Empirical Formula of the Absolute Value of Electrical Conductivity for Elemental Metals and Its Interpretation By Fluctuation Dissipation Theorem

Abstract

The absolute value of the electrical conductivity sigma of elemental metals even at the room temperature range is not well theoretically understood. This is particularly true in multivalent metals. This paper empirically found that sigma=n_{atom}e^2tau0/mG with tau0=hbar/k_{B}T reproduces the observations rather well for many metals as in Fig.1(b)-upper, if G is taken, by guessing to be a summed number of electric bands counted from outer most orbitals. We find by comparative study at the same time n_{atom}=n, namely Z=1 and m=m^* for majority of metals for sigma. Thus the only quantity remained is tau. The Bardeen's tau is found equal to tau0 if the deformation potential is equal to Fermi energy, using the observationally ascertained fact that thermal acoustic energy=the Fermi energy. Since electrons behave nearly as free electrons, the wave function should show the minimum uncertainty relation of Delta p_{x} Delta_{x}=hbar/2, which following the classical Fluctuation-Dissipation-Theorem shows in fact tau0=hbar/k_{B}T.