Yes, there are quite a few. You can try searching on fanfic websites like Archive of Our Own. Just type in 'Female Titan x Armin' in the search bar and you'll get a list of relevant fanfics. Some might be really well - written with interesting plot twists and character developments.
Power dynamics is a frequent theme. The Female Titan has great physical power, while Armin has intellectual power. Fanfics often play with how these two types of power interact in their relationship. Another theme could be redemption. Maybe the Female Titan is seeking redemption through her connection with Armin. It could also be about understanding the 'other'. Armin tries to understand the Female Titan, who is different from him in many ways, and vice versa.
Armin could be the storyteller. Sometimes characters take on this role to provide a unique viewpoint or to drive the narrative in a particular direction. But we need to know more about the story to confirm it for sure.
Armin is still alive in the manga. The story developments don't result in his demise. His presence remains significant and continues to shape the narrative.
One common theme is the exploration of the blurry line between friend and foe. Since the Female Titan is initially an enemy, fanfictions often delve into whether she can become an ally through her interactions with Armin. For example, Armin might try to convince her to side with the humans.
In many fanfics, Annie and Armin's relationship can be complex. It might start from a place of mutual suspicion as they were on different sides initially. But as the story progresses, they could find common ground. For example, they both have a deep understanding of the cruel world they live in. This shared understanding can lead to a more empathetic connection between them.
Another theme is his relationships. His friendship with Eren and Mikasa is frequently explored in different ways. Some fanfics might focus on how his relationship with them changes as they all grow older and face different challenges.