Why Is Normal Density Nonzero at Zero Temperature in Disordered Systems?

[welshtill]

By Landau's theory the normal mass density(total density minus the superfluid mass density) is the total mass carried by excitations. For the BCS state and weakly interacting Bose gas the normal density is zero at zero temperature because there are no excitations. However in the presence of disorder, the normal density is not zero even at zero temperature.

My question is: Is there a general argument (conservation law or symmetry consideration) by which one can determine whether the normal density is nonzero at zero temperature? Or genereally for what kind of system the superfluid density is not the total density at zero temperture?

 

[BigJDubs]

The answer to this question depends on the type of system under consideration. For most systems, the normal density is a result of thermal excitations, meaning that it is zero at zero temperature. However, in certain cases, the normal density can be nonzero even at zero temperature due to disorder or other effects. For example, in a disordered Bose-Einstein condensate, the normal density can be nonzero even at zero temperature due to the Anderson localization of bosons. Similarly, in a disordered two-dimensional superconductor, the normal density can be nonzero even at zero temperature due to the localization of Cooper pairs. In such cases, the normal density is not the result of thermal excitations but is instead a consequence of the disorder.