# Topological insulators: insulating inside, conducting at the edge

> The figure is the insulator: its frame is a two-lane edge channel where spin-up and spin-down electrons travel in opposite directions, while inside a quintuple-layer slab of Bi₂Se₃, a surface Dirac cone crossing the bulk gap (live 3D) and spin–momentum locking explain why the surface conducts and resists backscattering. Four landmark results run along the bottom.

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- Updated: 2026-10-14
- Category: Graphical abstracts
- Method: Graphical abstract
- Starting materials: Bi₂Se₃-family crystals: quintuple layers bound by van der Waals forces
- Product: An insulating bulk wrapped in metallic, spin-polarized surface states
- Key result: Nearly 100 % spin polarization, protected to 300 K in Bi₂Se₃ (Hsieh et al. 2009); ≈ 2e²/h edge conductance (König et al. 2007); h/e² at zero field (Chang et al. 2013)
- Figure: 1920 × 1080 px, 457 editable layers

## Steps

1. **Bulk vs surface**: A topological insulator has an insulating bulk band gap and metallic surface states (Kong et al. 2010); the gap comes from strong spin–orbit coupling (Roushan et al. 2009)
2. **One Dirac cone**: Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃ have a single Dirac cone on the surface (Kong et al. 2010; Chen et al. 2009); in Bi₂Se₃ it is spin–momentum locked, nearly 100 % spin-polarized and protected up to 300 K (Hsieh et al. 2009)
3. **No U-turns**: Backscattering between states of opposite momentum and opposite spin is absent even with strong disorder (Roushan et al. 2009)
4. **Landmarks**: Edge conductance near 2e²/h in HgTe wells thicker than 6.3 nm (König et al. 2007); quantum anomalous Hall resistance h/e² at zero field in Cr-doped (Bi,Sb)₂Te₃ (Chang et al. 2013)

## Uses

- Graphical abstracts on topological insulators and quantum materials
- Talks on spintronics and topological protection
- Teaching band inversion, Dirac cones and spin–momentum locking

## References

1. Kong et al., “Few-layer nanoplates of Bi2Se3 and Bi2Te3 with highly tunable chemical potential”, Nano Lett. 2010. https://doi.org/10.1021/nl101260j (primary)
2. Roushan et al., “Topological surface states protected from backscattering by chiral spin texture”, Nature 2009. https://doi.org/10.1038/nature08308 (primary)
3. Hsieh et al., “A tunable topological insulator in the spin helical Dirac transport regime”, Nature 2009. https://doi.org/10.1038/nature08234 (primary)
4. Chen et al., “Experimental realization of a three-dimensional topological insulator, Bi2Te3”, Science 2009. https://doi.org/10.1126/science.1173034 (primary)
5. König et al., “Quantum spin Hall insulator state in HgTe quantum wells”, Science 2007. https://doi.org/10.1126/science.1148047 (primary)
6. Chang et al., “Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator”, Science 2013. https://doi.org/10.1126/science.1234414 (primary)

Credit: Drawn by LabCanvas after Kong et al., Nano Lett. 2010 (doi:10.1021/nl101260j); Roushan et al., Nature 2009 (doi:10.1038/nature08308); Hsieh et al., Nature 2009 (doi:10.1038/nature08234); Chen et al., Science 2009 (doi:10.1126/science.1173034); König et al., Science 2007 (doi:10.1126/science.1148047); Chang et al., Science 2013 (doi:10.1126/science.1234414).

## Questions

**What does the “Topological insulators: insulating inside, conducting at the edge” template show?** The figure is the insulator: its frame is a two-lane edge channel where spin-up and spin-down electrons travel in opposite directions, while inside a quintuple-layer slab of Bi₂Se₃, a surface Dirac cone crossing the bulk gap (live 3D) and spin–momentum locking explain why the surface conducts and resists backscattering. Four landmark results run along the bottom.

**What are the steps shown in “Topological insulators: insulating inside, conducting at the edge”?** 1. Bulk vs surface: A topological insulator has an insulating bulk band gap and metallic surface states (Kong et al. 2010); the gap comes from strong spin–orbit coupling (Roushan et al. 2009). 2. One Dirac cone: Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃ have a single Dirac cone on the surface (Kong et al. 2010; Chen et al. 2009); in Bi₂Se₃ it is spin–momentum locked, nearly 100 % spin-polarized and protected up to 300 K (Hsieh et al. 2009). 3. No U-turns: Backscattering between states of opposite momentum and opposite spin is absent even with strong disorder (Roushan et al. 2009). 4. Landmarks: Edge conductance near 2e²/h in HgTe wells thicker than 6.3 nm (König et al. 2007); quantum anomalous Hall resistance h/e² at zero field in Cr-doped (Bi,Sb)₂Te₃ (Chang et al. 2013).

**What are the starting materials and the product?** Starting materials: Bi₂Se₃-family crystals: quintuple layers bound by van der Waals forces. Product: An insulating bulk wrapped in metallic, spin-polarized surface states.

**Which papers is “Topological insulators: insulating inside, conducting at the edge” based on?** Kong et al., “Few-layer nanoplates of Bi2Se3 and Bi2Te3 with highly tunable chemical potential”, Nano Lett. 2010 (doi:10.1021/nl101260j); Roushan et al., “Topological surface states protected from backscattering by chiral spin texture”, Nature 2009 (doi:10.1038/nature08308); Hsieh et al., “A tunable topological insulator in the spin helical Dirac transport regime”, Nature 2009 (doi:10.1038/nature08234); Chen et al., “Experimental realization of a three-dimensional topological insulator, Bi2Te3”, Science 2009 (doi:10.1126/science.1173034); König et al., “Quantum spin Hall insulator state in HgTe quantum wells”, Science 2007 (doi:10.1126/science.1148047); Chang et al., “Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator”, Science 2013 (doi:10.1126/science.1234414).

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