Investigation of the Energy Levels of the Kramers Degenerate 14NV-13C System in a Magnetic and Electric Field

This work investigates the three-spin system 14NV-13C, which includes the electronic spin of the NV center and the nuclear spins of the 13C and 14N atoms. In this system, a twofold degeneracy of the energy levels is observed in zero magnetic field (Kramers’ degeneracy) due to the time-reversal symmetry of the spin Hamiltonian. To study the influence of magnetic and electric fields on the energy levels of the system, optically detected magnetic resonance (ODMR) spectra of this hybrid quantum system were simulated within the framework of the spin Hamiltonian method under the simultaneous influence of magnetic and electric or intracrystalline fields. The constructed model agrees well with the experimental ODMR spectrum of a single 14NV-13C complex. Based on the ODMR spectrum splitting in zero magnetic field and quantum chemical modeling data, it was determined that the 13C atom is located in the third coordination sphere of the NV center. The corresponding hyperfine interaction tensor between the electronic spin of the NV center and the nuclear spin of the 13C isotope was used in the model. As a result, numerical calculations showed that the degeneracy is lifted only by the magnetic field, regardless of the presence of any electric (crystalline) field, making this quantum system promising for magnetometry.