title: Helical liquid and the edge of quantum spin Hall systems.
abstract: 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 appear when the time-reversal 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 time-reversal invariance.
authors.affiliation: Department of Physics, Stanford University, California 94305, USA.
authors.forename: Congjun
authors.initials: C
authors.lastname: Wu
authors.forename: B Andrei
authors.initials: BA
authors.lastname: Bernevig
authors.forename: Shou-Cheng
authors.initials: SC
authors.lastname: Zhang