First-Principles Electronic Structure Calculation of Crystals in Laboratory Magnetic Fields
External magnetic fields can qualitatively reshape the electronic structure of crystals, underpinning quantum Hall physics, Landau-level spectra and field-induced topological phases. Their first-principles treatment at laboratory-scale fields is, however, hindered by magnetic-flux quantization, which requires magnetic unit cells with areas inversely proportional to the applied field. Such cells contain a large number of chemical unit cells, rendering real-space and plane-wave calculations prohibitively expensive. Here we, for the first time, construct a magnetic Bloch basis built from linear combinations of gauge-including Gaussian-type atomic orbitals, which incorporate the magnetic-field phase factors required by magnetic translation symmetry. The framework requires far fewer basis functions than real-space or plane-wave representations of the same magnetic supercell and retains the sparsity of an atom-centred basis, together substantially reducing computational cost. We validate the framework by reproducing Landau-level spectrum of graphene from first principles. This approach provides a practical route to simulations of crystalline materials under experimentally accessible magnetic fields.