  The discovery of photonic topological insulators (PTIs) has opened the door
to fundamentally new topological states of light.Current
time-reversal-invariant PTIs emulate either the quantum spin Hall (QSH) effect
or the quantum valley Hall (QVH) effect in condensed-matter systems, in order
to achieve topological transport of photons whose propagation is predetermined
by either 'photonic pseudospin' (abbreviated as 'spin') or valley. Here we
demonstrate a new class of PTIs, whose topological phase is not determined
solely by spin or valley, but is controlled by the competition between their
induced gauge fields. Such a competition is enabled by tuning the strengths of
spin-orbit coupling (SOC) and inversion-symmetry breaking in a single PTI. An
unprecedented topological transition between QSH and QVH phases that is hard to
achieve in condensed-matter systems is demonstrated. Our study merges the
emerging fields of spintronics and valleytronics in the same photonic platform,
and offers novel PTIs with reconfigurable topological phases.
