General First-Principles Approach to Crystals in Finite Magnetic Fields

We introduce a general first-principles methodology for computing electronic structure in a finite uniform magnetic field which allows for an arbitrary rational magnetic flux and nonlocal pseudopotentials, at a comparable time complexity of conventional plane-wave pseudopotential approaches in zero-field conditions. The versatility of this method is demonstrated through comprehensive applications to both molecular and crystalline systems, including calculations of magnetizabilities, magnetically induced currents, and magnetic energy bands. Furthermore, we provide rigorous proofs of two fundamental properties for crystals in uniform magnetic fields: the "strong translational symmetry" and "magnetic bands shift" phenomena.