Pmmn borophene

Abstract

Two dimensional quantum materials possessing Dirac cones in their spectrum are fascinating due to their emergent low-energy Dirac fermions. In 8Pmmn borophene the Dirac cone is furthermore tilted, which is a proxy for spacetime geometry, since the future light-cone depends on the underlying metric. Therefore it is important to understand the microscopic origin of the tilt. Here, based on ab-initio calculations, we decipher the atomistic mechanism of the formation of tilt. First, nearest-neighbor hopping on a buckled honeycomb lattice forms an upright Dirac cone. Then, the difference in the renormalized anisotropic second-neighbor hopping, formed by virtual hoppings on one-dimensional chains of atoms, tilts the Dirac cone. We construct an accurate tight-binding model on honeycomb graph for analytical investigation, and we find that substitution of certain boron atoms by carbon provides a way to change the tilt of the cone.