For one-dimensional nonlinear lattices with momentum conserving interparticle interactions, intensive studies have suggested that the heat conductivity κ diverges with the system size L as κ~L(α) and the value of α is universal. But in the Fermi-Pasta-Ulam-β lattices with nearest-neighbor (NN) and next-nearest-neighbor (NNN) coupling, we find that α strongly depends on γ, the ratio of the NNN coupling to the NN coupling. The correlation between the γ-dependent heat conduction behavior and the in-band discrete breathers is also analyzed.

The power-law length (L) divergence of thermal conductivity (κ) in one-dimensional (1D) systems, i.e., κ ∼ L α , has been predicted by theories and also corroborated by experiments. The theoretical predictions of the exponent α are usually ranging from 0.2 to 0.5; however sometimes, the experimental observations can be higher, e.g., α = 0.6-0.8. This dispute has not yet been settled. Here we show the first convincing evidence that an exponent of α 0.7 that falls within experimental observations, can occur in a theoretical model of 1D long-range interacting Fermi-Pasta-Ulam chain. This, for the first time, theoretically supports the possibility of a higher divergent exponent and thus sheds new light on understanding of extremely high thermal conductivity in 1D materials at macroscopic scales.