The mass effects on two-dimensional relativistic fermions

We investigate chemical potential, internal energy and specific heat of ideal relativistic fermions in two spatial dimensions taking into account the finite mass effect and the finite carrier concentration. The results show that the heavy mass and low carrier concentration fermions trend to be non-relativistic. The light mass and high carrier concentration lead more relativistic behavior. For massless fermions, the total kinetic energy equals to a constant for a given density (n), which is a function of n^3/2. Meanwhile, the specific heat for massless fermions keeps the linear increasing behavior with temperature with constant slope rather than the slope of zero, which is deduced from the non-relativistic case.