Rippled state of double-layer quantum Hall systems

The incommensurate phase of a bilayer quantum Hall state is found to have a “rippled” dipole charge density whenever the layers are unbalanced. This tunable dipole-density-wave instability could be detected by sensitive capacitance measurements and by anisotropic transport. We demonstrate this explicitly by carrying out a Hartree-Fock calculation of the layer densities and capacitance for a double-layer quantum Hall state at a total filling factor of 1.