Electronic diamagnetism in a three-dimensional lattice

We calculate the ground-state properties of a noninteracting electron gas in a cubic tight-binding lattice in a uniform magnetic field. For small parallel hopping ${\mathit{t}}_{\mathrm{\parallel }}$ the ground-state energy shows local minima at values of the flux Φ satisfying the commensurability condition ν=ΦM+N, where ν is the filling fraction and N and M are integers. The ground-state energy at these minima is rigorously equal to the strictly two-dimensional value. For larger ${\mathit{t}}_{\mathrm{\parallel }}$ the cusps disappear. We also study the weak-field response of the system by calculating the current-current correlation function. The observed crossover from Landau diamagnetism to paramagnetism with increasing ν is explained in terms of the band structure.