Fermi energy and electronic specific heat in Mott insulators

Abstract

The Fermi energy of Mott insulators is calculated as a function of electronic density and temperature in the zero-bandwidth limit of the Hubbard model. For a half-filled band, the Fermi energy is pinned in the middle of the gap, as expected; however, the temperature dependence of ${\epsilon }_F$ also turns out to be very weak for (1/3)- and (2/3)-filled bands. The electronic specific heat as a function of temperature is calculated for the (1/3)-, (1/2)-, and (2/3)-filled bands. It is shown that even for the case of a half-filled band, the electronic specific heat dominates the lattice contribution over a range of temperatures, provided the intra-atomic Coulomb integral $U$ is less than 0.9 $k{\Theta }_D$. For larger values of $\frac{U}{k{\Theta }_D}$, the electronic contribution can still be observable at high temperatures, if the lattice specific heat saturates. It is shown that the electronic specific heat, if observable, can be used to distinguish between a Mott insulator and a normal semiconductor. Several classes of materials for which this test may be applicable are discussed.