In a fanfiction, the development of Izuku having a black fire quirk can be really multi - faceted. First, the visual aspect of the quirk can be described in detail. The black fire could have a smoky, otherworldly look that sets it apart from normal fire. Emotionally, Izuku could struggle with the fact that his quirk is so different from what he expected. He might feel like an outcast among his peers. Then, there could be a story arc where he discovers a hidden power within the black fire quirk. For instance, he might find out that it can absorb other forms of energy. This would not only make his quirk more powerful but also open up new storylines about him learning to use this new aspect and facing new enemies who are interested in his unique ability.
One common plot element is Izuku struggling to control his dual - natured quirk at first. Since fire and ice are opposite elements, it's a challenge for him to balance them. Another is that he might face discrimination or suspicion from others who are afraid of his powerful quirk. Also, there could be a lot of training montages as he tries to master using both elements effectively.
You can try searching on popular fanfiction websites like Archive of Our Own (AO3) or FanFiction.net. Just type in 'Izuku has black lightning quirk' in the search bar, and it should show you relevant stories.
One great izuku black fire quirk fanfiction could be 'Rising from the Ashes'. In this story, Izuku discovers his black fire quirk in a very unexpected way. Maybe he's in a dangerous situation and suddenly the quirk emerges to save him. Another one might be 'Black Fire's Potential'. It could explore how Izuku trains with his new quirk, facing difficulties and overcoming them.
Well, a great plot could be Izuku's journey to master his fire quirk. He might seek out a retired hero with a fire - related quirk to train him. Along the way, he discovers that his fire quirk has a unique property, like it can burn through certain types of energy shields that most other quirks can't. This makes him a target for villains who want to study his quirk, and he has to fight to protect himself and his secret.
He could start by training to absorb more types of energy. For example, if he can currently only absorb physical energy like kinetic or thermal, he could learn to absorb electromagnetic energy too. This would open up new possibilities for his quirk usage. Another way is to increase the efficiency of his absorption. Maybe he can work on reducing the time it takes to absorb energy or increase the amount he can hold at once.
You can start by looking on popular fanfiction websites like Archive of Our Own (AO3). Just search for 'Izuku fire and ice quirk' in the search bar, and it'll show you a bunch of relevant stories. There are also some good ones on Fanfiction.net, but the tagging system there might require a bit more digging.
There's a fanfic titled 'Izuku's Wolfish Abilities'. In this, his wolf quirk gives him enhanced senses. He uses these to his advantage during battles and rescue missions. The story also delves into how his quirk influences his relationships, especially with Bakugo and Todoroki.
One implication could be a change in his relationships. His friends might be initially afraid or distrustful. For example, Bakugo could see this as a sign of Izuku being a real threat now, instead of just a rival. Also, the teachers at UA might have to deal with a whole new set of problems regarding Izuku's training and control of his dark quirk.
A sentient quirk for Izuku in fanfiction could have a huge impact on the plot. It could be a source of both power and trouble. For instance, villains might try to target the quirk specifically, seeing it as a valuable asset or a threat. Izuku would have to constantly protect it while also using it to his advantage. The quirk could also communicate with other sentient entities in the fanfiction world, opening up new storylines and alliances.
The quirk could be turned into a 'vitality quirk'. Izuku's quirk might be that he can sense and transfer a type of life - force energy. This energy is related to the concept of sexual energy in a very abstract way in that it represents the life and passion within a person. But in the context of the story for a younger audience, it's just about him being able to boost the energy of his friends when they're tired or weak, or using it to heal minor injuries.