Theory of Orbital Susceptibility in the Tight-Binding Model: Corrections to the Peierls Phase

An extended formula for orbital susceptibility including corrections of the Peierls phase is introduced. By using the new developed formula, the orbital susceptibility of benzene is estimated analytically on the basis of the $\pi$ electron approximation. As a result, it is found that the orbital susceptibility is 1.2 times larger than that estimated only from the Peierls phase. The Coulomb interaction dependence of the orbital susceptibility of benzene is also discussed by using exact diagonalization. It is found that the absolute value of the orbital susceptibility decreases as the Coulomb interaction increases, while the ratio of the orbital susceptibility with and without the corrections of the Peierls phase increases. Finally, we discuss the orbital susceptibility of a single-band tight-binding model on a square lattice. We clarify that the correction of the Peierls phase is comparable to the Landau--Peierls orbital susceptibility and that it corresponds to the Fermi sea term.