As social robots get more deeply integrated intoour everyday lives, they will be expected to engage in meaningful conversations and exhibit socio-emotionally intelligent listening behaviors when interacting with people. Active listening and backchanneling could be one way to enhance robots' communicative capabilities and enhance their effectiveness in eliciting deeper self-disclosure, providing a sense of empathy,and forming positive rapport and relationships with people.Thus, we developed an LLM-powered social robot that can exhibit contextually appropriate sentiment-based backchannelingand active listening behaviors (active listening+backchanneling) and compared its efficacy in eliciting people's self-disclosurein comparison to robots that do not exhibit any of these listening behaviors (control) and a robot that only exhibitsbackchanneling behavior (backchanneling-only). Through ourexperimental study with sixty-five participants, we found theparticipants who conversed with the active listening robot per-ceived the interactions more positively, in which they exhibited the highest self-disclosures, and reported the strongest senseof being listened to. The results of our study suggest that the implementation of active listening behaviors in social robotshas the potential to improve human-robot communication andcould further contribute to the building of deeper human-robot relationships and rapport.