  Photonic materials are a rapidly growing platform for studying condensed
matter physics with light. The exquisite capability of state preparation and
detection, as well as the engineering of lattice geometries, is allowing us to
learn about the relation between microscopic dynamics and macroscopic
properties. Here we study Bose-Einstein condensation of exciton-polaritons into
a lowest Landau level of a strained honeycomb lattice of semiconductor
micropillars. The strain induces a pseudomagnetic field which has opposite sign
in each Dirac valley. With a suitably designed sublattice-asymmetry of the
incoherent pump, we find that the condensate spontaneously breaks the valley
symmetry and polaritons accumulate in the lowest Landau level of a given
valley. For growing condensate sizes, the interplay of the pseudomagnetic field
and the quantisation of circulation in the condensate leads to the formation of
a vortex array in analogy with an ultracold atomic superfluid in a rapidly
rotating trap. We explain how this peculiar non-equilibrium stationary state --
which takes place in the middle of the energy spectrum -- results from a
dynamical balance of incoherent pump and losses and is stabilised by the
sublattice polarisation of the lowest Landau level. Our results offer a new
platform where to study the exciting physics of arrays of quantised vortices
and pave the way to explore the transition from a vortex-dominated phase to the
fractional quantum Hall regime.
