Are There Negative Conductivities/Resistivities?

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Negative conductivities and resistivities can theoretically exist, particularly in certain materials exhibiting non-linear properties, but they do not conform to Ohm's law. In electromagnetic contexts, negative conductivity implies that an increase in electric field could lead to a decrease in current, which is counterintuitive. Such behavior is often associated with specific phenomena like negative resistance, where a system can amplify signals rather than dissipate energy. The implications of negative conductivity in practical applications remain complex and not fully understood. Overall, while negative conductivities are acknowledged in theory, their real-world applications and characteristics require further exploration.
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Are there such things as negative conductivities and/or resistivities in the real world? If so, what would these materials' electric characteristics be? This question is coming from my reading in an EM textbook where the EM wave equations are solved for a source-free, lossy medium (finite conductivity).

In the dispersion equation,

\gamma=\pm\sqrt{j\omega\mu(\sigma+j\omega\epsilon)}

the textbook states that the conductivity \sigma can be allowed to take on positive or negative values but they don't explain what a negative conductivity would mean.

Thanks!
 
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