Quantum magneto-transport property of two-dimensional semi-Dirac electron system

We theoretically investigate the quantum magneto-transport property of a two-dimensional semi-Dirac system under a perpendicular magnetic field. Based on the low-energy k ⋅ p Hamiltonian within the framework of linear response theory, we find that the Landau levels (LLs) are proportional to the two-thirds (2/3) power law of the magnetic field and level index. There is a gap in the LL spectrum and the LL spacing decreases with the increase of the level index. Further, the Hall conductance is strictly quantized with the sequential integer plateaus (in unit of 2 e 2 / h ) at 0, ± 1 , ± 2 , ⋯ as the Fermi energy increases. The Shubnikov–de Haas (SdH) oscillation shows some pronounced peaks when the Fermi energy coincides with the LLs. The width of the Hall plateau and the interval of the SdH peak decrease with the increase of Fermi energy due to the decreasing LL spacings. Moreover, the Hall resistance is dependent linearly on the magnetic field in the low field regime but quantized in the high field regime. The longitudinal resistance is nearly a constant and shows distinct peaks in the low and high magnetic field regimes, respectively. Those magneto-transport spectra reflect the structure of LLs well. Our results provide further understanding on the electron states of semi-Dirac electron systems and may be useful in explaining the result of magneto-transport experiment.