Identifying relevant research concepts is crucial for effective scientific search. However, primary sparse retrieval methods often lack concept-aware representations. To address this, we propose CASPER, a sparse retrieval model for scientific search that utilizes both tokens and keyphrases as representation units (i.e., dimensions in the sparse embedding space). This enables CASPER to represent queries and documents via research concepts and match them at both granular and conceptual levels. Furthermore, we construct training data by leveraging abundant scholarly references (including titles, citation contexts, author-assigned keyphrases, and co-citations), which capture how research concepts are expressed in diverse settings. Empirically, CASPER outperforms strong dense and sparse retrieval baselines across eight scientific retrieval benchmarks. We also explore the effectiveness-efficiency trade-off via representation pruning and demonstrate CASPER's interpretability by showing that it can serve as an effective and efficient keyphrase generation model.