  It is shown that vibrated packings of frictional disks self-organize
cooperatively onto a rotational-transport state where the long-time angular
velocity $\bar\omega_i$ of each disk $i$ is nonzero. Steady rotation is
mediated by the spontaneous breaking of local reflection symmetry, arising when
the cages in which disks are constrained by their neighbors acquire quenched
disorder at large packing densities. Experiments and numerical simulation of
this unexpected phenomenon show excellent agreement with each other, revealing
two rotational phases as a function of excitation intensity, respectively the
low-drive (LDR) and the moderate-drive (MDR) regimes. In the LDR, interdisk
contacts are persistent and rotation happens due to frictional sliding. In the
MDR, disks bounce against each other, still forming a solid phase. In the LDR,
simple energy-dissipation arguments are provided, that support the observed
dependence of the typical rotational velocity on excitation strength.
