Edge states and thermodynamics of rotating relativistic fermions under magnetic field

Abstract

We discuss free Dirac fermions rotating uniformly inside a cylindrical cavity in the presence of background magnetic field parallel to the cylinder axis. We show that, in addition to the known bulk states, the system contains massive edge states with the masses inversely proportional to the radius of the cylinder. The edge states appear at quantized threshold values of the fermion mass, which depend on the details of (chiral) MIT boundary conditions imposed at the surface of the cylinder. In the limit of infinite fermion mass, the masses of the edge states remain finite but, generally, nonzero as contrasted to the masses of the bulk states which become infinitely large. The presence of magnetic field affects the spectrum of both bulk and edge modes, and the masses of the edge states may vanish at certain quantized values of magnetic field. The moment of inertia of Dirac fermions is nonmonotonically increasing, oscillating function of magnetic field. The oscillations are well pronounced in a low-temperature domain and disappear at high temperatures. We also show that the edge modes alone do not support the anomalous transport phenomena such as chiral magnetic and chiral vortical effects.