Quantum Phases of Electron Double Layers: Soft Collective Modes and Finite-Temperature Phase Transitions

The extreme softening of spin-excitations in electron double-layers is studied by resonant inelastic light scattering. At even integer quantum Hall states, we find evidence of three distinct configurations of spin. Transformations among these spin states appear as quantum phase transitions tuned by interlayer interactions and Zeeman energies. A broken-symmetry phase emerges when a long wavelength spin-excitation across the tunneling gap goes soft. Spectra measured in this phase offer remarkable evidence of a finite-temperature phase transitions. Critical temperatures determined from spectra display significant dependence on magnetic field.