Anomalous Friedel oscillations in a quasihelical 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 a finite magnetic field. In the quasihelical 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 total tunneling rate from a scanning tunneling microscope tip, accompanied by a peculiar oscillation of spin-resolved transport properties. Both effects are analyzed in detail. 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.