Analogy between rotation and density for Dirac fermions in a magnetic field

We analyze the energy spectra of Dirac fermions in the presence of rotation and magnetic field. We find that the Landau degeneracy is resolved by rotation. A drastic change in the energy dispersion relation leads to the “rotational magnetic inhibition” that is a novel phenomenon analogous to the inverse magnetic catalysis in a magnetic system at finite chemical potential.

Figure 1

Dynamical mass with $eB=0.2{\mathrm{\Lambda }}^2$ obtained from the gap equation (21) with rotation (red line) and with chemical potential $\mu ={\mu }_N$ (blue line). The model parameters are chosen as in Eq. (28).

Figure 2

3D plot for the dynamical mass as a function of $\mathrm{\Omega }$ and $eB$ at weak coupling. For small $\mathrm{\Omega }$ the dynamical mass grows exponentially with $1/eB$ (i.e. the magnetic catalysis). The critical ${\mathrm{\Omega }}_c$ is also amplified exponentially as $1/eB$ decreases (see also Fig. 3).

Figure 3

$eB$-dependence of ${\mathrm{\Omega }}_c$ for $0.1\le eB/{\mathrm{\Lambda }}^2\le 0.2$. The linearity of $\ln {\mathrm{\Omega }}_c$ vs $1/eB$ confirms the validity of the functional form of ${\mathrm{\Omega }}_c$ given by Eq. (36).

Figure 4

3D plot for the dynamical mass as a function of $\mathrm{\Omega }$ and $eB$ at strong coupling. For large $\mathrm{\Omega }$, chiral symmetry is restored by $eB$, which manifests the inverse magnetic catalysis or the rotational magnetic inhibition.