Hall effect on the triangular lattice

We investigate the Hall effect on the two-dimensional triangular lattice. We calculate the high frequency Hall constant $R_H$ and its temperature dependence for three regimes of the Hubbard interaction $U$. In the non-interacting case $U=0$ we find that $R_H$ behaves at temperature $T=0$ like the classical dc Hall constant, $R_H\sim1/ne$. At high $T$ we find a positive $R_H$ increasing linearly with temperature, with a slope depending on the electron density. For small to moderate values of $U$, we study the effect of interactions on $R_H$ within second-order perturbation theory, and we find these effects to be small. The perturbation theory also shows that the electron self-energy is almost local ($k$-independent), suggesting the use of a local approximation as the Dynamical Mean Field Theory (DMFT) method to treat higher values of $U$. We therefore evaluate $R_H$ at large $U$ using both DMFT and the atomic limit of the self-energy, and we compare the results with those obtained at small $U$. Finally, we discuss the relevance of our calculations for the interpretation of recent Hall measurements in cobaltates.