Generating Weyl nodes in non-centrosymmetric cubic crystal structures

Weyl nodes are band degeneracy points with relativistic dispersion and topological properties arising in certain three-dimensional periodic systems with broken parity-time symmetry. Despite their fundamental importance, the intrinsic accidental nature of Weyl nodes makes the general endeavor of finding them a challenging task. In this work, we show how Weyl nodes can be generated in cubic crystal structures with a single orbital per site based on a systematic approach that combines a tight-binding analysis with general principles which can be applied to both fermionic and bosonic systems. The cubic Weyl systems generated here preserve time-reversal symmetry but break inversion symmetry hosting the minimum four Weyl points allowed. Laser assisted hopping techniques on cubic optical lattices can allow the artificial generation of such Weyl semimetals. Magnetic oscillation experiments can be used to probe the Weyl orbits along the Fermi arcs on opposite sides of the sample connected through the bulk Weyl nodes.