Orbital angular momentum in a topological superconductor with Chern number higher than $1$

We investigate the bulk orbital angular momentum (AM) in a two-dimensional hole-doped topological superconductor (SC) which is composed of a hole-doped semiconductor thin film, a magnetic insulator, and an $s$-wave SC and is characterized by the Chern number $C = -3$. In the topological phase, $L_z/N$ is strongly reduced from the intrinsic value by the non-particle-hole-symmetric edge states as in the corresponding chiral $f$-wave SCs when the spin-orbit interactions (SOIs) are small, while this reduction of $L_z/N$ does not work for the large SOIs. Here $L_z$ and $N$ are the bulk orbital AM and the total number of particles at zero temperature, respectively. As a result, $L_z/N$ is discontinuous or continuous at the topological phase transition depending on the strengths of the SOIs. We also discuss the effects of the edge states by calculating the radial distributions of the orbital AM.