  Experiments reveal that a confined electron system with two equally-populated
layers at zero magnetic field can spontaneously break this symmetry through an
interlayer charge transfer near the magnetic quantum limit. New fractional
quantum Hall states at unusual total filling factors such as \nu = 11/15 (= 1/3
+ 2/5) stabilize as signatures that the system deforms itself, at substantial
electrostatic energy cost, in order to gain crucial correlation energy by
"locking in" separate incompressible liquid phases at unequal fillings in the
two layers (e.g., layered 1/3 and 2/5 states in the case of \nu = 11/15).
