Renormalization of anticrossings in interacting quantum wires with Rashba and Dresselhaus spin-orbit couplings

Abstract

We discuss how electron-electron interactions renormalize the spin-orbit induced anticrossings between different subbands in ballistic quantum wires. Depending on the ratio of spin-orbit coupling and subband spacing, electron-electron interactions can either increase or decrease anticrossing gaps. When the anticrossings are closing due to a special combination of Rashba and Dresselhaus spin-orbit couplings, their gap approaches zero as an interaction dependent power law of the spin-orbit couplings, which is a consequence of Luttinger liquid physics. Monitoring the closing of the anticrossings allows to directly measure the related renormalization group scaling dimension in an experiment. If a magnetic field is applied parallel to the spin-orbit coupling direction, the anticrossings experience different renormalizations. Since this difference is entirely rooted in electron-electron interactions, unequally large anticrossings also serve as a direct signature of Luttinger liquid physics. Electron-electron interactions furthermore increase the sensitivity of conductance measurements to the presence of anticrossing.

12 Pages, 10 figures, final version

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• Helical Liquids in Semiconductors
• Andreev spectrum with high spin-orbit interactions: revealing spin splitting and topologically protected crossings
• Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields
• Missing Shapiro steps and the $8\pi$-periodic Josephson effect in interacting helical electron systems
• Strong Electron-Electron Interactions of a Tomonaga--Luttinger Liquid Observed in InAs Quantum Wires
• Three-Dimensional Fractional Topological Insulators in Coupled Rashba Layers
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• Magnetically-Confined Bound States in Rashba Systems
• Conductance of fractional Luttinger liquids at finite temperatures
• Crystallization of fractional charges in a strongly interacting quasi-helical quantum dot
• Interaction Driven Floquet Engineering of Topological Superconductivity in Rashba Nanowires
• Suppression of Coulomb blockade peaks by electronic correlations in InAs nanowires
• Detection of fractional solitons in quantum spin Hall systems