Köhler was appointed Professor of Physics and Chair of Soft Matter Optoelectronics at the University of Bayreuth in 2007. Her research considers organic semiconducting materials for solar cells and light-emitting diodes. In particular, Köhler has studied the spin states of organic semiconductors. Köhler was made executive director of the Bayreuth University Centre of International Excellence in 2019.. In 2022, Köhler was elected as a full member of the section III of the Bavarian Academy of Sciences and Humanities, the fourth scientist and the first woman ever to do so.