Magneto-Electronic Specific Heat of Graphene

The electronic specific heat of monolayer graphene in response to a magnetic field is studied within the Peierls tight-binding model. The low-temperature thermal properties are dominated by the two lowest Landau levels, which are induced by the Zeeman effect. The temperature and the magnetic field compete with each other in the specific heat, which reveals a composite form of $1/T^{2}$ and exponential function. In addition, a prominent peak at the critical temperature $T_{\text{m}}$ (critical magnetic field $B_{\text{m}}$) exists in the temperature (field) evolution, where $T_{\text{m}}$ ($B_{\text{m}}$) and $B$ ($T$) are in a simple linear relation. In slightly-doped cases, shoulder structures are further introduced in the specific heat, which come from the second lowest unoccupied state and second highest occupied state. All those special feature basically reflect the main characteristics of the subbands near the chemical potential. There are certain important differences between graphene and carbon nanotubes in terms of magneto-electronic specific heat.