Theoretical study of energy band splitting induced by spin–orbit interaction in helically coiled carbon nanotubes

• We derive the effective spin–orbit interaction in helically coiled carbon nanotubes.
• The spin–orbit interaction causes the electron–hole asymmetric splitting.
• The asymmetric splitting depends on coil pitch p and coil radius r.

Recent theoretical and experimental works on straight carbon nanotubes (SCNTs) have revealed that the curvature could enhance the spin–orbit interaction (SOI). Motivated by this, we further explore the effective SOI with another different curvature in helically coiled carbon nanotubes (HCCNTs) using the tight-binding model and perturbation approach. Finally, we derive the effective SOI in HCCNTs, and find the electron–hole asymmetric spin splitting. Interestingly, the asymmetric splitting largely depends on coil pitch p and coil radius r, which are not known in SCNTs. These results should be valuable for spintronic applications of carbon nanotubes.