Spontaneous Inter-layer Coherence in Double-Layer Quantum-Hall Systems   I: Charged Vortices and Kosterlitz-Thouless Phase Transitions
  At strong magnetic fields double-layer two-dimensional-electron-gas systems can form an unusual broken symmetry state with spontaneous inter-layer phase coherence. In this paper we explore the rich variety of quantum and finite-temperature phase transitions associated with this broken symmetry. We describe the system using a pseudospin language in which the layer degree-of-freedom is mapped to a fictional spin 1/2 degree-of-freedom. With this mapping the spontaneous symmetry breaking is equivalent to that of a spin 1/2 easy-plane ferromagnet. In this language spin-textures can carry a charge. In particular, vortices carry e/2 electrical charge and vortex-antivortex pairs can be neutral or carry charge e. We derive an effective low-energy action and use it to discuss the charged and collective neutral excitations of the system. We have obtained the parameters of the Landau-Ginzburg functional from first-principles estimates and from finite-size exact diagonalization studies. We use these results to estimate the dependence of the critical temperature for the Kosterlitz-Thouless phase transition on layer separation. 
K. Moon, H. Mori, Kun Yang, S.M. Girvin, A.H. MacDonald, L. Zheng, D.   Yoshioka and Shou-Cheng Zhang