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Anomalous Friedel oscillations in a quasi-helical quantum dot

The charge and spin patterns of a quantum dot embedded into a spin-orbit coupled quantum wire subject to a magnetic field are investigated. A Luttinger liquid theory is developed, taking into account open boundaries and finite magnetic field. In the quasi-helical regime, when spin-orbit effects dominate over the Zeeman interaction, peculiar states develop at the Fermi surface of the dot. Anomalous Friedel oscillations with twice the expected wavelength develop in the wavefunction of collective excitations of such states, accompanied by peculiar spin patterns in their magnetization. Both effects are analyzed in detail and shown possible to be probed in transport experiments. The stability against electron interactions and magnetic field is investigated. We also discuss how signatures of such states survive in the total charge and spin densities.