One reason could be to control him. Vader wants Luke on his side, and by locking him up, he can limit Luke's actions and try to influence his decisions.
Maybe it's out of jealousy. Luke has the potential for great power in the Force, and Vader, having fallen to the dark side, doesn't want Luke to succeed where he 'failed' in a sense. So, he locks him up to prevent Luke from achieving great things as a Jedi.
In some fanfics, Vader locks up Luke as part of a grander plan. He might be working for a more powerful Sith lord who has an interest in Luke. By imprisoning Luke, Vader is following orders and also trying to figure out Luke's true potential for this other, more powerful figure.
One reason could be that Vader represents the dark side which has brought so much destruction in the galaxy. Luke, being on the side of the Jedi and good, would naturally despise the evil deeds associated with Vader.
Often in these fanfics, Vader's act of locking up Luke is a complex situation. It can be seen as a way to assert his dominance as Luke's father. He may feel that Luke is not ready to face the challenges of the galaxy on his own. However, this imprisonment also serves as a catalyst for Luke's growth. It forces him to face his fears, his connection to Vader, and his own identity. Luke might use the time in captivity to meditate and strengthen his connection to the Force, preparing for an eventual escape and confrontation with Vader.
In some fanfiction, if Luke and Darth Vader teamed up, they could be an unstoppable force for good. They could use their combined Force abilities to fight against a greater evil in the galaxy. Maybe they would start by taking on the Emperor together, using Vader's knowledge of the Sith and Luke's purity in the Force.
The relationship could develop in a complex way. Since Vader has captured Luke, there's a power imbalance. However, as they interact, Luke might try to reach out to the good in Vader. Vader, in turn, might be conflicted. He could start to protect Luke from the Emperor's harsher plans, leading to a strange alliance within the captivity.
One great fanfic could be 'The Redemption of Vader and the Ascent of Luke'. It delves deep into the relationship between the two. It shows how Luke's unwavering belief in the good in Vader starts to chip away at Vader's dark side. It's filled with intense lightsaber battles and emotional dialogues that really capture the essence of their connection in the Star Wars universe.
In certain fanfictions, Luke sees Darth Vader's fall symbolically. For example, he might see the destruction that Vader has caused on a planet or to a group of people. This destruction represents Vader's fall from grace. It could be that Vader has ordered the massacre of innocents, and Luke witnesses the aftermath. This makes Luke realize the true nature of the dark side that Vader has embraced and how far he has fallen from being a Jedi.
A good fanfic about Luke and Darth Vader should first and foremost have a strong understanding of the characters. They need to stay true to their personalities as seen in the movies. For example, Vader's internal struggle between the light and dark side should be well - represented. Also, a great plot that ties into the existing Star Wars mythology is important. Maybe it could involve a new threat that forces Luke and Vader to work together, or explore their relationship in a different time period.
One possible plot in such a fanfic is that Vader has been ordered by the Emperor to capture Luke alive. He does so, but during the capture, Luke discovers some long - hidden secrets about his father. Vader, on the other hand, starts to have second thoughts about handing Luke over to the Emperor. This creates a complex dynamic between them, with Vader torn between his loyalty to the Emperor and his new - found feelings for his son.
Vader might initially be shocked. His son reaching out to him is unexpected. He could respond with a moment of silence, trying to process what is happening.
There's a fanfic titled 'Vader's Redemption'. In this story, Vader starts to question his loyalty to the Emperor much sooner, especially after some profound encounters with Luke. It's a great read as it shows the internal struggle of Vader while also exploring the bond between father and son in a new light. It's full of action-packed scenes and deep emotional moments.