Hubbard U is a parameter that describes the strength of the on-site Coulomb interactions between electrons in a material. In graphene and nanotubes, it is used to account for the strong electron-electron interactions that occur due to their unique atomic and electronic structures.
Hubbard U plays a crucial role in determining the electronic properties of graphene and nanotubes. It can lead to the formation of localized electronic states, known as Hubbard bands, which can significantly impact the material's conductivity, bandgap, and other electronic properties.
Hubbard U can induce a bandgap in graphene and nanotubes, which are otherwise known as zero-bandgap materials. This is because it can open up a gap between the valence and conduction bands, allowing for the control of the material's conductivity and other electronic properties.
Hubbard U is typically calculated using theoretical methods such as density functional theory (DFT) or many-body perturbation theory (MBPT). These methods take into account the atomic and electronic structure of the material to determine the strength of the on-site Coulomb interactions.
While it is challenging to directly measure Hubbard U in graphene and nanotubes, its effects can be observed through various experimental techniques such as angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM).