Chapter 26: Some Examples in Condensed Matter Physics

Among the very large number of tunneling problems in solid state physics [1]–[3] we will briey discuss four very important and yet conceptually simple problems. The first one is about the motion of electrons in a periodic potential which is similar to the problem of tunneling through a series of identical barriers discussed in Sec. 3.3, only now the number of barriers is infinite. Then we study the tunneling of electrons in a simple metal-insulator-metal structure. While, in principle, this should be formulated as a many-electron tunneling problem and the current associated with it, we observe that one encounters certain difficulties with such a formulation and for this reason we replace it with a very simple model for such a tunneling. We then turn our attention to an elementary theory of electron tunneling through heterostructures. Finally we study the Josephson effect for both d.c. and a.c. currents.