Classical Collective Systems: Resistor Networks

It has recently been discovered that the resistance of doped silver chalcogenides increases linearly with magnetic field, with no signs of saturation at the highest fields measured. There have been various attempts to explain this quantum mechanically, but we believe that this is a classical phenomenon resulting from the spatially inhomogeneous electrical conductivity in these materials.

We are currently developing a random resistor network model to describe this anomalous resistance of the silver chalcogenides. As the figure above demonstrates, the transport behaviour of these networks is generally non-trivial. The colours represent voltages, and the black arrows currents, calculated from our model. In a large magnetic field, the local current can reverse direction or form loops, whilst the voltages become a complex landscape.

These random networks have so far successfully reproduced the linear dependence of resistance on magnetic field, but we are still working towards gaining a comprehensive understanding of the physics involved.