  The toolbox quantities used for manipulating the flow of light include
typically amplitude, phase, and polarization. Pseudospins, such as those
arising from valley degrees of freedom in photonic structures, have recently
emerged as an excellent candidate for this toolbox, in parallel with rapid
development of spintronics and valleytronics in condensed-matter physics. Here,
by employing symmetry-broken honeycomb photonic lattices, we demonstrate
valley-dependent wavepacket self-rotation manifested in spiraling intensity
patterns, which occurs without any initial orbital angular momentum.
Theoretically, we show that such wavepacket self-rotation is induced by the
Berry phase and results in Zitterbewegung oscillations. The "center-of-mass" of
the wavepacket oscillates at a gap-dependent frequency, while the helicity of
self-rotation is valley-dependent, that is, correlated with the Berry
curvature. Our results lead to new understanding of the venerable
Zitterbewegung phenomenon from the perspective of topology and are readily
applicable on other platforms such as two-dimensional Dirac materials and
ultracold atoms.
