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We study the time reversal (T) symmetry breaking of 2d helical fermi liquid,with application to the edge states of 3d topological band insulators with onlyone two-component Dirac fermion at finite chemical potential, as well as othersystems with spin-orbit coupling. The T-breaking Ising order parameter is notover-damped and the theory is different from the ordinary Hertz-Millis theoryfor order parameters at zero momentum. We argue that the T-breaking phasetransition is an 3d Ising transition, and the quasiparticles are well-definedin the quantum critical regime.

Time-Reversal Phase Transition at the Edge of 3d Topological Band Insulator