has a strong dependency on certain system parameters: dimensionality, strength of interatomic interactions and Fermi level. This law is not valid or the value of the Lorenz number can be reduced at least in the following cases: manipulating electronic density of states, varying doping density and layer thickness in superlattices and materials with correlated carriers. In thermoelectric materials there are also corrections due to boundary conditions, specifically open circuit vs. closed circuit. Violations In 2011, N. Wakeham et al. found that the ratio of the thermal and electrical Hall conductivities in the metallic phase of quasi-one-dimensional lithium molybdenum purple bronze Li0.9Mo6O17 diverges with decreasing temperature, reaching a value five orders of magnitude larger than that found in conventional metals obeying the Wiedemann–Franz law. This due to spin-charge separation and it behaving as a Luttinger liquid. A Berkeley-led study in 2016 by S. Lee et al. also found a large violation of the Wiedemann–Franz law near the insulator-metal transition in VO2 nanobeams. In the metallic phase, the electronic contribution to thermal conductivity was much smaller than what would be expected from the Wiedemann–Franz law. The results can be explained in terms of independent propagation of charge and heat in a strongly correlated system. Molecular systems In 2020, Galen Craven and Abraham Nitzan derived a Wiedemann-Franz law for molecular systems in which electronic conduction is dominated not by free electron motion as in metals, but instead by electron transfer between molecular sites. The molecular Wiedemann-Franz law is given by where is the Lorenz number for molecules and is the reorganization energy for electron transfer. See also Drude model References Heat conduction Electrical resistance and conductance