  We propose four different thermodynamically stable structural phases of
arsenic monolayers based on ab-initio density functional theory calculations
all of which undergo a topological phase transition on application of a
perpendicular electric field. All the four arsenic monolayer allotropes have a
wide band gap, varying from 1.21 eV to 3.0 eV (based on GW calculations), and
in general they undergo a metal-insulator quantum phase transition on
application of uniaxial in-layer strain. Additionally an increasing transverse
electric field induces band-inversion at the {\Gamma} point in all four
monolayer allotropes, leading to a nontrivial topological phase (insulating for
three and metallic for one allotrope), characterized by the switching of the Z2
index, from 0 (before band inversion) to 1 (after band inversion). The
topological phase tuned by the transverse electric field, should support
spin-separated gapless edge states which should manifest in quantum spin Hall
effect.
