Fractional Wigner Crystal in the Helical Luttinger Liquid

Area of Science:

• Condensed Matter Physics
• Topological Materials Science
• Quantum Phenomena

Background:

• Topological insulators possess unique edge states with protected transport properties.
• Understanding strongly interacting systems is crucial for novel quantum phenomena.
• Two-particle backscattering can significantly alter edge state behavior.

Purpose of the Study:

• Investigate the properties of strongly interacting edge states in 2D topological insulators.
• Analyze the impact of two-particle backscattering on these edge states.
• Characterize emergent phenomena like fractional charges and spin textures.

Main Methods:

• Analysis of density-density correlation functions.
• Investigation of the Fermi operator.
• Comparison of spin-spin and density-density correlation functions.

Main Results:

• Observed anomalous oscillations in density-density correlations, indicative of a Wigner crystal.
• Identified fractional charge (e/2) excitations within this Wigner crystal.
• Demonstrated the persistence of spin-momentum locking in the fractional state.
• Revealed a nontrivial spin texture associated with the fractional Wigner crystal.

Conclusions:

• Strongly interacting edge states in topological insulators can host fractional Wigner crystals.
• These fractional states exhibit unique properties including spin-momentum locking and complex spin textures.
• The findings offer new insights into exotic quantum phases in topological materials.