Dephasing of spin and charge interference in helical Luttinger liquids

We consider a four-terminal Aharonov-Bohm interference setup formed out of two edges of a quantum spin Hall insulator, supporting helical Luttinger liquids (HLLs). We show that the temperature and bias dependence of the interference oscillations are linked to the amount of spin flips in tunneling between two HLLs which is a unique signature of a HLL. We predict that spin dephasing depends on the electron-electron (e-e) interaction but differently from the charge dephasing due to distinct dominant tunneling excitations. In contrast, in a spinful Luttinger liquid with SU(2) invariance, uncharged spin excitations can carry spin current without dephasing in spite of the presence of e-e interactions.