Spontaneous Interlayer Coherence in Double-Layer Quantum Hall Systems:   Symmetry Breaking Interactions, In-Plane Fields and Phase Solitons
  At strong magnetic fields double-layer two-dimensional-electron-gas systems can form an unusual broken symmetry state with spontaneous inter-layer phase coherence. The system can be mapped to an equivalent system of pseudospin $1/2$ particles with pseudospin-dependent interactions and easy-plane magnetic order. In this paper we discuss how the presence of a weak interlayer tunneling term alters the properties of double-layer systems when the broken symmetry is present. We use the energy functional and equations of motion derived earlier to evaluate the zero-temperature response functions of the double-layer system and use our results to discuss analogies between this system and Josephson-coupled superconducting films. We also present a qualitative picture of the low-energy charged excitations of this system. We show that parallel fields induce a highly collective phase transition to an incommensurate state with broken translational symmetry. 
Kun Yang, K. Moon, Lotfi Belkhir, H. Mori, S.M. Girvin, A.H.   MacDonald, L. Zheng, and D. Yoshioka