Quantum critical points of helical Fermi liquids

Following our previous work, we study the quantum phase transitions, which spontaneously develop ferromagnetic spin order in helical Fermi liquids, which breaks continuous spin-space rotation symmetry, with the application to the edge states of three-dimensional topological band insulators. With finite Fermi surface, the critical point has both z = 3 overdamped and z = 2 propagating quantum critical modes, and the z = 3 mode will lead to non-Fermi-liquid behavior on the entire Fermi surface. In the ordered phase, the Goldstone mode is overdamped, unless it propagates along special directions, and quasiparticle is ill defined on most parts of the Fermi surface except for special points. Generalizations of our results to other systems with spin-orbit couplings are also discussed.