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Based on first principle calculations, we show that a family of nonmagneticmaterials including TaAs, TaP, NbAs and NbP are Weyl semimetal (WSM) withoutinversion center. We find twelve pairs of Weyl points in the whole Brillouinzone (BZ) for each of them. In the absence of spin-orbit coupling (SOC), bandinversions in mirror invariant planes lead to gapless nodal rings in theenergy-momentum dispersion. The strong SOC in these materials then opens fullgaps in the mirror planes, generating nonzero mirror Chern numbers and Weylpoints off the mirror planes. The resulting surface state Fermi arc structureson both (001) and (100) surfaces are also obtained and show interesting shapes,pointing to fascinating playgrounds for future experimental studies.

Weyl semimetal phase in non-centrosymmetric transition metal monophosphides