Broken-symmetry ground states for the two-dimensional electron gas in a double-quantum-well system

Working in the Hartree-Fock approximation, we calculate the ground-state energy of different states of the two-dimensional electron gas in a double-quantum-well system as a function of the separation of the wells. Our calculation takes tunneling between the wells as well as the finite thicknesses of the wells into account. In the absence of interlayer hopping the ground state at small layer separations has a spontaneously broken symmetry in which hopping matrix elements have nonzero expectation values. We find that, as the separation of the wells is increased to some critical distance ${\mathit{d}}_{\mathit{c}}$, the Hartree-Fock ground state breaks translational symmetry and the hopping order parameters rapidly diminish.