Type: Character Cliché
What made it popular: Fetishization of the real life condition with the same name + Eastern Folklore
Cliché Level: Medium
Where can you find it: Haganai, Another, K – Project, Rozen Maiden, Dragon Crisis, Gundam 00, Overlord, Fate/Stay Night, Sankarea, Petshop of Horrors, Zero no Tsukaima, Legend of the Galactic Heroes etc.
Heterochromia refers to characters whose one iris is of a different colour than the other, either as a result of naturally being born this way, injury or due to the usage of contact lens. It does not in fact refer to temporary change in eye-colour (due to some power or magic), it has to be permanent, which means shows like Naruto or Date A Live do not apply here.
The real life Heterochromia iridum does not always result in fully different iris colours (sometimes its only partial), but in the medium of anime only the full kind is shown (Due to obviously being more appealing). This cliché arose as a result of mostly the fetishization of something that is exotic and rare, it is something that people get turned on by and feel attracted to ( I know do). There is also some Folklore and Mythological influence due to the fact that many Chinese Gods and Japanese Youkai are most commonly depicted with unnatural eye colours (Meaning not common to the Japanese people such as Green or Blue).
Why its bad: Heterochromia in reality is quite rare, especially in humans. It mostly occurs as a result of inbreeding or due to genetic defects. So having a heterochromatic character is quite unrealistic, to the point that you might as well represent people with albinism, since it would make little difference. Although some modern-day anime manage to excuse heterochromia via the usage of contacts (Chuunibyou, Another).
In supernatural or fantasy anime, heterochromia is an usual indicator of a character’s godhood, demonhood or general unnaturalness (Ayanami Rei and other Science abominations.)