The Helical Edge Liquid


Topological insulators (TIs) are a major research focus of contemporary condensed matter physics. A common picture is that time-reversal symmetry of the Kramers type protects the stability of one dimensional (1D) helical edge modes of two dimensional (2D) TIs by forbidding the single-particle back-scattering, which would break the Kramers symmetry. However, this analysis is purely based on non-interacting physics. Since interaction effects in 1D are particularly strong, it is important to examine the issue of the interaction-driven edge instability .

Helical edge liquid state and interaction-driven instability

In 2006, we constructed the theory of the "helical edge liquid state", or, the interacting Luttinger edge liquid state of 2D TIs (Ref. [1]) , and this concept has been widely used in literature. The helical edge liquid constitutes a new type of the 1D interacting liquid state, which is different from the chiral Luttinger liquid and usual 1D Luttinger liquids for spinless and spinful fermions. The fermion doubling theorem proves that it must arise as an edge effect of the bulk 2D systems. The evidence of interaction effects in the helical edge liquids has been recently reported in the transport measurements in InAs/GaSb quantum-wells by R. R. Du's group at Rice University (PRL 115, 136804 (2015)) .

We analyzed the stability problem of interacting helical edge modes and found the leading instability allowed by time-reversal symmetry is due to the 2-particle correlated backscattering. The helical edge states are stable in the weak interacting region, but become unstable under strong interactions, accompanied by gap opening and spontaneous time-reversal symmetry breaking. Concrete instability criteria in terms of the edge channel Luttinger parameter were derived. The Kondo problem in the helical Luttinger liquid state is also studied. Different from the usual case, the conducting electrons are interacting and helical. It has been found that the repulsive interaction shifts the critical Kondo coupling to the ferromagnetic side, and the Kondo singlet exhibits a spin-current vortex structure.

Sign-problem free quantum Monte-Carlo (QMC) simulations

We have tested the above effective field theory study by performing quantitative QMC simulations on the interaction-driven instabilities in topological insulators (Ref. [2]) . The simulation is based on the Kane-Mele model agumented by the Hubbard interaction. The simulations are proved to be sign-problem-free, and, hence, yield accurate and Unbiased results. The interaction effects are already strong in the helical edge liquids nearly driving magnetic instability even though the bulk interaction is weak.

References and talks

  • 1. Congjun Wu, B. Andrei Bernevig, and Shou-Cheng Zhang, " The Helical Liquid and the Edge of Quantum Spin Hall Systems ", Phys. Rev. Lett. 96 , 106401(2006), see, pdf file .

  • 2. Dong Zheng, Guang-Ming Zhang Congjun Wu, "Particle-hole symmetry and interaction effects in the Kane-Mele-Hubbard model", Phys. Rev. B 84 , 205121 (2011) , see, pdf file .

  • Talk: "Interacting effects in topological states" .


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    Last modified: Oct 16, 2018.