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. ) ,
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
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. ) .
The simulation is based on the Kane-Mele model agumented by the
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,
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,
"Interacting effects in topological states"
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Last modified: Oct 16, 2018.