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‖>Bc 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‖ 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‖-Bc|-1 when the CI transition is approached from the SL state.
Hanna, Charles B.; MacDonald, A. H.; and Girvin, S. M.. (2001). "Incommensurate Ground State of Double-Layer Quantum Hall Systems". Physical Review B, 63(12), 125305-1 - 125305-12.