The Helical Liquid and the Edge of Quantum Spin Hall Systems

The edge states of the recently proposed quantum spin Hall systems constitute a new symmetry class of one-dimensional liquids dubbed the ``helical liquid,'' where the spin orientation is determined by the direction of electron motion. We prove a no-go theorem which states that a helical liquid with an odd number of components cannot be constructed in a purely 1D lattice system. In a helical liquid with an odd number of components, a uniform gap in the ground state can only appear when the time-reversal (TR) symmetry is spontaneously broken by interactions. On the other hand, a correlated two-particle backscattering term by an impurity can become relevant while keeping the TR invariance. We further study the Kondo effect in such a liquid which exhibits new features in the structure of the screening cloud.