Two Interacting Helical Edge Modes in Quantum Spin Hall Systems

We study theoretically two interacting one-dimensional helical modes at the edges of the quantum spin Hall systems. A new type of interedge correlated liquid without a spin gap is found when the intraedge repulsion is stronger than the interedge repulsion. This liquid shows a diverging density wave and superconductivity correlations much stronger than those of the spinfull electrons. Possible experimental observations are also discussed.