Magneto-electronic specific heat of graphene*

The electronic specific heat related to the Landau levels of monolayer graphene is studied by the Peierls tight-binding model. The low-temperature thermal properties are dominated by the two low-lying Landau levels with the Zeeman splitting. They give rise to rich temperature and magnetic-field dependence. The T-dependent specific heat reveals the composite form of 1/T and exponential function. Also, a prominent peak appears in the T-dependent (B-dependent) spectrum with its critical temperature T$_{c}$ (critical magnetic field B$_{c})_{.}$ Moreover, there has a simple linear relationship between T$_{c }$and B$_{c}$. In a slightly doped graphene, there exists an extra shoulder structure in the specific heat. Such structure mainly comes from the Zeeman effect and temperature-dependent carrier distribution.