Professors Hellman and Gilbert has this article, Political Corruption, forthcoming in the Oxford Handbook of American Election Law (Eugene Mazo, ed.). The abstract:

This chapter studies political corruption and its many relationships to the law of democracy. It begins with bribery laws, which forbid officials from selling official acts. Federal bribery law is circular, reflecting uncertainty and disagreement around the concept of bribery itself. Next, the chapter studies campaign finance regulations, which raise First Amendment concerns but are nevertheless often justified on anti-corruption grounds. Then the chapter examines vote buying, which relates to the secret ballot and the complicated connections between corruption and publicity. The chapter addresses the constitutional dimensions of corruption, including its role in impeachment and the Emoluments Clauses, and it concludes with a discussion of the appearance of corruption, a concern that surfaces in many areas, including judicial recusal and misuse of office. The law of political corruption is often vague, and scholars disagree about the very nature of corruption. This leaves much authority in the hands of the actors, including judges, empowered to define corruption in practice.