# Edge states and thermodynamics of rotating relativistic fermions under magnetic field

## TL;DR

This paper studies rotating relativistic fermions in a magnetic field within a cylindrical cavity, revealing the existence of massive edge states, their spectral properties, and how magnetic fields influence the system's thermodynamics and moment of inertia.

## Contribution

It introduces the concept of massive edge states in rotating fermions under magnetic fields and analyzes their spectral behavior and thermodynamic implications.

## Key findings

- Existence of massive edge states with inverse radius mass dependence.
- Edge states appear at quantized fermion mass thresholds.
- Magnetic field causes oscillations in the moment of inertia, especially at low temperatures.

## 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. In the limit of infinite fermion mass the masses of the edge states remain finite but, generally, nonzero as contrasted to the bulk states whose masses become infinite. 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 values of magnetic field. The moment of inertia of Dirac fermions is non-monotonically increasing, oscillating function of magnetic field. The oscillations are well pronounced in a low-temperature domain and they disappear at high temperatures.