Well, the contrast between law and lust is a big one. Cops represent the law, and when you mix in erotic elements, it creates a tension. There are also themes related to the cop's work environment, like the police station or patrol cars being the backdrop for the erotic encounters. And the relationship between the cop and the civilian, which can be full of power struggles and sexual tension.
Power dynamics. There's often a play on the authority that cops have, which can be an exciting element in an erotic story. Another theme is the forbidden nature, as cops are supposed to uphold the law and engaging in erotic activities might be against the rules.
One common theme is sacrifice. Cops often have to sacrifice their personal time with their loved ones because of their dangerous and demanding jobs. For example, in many stories, a cop might miss an important date or family event due to an emergency call.
One common theme is acceptance. Gay cops often have to deal with acceptance within the police force, whether it's from colleagues or superiors. Another theme is using their identity to better serve the community, especially the gay community.
One common theme is the contrast between their femininity and the tough cop image. For example, memes might show a girl cop with perfectly manicured nails while holding a gun. Another theme is their ability to handle difficult situations with grace. There are memes that depict a girl cop calmly diffusing a tense situation. Also, the idea of girl cops being a new and different presence in a male - dominated field is often a theme. Memes may play on this by showing a girl cop's unique style or approach compared to male cops.
One common theme could be justice. Since Amy is a cop, stories might revolve around her seeking justice in the face of crime. Another could be loyalty, either to her fellow officers or to the community she serves.
One common theme is the battle of wits. The cop has to outthink the robber and vice versa. For example, in many fanfics, the robber will set up elaborate traps, and the cop has to figure out how to avoid them while still catching the criminal.
Another theme is justice. They are usually on a mission to bring bad guys to justice, whether it's solving a murder or taking down a crime syndicate. And friendship can also be a theme. In many stories, girl cops form strong bonds with their partners or other female colleagues while on the job.
In gay literature with this plot, a frequent theme is the contrast between the structured, rule - bound world of the cop and the more fluid, often marginalized world of the gay character. This contrast can create a lot of tension and drama. Another theme is the search for connection. The gay character might be seeking a deeper connection with someone who represents stability (the cop), while the cop may be exploring a side of themselves that they've kept hidden due to their profession. And then there's the theme of identity conflict, as the cop may have to reconcile their public identity with their private desires in a gay relationship.
Often, themes like power dynamics, corruption, and transformation are common. But it's a pretty controversial and inappropriate topic.
Often, there are themes related to family. Since the main character has to deal with the kids as if they were his own in a way, fan fiction may explore how this affects his view on family. Also, themes of friendship among the kids themselves are quite common. For example, stories might focus on how the kids support each other through difficulties in the kindergarten. Some fan fiction might also play with the idea of the main character's past experiences influencing his actions in the kindergarten, like if his own childhood had an impact on how he deals with the current kids.