In medical image analysis, multi-organ semi-supervised segmentation faces challenges such as insufficient labels and low contrast in soft tissues. To address these issues, existing studies typically employ semi-supervised segmentation techniques using pseudo-labeling and consistency regularization. However, these methods mainly rely on individual data samples for training, ignoring the rich neighborhood information present in the feature space. In this work, we argue that supervisory information can be directly extracted from the geometry of the feature space. Inspired by the density-based clustering hypothesis, we propose using feature density to locate sparse regions within feature clusters. Our goal is to increase intra-class compactness by addressing sparsity issues. To achieve this, we propose a Density-Aware Contrastive Learning (DACL) strategy, pushing anchored features in sparse regions towards cluster centers approximated by high-density positive samples, resulting in more compact clusters. Specifically, our method constructs density-aware neighbor graphs using labeled and unlabeled data samples to estimate feature density and locate sparse regions. We also combine label-guided co-training with density-guided geometric regularization to form complementary supervision for unlabeled data. Experiments on the Multi-Organ Segmentation Challenge dataset demonstrate that our proposed method outperforms state-of-the-art methods, highlighting its efficacy in medical image segmentation tasks.