Memory-function approach to the Hall constant in strongly correlated electron systems

The anomalous properties of the Hall constant in the normal state of high-${\mathrm{T}}_{\mathrm{c}}$ superconductors are investigated within the single-band Hubbard model. We argue that the Mori theory is the appropriate formalism to address the Hall constant, since it aims directly at resistivities rather than conductivities. More specifically, the frequency-dependent Hall constant decomposes into its infinite frequency limit and a memory-function contribution. The latter naturally introduces a second time scale that is identified with the spinon relaxation time of Anderson within the t-J model. This provides us with a phenomenological understanding of the interplay between the frequency and temperature dependence of the Hall constant for frequencies below the Mott-Hubbard gap. As a first step, both terms of ${\mathrm{R}}_{\mathrm{H}}$ are calculated perturbatively in U and on an infinite dimensional lattice, where U is the correlation strength. If we allow U to be of the order of twice the bare bandwidth, the memory-function contribution causes the Hall constant to change sign as a function of doping and to decrease as a function of temperature. In the strong correlation regime, U≫:t (t is the hopping amplitude), the memory function is calculated via its moments and shown to project out the high-energy scale U. This causes the Hall constant to decrease by a factor (1+δ)/2 (δ indicates doping), when the frequency is lowered from infinity to values within the Mott-Hubbard gap. Finally, it is outlined how the Hall constant may be calculated in the low-frequency regime.