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Understanding of physics on electrical conductivity in metals; Drude – Sommerfeld-Kubo

1. Overview Around 1900, Drude (Paul Karl Ludwig Drude) improved the theory of classical conduction given by Lorentz. He reasoned that since metals conduct electricity so well, they must contain free electrons that move through a lattice of positive ions (the discovery of electron by J.J. Thomson in 1897). This motion of electrons led to the formation of Ohm’s law. The free-moving electrons act just as atomic gas; moving in every direction throughout the lattice. These electrons collide with the lattice ions as they move about, which is key in understanding thermal equilibrium. The average velocity due to the thermal energy is zero since the electrons are going in every direction. There is a way of affecting this free motion of electrons, which is by use of an electric field. This process is known as electrical conduction and theory is called Drude-Lorentz theory; Conventionally we call the Drude model here. In Modern Physics (Phy.323 in Binghamton University)) and Solid State Physics (Phys.472/572 in BU) of the undergraduate physics courses in U.S.A., it is taught that the electrical resistivity of metal can be explained in terms of the quantum mechanical model (Sommerfeld model) that the electrons are fermions and obeys the Fermi-Dirac statistics. In this model, only the conduction electrons near the Fermi surface contribute to the electrical resistivity. These electrons have the Fermi velocity F v (10 6 m/s) for copper (Cu) metal. The mean free path is evaluated as