Question

Consider a two-dimensional solid measuring LxL in which the atoms are arranged in a square lattice with lattice parameter a. There is only a single atomic species in the solid, and the valence is equal to one, that is, each atom contributes one electron to the electron “sea”. (i) Sketch the reciprocal lattice for this crystal and include units. (ii) Compute the Fermi wave-vector kF. (iii) Make a two-dimensional sketch and indicate, the Fermi circle (i.e. the occupied states at T=0K) and the reciprocal lattice. (iv) Sketch a plot of Energy versus k for nearly-free electrons travelling in the i and i+j directions. Indicate on each plot the occupied states at T=0 and comment on the electrical conductivity of the system. Explain your reasoning.

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Answer 1