Traditional data-driven automatic taxonomy generation methods struggle with complex, large, and domain-specific datasets. To address these issues, this study leverages Large Language Models (LLMs) to automate key stages of taxonomy generation, focusing on scientific concepts. Our approach employs LLMs at several stages of the taxonomy generation process, including extracting candidate concepts and organizing keywords into taxonomies centered around chosen scientific concepts. By incorporating LLMs, we aim to enhance depth, accuracy, and coherence of generated taxonomies. Comparative analyses show that the proposed LLM-based taxonomy generation method outperforms state-of-the-art taxonomy generation methods on several metrics, such as concept coherence and coverage. Using a hybrid evaluation framework that combines automatic and human assessments, we demonstrate that our LLM-based solution is scalable, adaptable, and capable of generating high-quality taxonomies tailored to specific scientific concepts.