Behavior near CDW

Behavior of Physical quantities near CDW¶

Several properties are measured to identify the signature of CDW, like Resistivity, Specific heat etc. \(T_{CDW}\) is the transition temperature for the onset of CDW. Several examples such as CDW in NbSe3 shows the behavior of normalized Resistivity near the onset temperature. This can also be seen in experiments performed on Kagome metal like AV3Sb5 family

Resistivity¶

The normalized resistivity is plotted for \(NbSe_3\) and has the signature of CDW. For high temperatures, the behavior is metallic (i.e., decreases with decrease in temperature) but it hits minima at around 145K. This is the onset of charge ordering, and the Peierls Transition rearranges the ions closely and localizes the electrons. This is charge ordering.

Once the temperature is decreased further, the electrons starts getting delocalized and due to increase in scattering, the normalized Resistivity starts increasing until there is no charge order and the system starts showing metallic behavior.

Resistivity	Derivative

The Phase diagram of AV3Sb5 has similar resistivity experiments which shows anomaly for different pressure. The temperatures at which the anomaly happens is the transition temperature \(T_{CO}\) of the charge ordering. A similar explanation as above holds for this case, with the addition that the derivative of the resistivity shows the clear dip at that temperature.

The resistivity shows metallic behavior (linear) for \(T > T_{CO}\) and hence the slope is almost constant for the \(d\rho/dT\) until the temperature is equal to transition temperature (\(T = T_{CO}\)). The increase in Resistivity is reflected in the derivative. When the CO vanishes, the system starts showing metallic behavior. For \(T < T_{CO}\) the decrease in resistivity is not exactly linear(less steep) which is then reflected in the derivative as well.

Remark: The derivative of a constant linear variation is zero, i.e, flat and if we have square like variation then the slope is linear.