The Hall Number, Optical Sum Rule and Carrier Density for the $t$-$t'$-$J$ model

Details The Hall Number, Optical Sum Rule and Carrier Density for the $t$-$t'$-$J$ model The Hall Number, Optical Sum Rule and Carrier Density for the $t$-$t'$-$J$ model

2007-08-13

arxiv.org/abs/0708.1651v2

Physics

Condensed Matter

Strongly Correlated Electrons

Typos removed,9 Figures, (Revised Figure.3 contains comparison with experiments)

Scientific paper

10.1103/PhysRevB.77.045127

We revisit the relationship between three classical measures of particle number, namely the chemical doping $x$, the Hall number $x_{hall}$ and the particle number inferred from the optical sum rule $x_{opt}$. We study the $t$-$t'$-$J$ model of correlations on a square lattice, as a minimal model for High $T_c$ systems, using numerical methods to evaluate the low temperature Kubo conductivites. These measures disagree significantly in this type of system, owing to Mott Hubbard correlations. The Hall constant has a complex behavior with several changes of sign as a function of filling $x$, depending upon the model parameters. Thus $x_{hall}$ depends sensitively on $t'$ and $J$, due to a kind of quantum interference.

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