Topological Insulators and Inversion Symmetry

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SUMMARY

Inversion symmetry is not a strict requirement for the formation of topological insulators (TIs), specifically the Z2 variety. The only necessary symmetry is time-reversal symmetry. Both inversion symmetric and asymmetric crystals can realize the TI state, although inversion symmetry simplifies the identification of TIs in materials. This conclusion is supported by the findings in the paper by Fu and Kane (2007).

PREREQUISITES
  • Understanding of topological insulators and their classifications
  • Familiarity with time-reversal symmetry in quantum mechanics
  • Knowledge of crystal lattice structures
  • Ability to interpret scientific literature, particularly in condensed matter physics
NEXT STEPS
  • Read the paper "Topological Insulators" by Fu and Kane (2007) for detailed insights
  • Explore the implications of time-reversal symmetry in quantum materials
  • Investigate the properties of inversion asymmetric crystals in relation to TIs
  • Study the experimental techniques used to identify topological insulators in materials
USEFUL FOR

Physicists, materials scientists, and researchers interested in condensed matter physics, particularly those studying topological insulators and their properties.

Goalie33
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Hi,

I was curious if specific symmetries (or lack thereof) in crystal structure are necessary for the formation of topological insulators. Specifically, do we require that inversion symmetry (or inversion asymmetry) be present in the lattice in order to form the TI state?

Thanks,
Goalie33
 
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No, the only symmetry that is required is Time reversal (I presume that by topological insulators you mean the Z2 variety). There are material realizations for both inversion symmetric and asymmetric crystals.
 
Inversion symmetry is convient though, because it allows for an easy way to determine if a material is a TI. (See Fu, Kane 2007)
 
Thanks,
I found that paper and it clarifies some questions. Originally, I wasn't sure if it was required or just convenient, but now I know.
Thanks!
 

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