Magnetizations of Dirac fermions M Shoufie Ukhtary(a*) , F. Rizki Pratama (b), Riichiro Saito (b)
a) Research Center for Physics, Indonesian Institute of Sciences
* msho001[at]lipi.go.id
b) Department of Physics, Tohoku University
Abstract
Graphene and related two-dimensional materials are known to possess intrinsic orbital diamagnetism (OD), which is originated from the coalescence of states of the Dirac fermions at the valence bands to form the zeroth Landau levels (LLs) in the presence of an external magnetic field B. Magnetizations is used to characterize the OD of graphene. A method to calculate the magnetization is by using the Euler-Maclaurin summation formula, however, this method gives divergent magnetization since the summation of the infinite number of the occupied LLs at the valence bands should be included.
In this work, we analytically calculate the magnetizations for strong magnetic field/low temperature and weak magnetic field/high temperature limits with the method of zeta function regularization, in order to avoid the divergence in the expression of magnetization. Our formula reproduces the experimental observation of the magnetization of graphene. In the case of gapped Dirac fermions, a large band-gap gives a smaller but more robust magnetization with respect to temperature. In the doped system, we also observe the oscillation of magnetization with respect to magnetic field.
