Collective excitations of an electron Wigner lattice in double-quantum-well systems

The time-dependent Hartree-Fock approximation is used to study the collective excitations of an electron Wigner solid state in a double quantum well under strong magnetic fields. The electronic tunneling between the two quantum wells is taken into account explicitly. The low-lying excitations consist of an intralevel acoustic phonon and an interlevel optical phonon. When the well separation is increased beyond a certain value, a soft mode is developed in the energy spectrum of the interlevel optical phonon, indicating that the system undergoes a phase transition to a new type of density wave state. We find that independent of the electronic filling factor ν, the position at which the soft mode occurs is always located at the symmetry point J of the first Brillouin zone.