Multi-band topological phases of periodically kicked molecules

We show that the simplest of existing molecules -- closed-shell diatomics not interacting with one another -- host topologically nontrivial phases when driven by periodic far-off-resonant laser pulses. A periodically kicked molecular rotor can be mapped onto a "crystalline" lattice in angular momentum space. This allows to define quasimomenta and the band structure in the Floquet representation, by analogy with the Bloch waves of solid-state physics. Applying laser pulses spaced by 1/3 of the molecular rotational period creates a lattice with three atoms per unit cell with staggered hopping, whose band structure features Dirac cones. These Dirac cones, topologically protected by reflection and time-reversal symmetry, are reminiscent of (although not equivalent to) the ones seen in graphene. They -- and the corresponding edge states -- are broadly tunable by adjusting the laser intensities and can be observed in present-day experiments by measuring molecular alignment and populations of rotational levels. This paves the way to study controllable topological physics in gas-phase experiments with small molecules as well as to classify dynamical molecular states by their topological invariants.