Incommensurate ground state of double-layer quantum Hall systems

Double-layer quantum Hall systems possess interlayer phase coherence at sufficiently small layer separations, even without interlayer tunneling. When interlayer tunneling is present, application of a sufficiently strong in-plane magnetic field $B_\parallel > B_c$ drives a commensurate-incommensurate (CI) transition to an incommensurate soliton-lattice (SL) state. We calculate the Hartree-Fock ground-state energy of the SL state for all values of $B_\parallel$ within a gradient approximation, and use it to obtain the anisotropic SL stiffness, the Kosterlitz-Thouless melting temperature for the SL, and the SL magnetization. The in-plane differential magnetic susceptibility diverges as $(B_\parallel - B_c)^{-1}$ when the CI transition is approached from the SL state.