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Rashba spin-orbit coupling and a magnetic field perpendicular to the Rashbaaxis have been predicted to open a partial gap ("helical gap") in the energyspectrum of noninteracting or weakly interacting one-dimensional quantum wires.By comparing kinetic energy and Coulomb energy we show that this gap openingtypically occurs at low electron densities where the Coulomb energy dominates.To address this strongly correlated limit, we investigate Rashba wires usingWigner crystal theory. We find that the helical gap exists even in the limit ofstrong interactions but its dependence on electron density differssignificantly from the weakly interacting case. In particular, we find that thecritical magnetic field for opening the gap becomes an oscillatory function ofelectron density. This changes strongly the expected signature of the helicalgap in conductance measurements.

Helical gaps in interacting Rashba wires at low electron densities