Redemption can also be a theme. Sometimes the cop is dealing with personal issues or a past mistake, and through the relationship with the love interest, they find a way to redeem themselves. This is shown in 'Undercover Redemption' where the cop is trying to make up for a past wrong while falling in love.
Secrecy is another big theme. The undercover cop often has to keep his or her true identity a secret from the love interest, which creates a lot of tension. In 'The Silent Protector' for instance, the cop has to hide his identity from the woman he loves, and this secrecy adds a lot of drama to the story.
One common theme is the conflict between duty and love. The hero is usually on an important undercover mission, and falling in love can put that mission at risk. Another theme is secrecy. The hero often has to keep his true identity a secret from the heroine, which adds a lot of tension to the relationship.
One popular undercover cop romance novel is 'The Protector' by Lori Foster. It tells a story where the female lead gets involved with an undercover cop, and there are lots of thrilling moments and steamy romance scenes.
A really popular one is 'The Departed' which was later made into a movie. It's about an undercover cop in the Irish mob. The story is full of twists and turns, with the cop having to constantly balance his true identity and his cover.
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 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.
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 the revelation of secrets. The undercover professor usually has a hidden past or a special mission, and as the story unfolds, these secrets are gradually revealed, which keeps the readers intrigued.
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.