The chiral magnetic effect is concisely derived by employing the Wigner function approach in the chiral fermion system. Subsequently, the chiral magnetic effect is derived by solving the Landau levels of chiral fermions in detail. The second quantization and ensemble average leads to the equation of the chiral magnetic effect for righthand and lefthand fermion systems. The chiral magnetic effect arises uniquely from the contribution of the lowest Landau level. We carefully analyze the lowest Landau level and find that all righthand (chirality is +1) fermions move along the direction of the magnetic field, whereas all lefthand (chirality is −1) fermions move in the opposite direction of the magnetic field. Hence, the chiral magnetic effect can be explained clearly using a microscopic approach.

We construct the grand partition function of the system of massive Dirac fermions in a uniform magnetic field from Landau levels, through which all thermodynamic quantities can be obtained. Making use of the Abel–Plana formula, these thermodynamic quantities can be expanded as power series with respect to the dimensionless variable b = 2eB/T 2. The zero-field magnetic susceptibility is expanded at zero mass, and the leading order term is logarithmic. We also calculate scalar, vector current, axial vector current and energy-momentum tensor of the system through ensemble average approach. Mass correction to chiral separation effect is discussed. For massless chiral fermions, our results recover the chiral magnetic effect for right- and left-handed fermions, as well as chiral separation effect.

We explored the interplay between magnetic field and rotation in the de Hass -van Alphen oscillation.The effect is found to be reduced because of the re-weighting of different states within the same Landau level by rotation energy. The implications of our results on high energy physics and condensed matter physics are speculated.

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