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We study one dimensional wires with spin-orbit coupling. We show that in thepresence of Zeeman field and strong electron-electron interaction a clean wiremay form fractional helical liquid states with phenomenology similar tofractional quantum Hall liquids. Most notably, the wire's two terminalconductance is predicted to show fractional quantized conductance plateaus atlow electron density. When the system is proximity-coupled to a superconductor,fractional Majorana bound states may be stabilized. We discuss how disorderdestabilizes these fractional phases. Possible experimental realizations ofsimilar states in double wire systems are discussed.

Fractional Helical Liquids and Non-Abelian Anyons in Quantum Wires