optical studies of gap, exchange, and hopping energies in the insulating cuprates

We have measured the insulating energy gap {Delta} and the exchange interaction {ital J} in a series of cuprate crystals, including {ital T}{prime}-phase {ital M}{sub 2}CuO{sub 4} ({ital M}=Pr, Nd, Sm, Eu, and Gd), {ital T}{sup *}-phase La,Tb,Sr{sub 2}CuO{sub 4}, and {ital T}-phase La{sub 2}CuO{sub 4}. We find that the energy gap scales predominantly with the in-plane Cu-O distance, scaling as {delta} log{Delta}/ {delta} log{ital d}{similar to}{minus}6. Furthermore, contrary to simple expectations, the energy gap increases with decreasing Cu-O distance, suggesting that Coulomb and other repulsive energies dominate the effects of band hybridization. Using a three-band Hubbard-model expression, our studies of {Delta} and {ital J} in the cuprates allow us to estimate that the hopping energy {ital t} scales with Cu-O distance as {delta} log{ital t}/{delta} log{ital d}{similar to}{minus}4.