In the field of particle physics, the search for rare phenomena by means of low background experiments occupies a fundamental place. The nature of dark matter and neutrinos are among the major remaining unknowns in particle physics today. Their understanding is the subject of intense effort by the scientific community and relies on the observation of extremely rare physical processes, such as the direct interaction of dark matter candidates with a detector target and the search for neutrinoless double beta decays. To this end, the XENON collaboration has been developing for several years multiple low background experiments, based on the xenon dual-phase time projection chamber technology having as main objective the direct detection of the interaction of weakly interacting massive particle (WIMP) candidate with a xenon target nucleus. The XENONnT experiment, currently operating in the underground INFN Laboratori Nazionali del Gran Sasso in Italy, is the fourth generation of experiment from the XENON collaboration. Thanks to its unprecedented low level of background and its large target mass of xenon, XENONnT is sensitive to other rare processes, including the search for neutrinoless double beta decay of 136Xe. In this thesis I will present a first analysis of XENONnT calibration data used to monitor the detector stability during the first scientific run between July and November 2021 and a sensitivity study on the projection for neutrinoless double beta decay search in XENONnT.