Self-supervised learning (SSL) has drawn an increased attention in the field of speech processing. Recent studies have demonstrated that contrastive learning is able to learn discriminative speaker embeddings in a self-supervised manner. However, base contrastive self-supervised learning (CSSL) assumes that the pairs generated from a view of anchor instance and any view of other instances are all negative, which introduces many false negative pairs in constructing the loss function. The problem is referred as $class$-$collision$, which remains as one major issue that impedes the CSSL based speaker verification (SV) systems from achieving better performances. In the meanwhile, studies reveal that negative sample free SSL frameworks perform well in learning speaker or image representations. In this study, we investigate SSL techniques that lead to an improved SV performance. We first analyse the impact of false negative pairs in the CSSL systems. Then, a multi-stage Class-Collision Correction (C3) method is proposed, which leads to the state-of-the-art CSSL based speaker embedding system. On the basis of the pretrained CSSL model, we further propose to employ a negative sample free SSL objective (i.e., DINO) to fine-tune the speaker embedding network. The resulting speaker embedding system (C3-DINO) achieves 2.5% EER with a simple Cosine Distance Scoring method on Voxceleb1 test set, which outperforms the previous SOTA SSL system (4.86%) by a significant +45% relative improvement. With speaker clustering and pseudo labeling on Voxceleb2 training set, a LDA/CDS back-end applying on the C3-DINO speaker embeddings is able to further push the EER to 2.2%. Comprehensive experimental investigations of the Voxceleb benchmarks and our internal dataset demonstrate the effectiveness of our proposed methods, and the performance gap between the SSL SV and the supervised counterpart narrows further.