A common theme could be the relationship development between rk900 and gavin. It might explore how they go from being at odds to understanding each other better.
One common theme is the clash of personalities. Gavin is often hot - headed while RK900 is more stoic. Another theme is the exploration of what it means to be human, especially when RK900 is involved. They also often have themes of redemption, where Gavin might see RK900 in a new light and vice versa.
In 'barbara gavin fanfic', themes related to family can also be present. If she has a family in the original, fanfics can explore family dynamics, like sibling relationships or parent - child interactions. Another common theme is heroism. If Barbara Gavin is a heroic figure, fanfics may showcase her heroics in new and exciting ways, perhaps in different worlds or against new enemies. And of course, there could be themes of mystery, where she has to solve some enigma or uncover a secret.
Sure. One popular 'gavin x rk900 fanfic' is 'Parallel Paths'. It explores their relationship in a post - apocalyptic Detroit. Another great one is 'Unlikely Allies' which focuses on how they team up to solve a complex case and slowly start to understand each other.
I'm not sure about specific titles off - hand, but you can also join Detroit: Become Human fan communities on platforms like Reddit or Discord. There, fellow fans can recommend their favorite dbh gavin x rk900 fanfics. They might be able to point you towards some hidden gems that you wouldn't find easily through general searches.
I'm not sure of specific 'rk900 x gavin fanfic' stories off the top of my head. But you can try looking on fanfiction websites like Archive of Our Own. There are usually a lot of works in various fandoms there.