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

Borophene, a single layer of boron atoms, has many of the exotic properties of its better-known cousin graphene. Here, the authors use ab initio calculations to understand the atomic origin of the tilt in the two-dimensional Dirac cone of 8Pmmn borophene, thereby suggesting atomic substitutions to vary the tilt. 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.

Automated summary

The authors use ab initio calculations to understand the atomic origin of the tilt in the two-dimensional Dirac cone of 8Pmmn borophene and suggest atomic substitutions to vary the tilt. Borophene, a single layer of boron atoms, has many of the exotic properties of graphene.