Solid State Physics 2013
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Energies in 1st Brillouin zone of 2D square lattice

Posted by Ali on April 7, 2013, 10:37 pm

 I don't understand something on question 7 part (i) from the 2011 condensed matter paper. If you look at pages 9 and 10 of the solution provided on the 'examination papers' section on the physics website [http://www.physics.ox.ac.uk/expapers/ExamSolutions_for%20Students/2012-2013/B3%20V.pdf.pdf], it calculates the energy in the reciprocal lattice for a given (k_x, k_y). The same thing is done in pages 167 and 176 of the notes. I understand that the energy at these points is (h^2)(k^2)/2m (pretend that's a h bar), and I understand why k^2 is (pi/a)^2 on the edge of the Brillouin zone boundaries and its 2(pi/a)^2 in the corner, what I don't understand is m, the mass. What is this the mass of? I figured its the mass of electrons because they occupy these k-states but I calculated backwards from the mass used in the solution and it is about 0.02 the mass of a proton/neutron or the mass of 40 electrons. Is it some kind of effective mass of electrons? The reason I'm not sure about this is because for effective mass formula requires V, which is not given in the question. Any help is appreciated.

 Message Thread Energies in 1st Brillouin zone of 2D square lattice - Ali April 7, 2013, 10:37 pm Re: Energies in 1st Brillouin zone of 2D square lattice - Steve Simon April 7, 2013, 10:53 pm Re: Energies in 1st Brillouin zone of 2D square lattice - Ali April 8, 2013, 12:13 am « Back to index