Dark circle is a symptom of udavarta (improper functions of all vaat).
It's mainly due to
1) dharniya vega (urges, should b controlled, we you aren't) like chinta-stress, bhaya-fear, shoka-, krodha-short temper, maan- ego, lobha-greedy etc mental condition you should control yourself
2) adharniya vega (urges that should not be controlled, but we are controling) like sleep, urine, stool, hunger, thirst, yawn, sneeze, vomit etc. Think deeply. It's a very spiritual concept
main treatment is to stop causative factor among this. So manage your sleep & time. Also there are some ayurveda medicine, lepa-cream, face treatment, or panchakarma (detoxification) will definitely help you
you can use kumkumadi ointment of nagarjun pharma. It will lighten your circle.
I am giving you some more tips, follow it.
* eat turmeric 1 tsp before meal
* eat ajvayan 1 tsp & jeera 1 tsp after each meal
* avoid sour salty spice food
* avoid curd, but take butter milk
* use only cow milk & ghee
* avoid stress, late sleep, day sleep, oily food, cold water
* for local application you can use triphala, yastimadhu, lodhra, nimb powder mix with buttermilk
for better suggestions & medicine