3. Consider a one-dimensional tight-binding conductor of length L with a partially filled energy band upto the Fermi wav

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3 Consider A One Dimensional Tight Binding Conductor Of Length L With A Partially Filled Energy Band Upto The Fermi Wav 1 (56.55 KiB) Viewed 20 times

3. Consider a one-dimensional tight-binding conductor of length L with a partially filled energy band upto the Fermi wavevector kƑ </a, where a is the lattice constant. The dispersion relation of its energy band is given by: E₁ E(k)= Eo cos(ka) A static electric field E is applied to the conductor. (a) Show that an electron with crystal momentum ħko 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]