Electron transport in nanostructures: A key to high temperature superconductivity?

Nanostructured GaAs Schottky barrier diodes are used as low noise THz heterodyne detectors. Different diodes show that the electron transport is ballistic and given by an optimized depletion thickness DDepl which is shorter than the mean free path length. The best THz mixer noise temperature is achieved when the depletion thickness is twice the doping distance in GaAs with DDepl=2x. There also is a linear relation between the depletion thickness and the carrier mobility μ by (2x)2≈h/(2e)μ. Since the mobility is proportional to 1/energy and because of many similarities when comparing with properties of high temperature superconductors (HTSC) it has been investigated if the doping distance x in HTSCs is connected with 1/(kTc). It turns out that there is also a strong correlation between x and the critical transition temperature Tc given by (2x)2∼1/Tc. A detailed analysis and comparison suggest that the correlation equation for HTSCs is linked to the transition temperature Tc, the density of states in a 1D quantum wire, the lowest energy E1 in a 1D quantum well, and to the Fermi energy EF.