(Solved): Consider a one-dimensional tight-binding conductor of length L with a partially filled energy band ...

Consider a one-dimensional tight-binding conductor of length L with a partially filled energy band upto the Fermi wavevector kf < 7/a, where a is the lattice constant. The dispersion relation of its energy band is given by: E1 E(k) = Eo - cos(ka) 2 = A static electric field E is applied to the conductor. — (a) Show that an electron with crystal momentum hko at time t = 0 has a group velocity given by v(t) = = vo sin(koa – wot) at time t. Give expressions for vo and wo in your answer. [5] (b) Determine the Fermi wavevector ky for a given number density n= N/L, where N is the total number of electrons in the conductor. [2] (c) If all the electronic states below the Fermi level are occupied at time t = 0, use your answers above to derive an expression for the current density as a function of time t. [5] (d) In a steady state condition, what happens to the current as n is increased from n = 0 to n=2/a? Using physical arguments, explain why this effect is observed. [4]