Orbit topology analyzed from pi phase shift of magnetic quantum oscillations in three-dimensional Dirac semimetal

Abstract

With the emergence of Dirac fermion physics in the field of condensed matter, magnetic quantum oscillations (MQOs) have been used to discern the topology of orbits in Dirac materials. However, many previous researchers have relied on the single-orbit Lifshitz- Kosevich (LK) formula, which overlooks the significant effect of degenerate orbits on MQOs. Since the single-orbit LK formula is valid for massless Dirac semimetals with small cyclotron masses, it is imperative to generalize the method applicable to a wide range of Dirac semimetals, whether massless or massive. This report demonstrates how spin-degenerate orbits affect the phases in MQOs of three-dimensional massive Dirac semimetal, NbSb2. With varying the direction of the magnetic field, an abrupt pi phase shift is observed due to the interference between the spin-degenerate orbits. We investigate the effect of cyclotron mass on the pi phase shift and verify its close relation to the phase from the Zeeman coupling. We find that the pi phase shift occurs when the cyclotron mass is half of the electron mass, indicating the effective spin gyromagnetic ratio as gs = 2. Our approach is not only useful for analyzing MQOs of massless Dirac semimetals with a small cyclotron mass but also can be used for MQOs in massive Dirac materials with degenerate orbits, especially in topological materials with a sufficiently large cyclotron mass. Furthermore, this method provides a useful way to estimate the precise gs value of the material.