Vitamin K has been widely marketed as the "cure" for dark circles. Research done has shown that it improves dark circles. However, the study did not use Vitamin K exclusively but a combination of emu oil and caffeine though Vitamin K was sole credited for the results. There is no direct evidence that Vitamin K can improve dark circles.

Ref:
Ahmadraji F, Shatalebi MA. Evaluation of the clinical efficacy and safety of an eye counter pad containing caffeine and vitamin K in emulsified Emu oil base. Adv Biomed Res. 2015 Jan 6;4:10. doi: 10.4103/2277-9175.148292. PMID: 25625116; PMCID: PMC4300604.