In lecture 1, you have learned that in a diffusive electronic system, the electron mean free path, Le = VpT is related to the Fermi velocity vr. Using Ohm's law for a planar (2D) conductor (see slide 13 of uploaded presentation slides), W G= 02T (1) with Drude conductivity o2 ner, derive the Landauer formula, 2e? -NT h G (2) %3D for a long conductor (L > L.) and show that it has an effective transmission coefficient per mode can be expressed as T = for this 2D electronic system. Hint: The electron's Fermi velocity can be estimated as vp mAp where Ap = V2 is the electron's Fermi wave length and n, is the electron density in the conductor. Also remember that the number of modes can be estimated as N = W %3D Ohm's Law: Diffusive limit Ohm's Law | V R = I m* !! A ne?r resistivity T = Le/VF Scattering time mean free path effective mass Le m*