homework10

# homework10 - Physics 481 Condensed Matter Physics Homework...

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Physics 481: Condensed Matter Physics - Homework 10 due date: April 15, 2011 Problem 1: Fermi surfaces in two dimensions (10 points) Consider a two-dimensional system of nearly free electrons (weak periodic potential) with a square unit cell (lattice constant a ). Determine the Fermi surfaces for the cases of 1, 2, 3, and 5 electrons per unit cell. To this end, ﬁrst project the free electron Fermi surface into the 1st Brillouin zone and then think about at what points gaps open. Plot the Fermi surfaces in the Brillouin zone. It might be useful to make separate plots for the diﬀerent bands. (Note: Semi-quantitative plots are OK, i.e., you need to get the topology right, the exact positions are not so important.) Problem 2: Kronig-Penney model (Marder, problem 7.5, 15 points + 10 BONUS points) Consider an electron in 1D in the presence of the periodic potential (Kronig-Penney model) U ( x ) = X m = -∞ U 0 Θ( x - ma )Θ( ma + b - x ) . a) Restrict your attention to a single unit cell, and write down the boundary conditions for the

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## This note was uploaded on 10/04/2011 for the course PHYSICS 481 taught by Professor Thomasvojta during the Spring '11 term at Missouri S&T.

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homework10 - Physics 481 Condensed Matter Physics Homework...

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