Commit 42497c41 by Anton Akhmerov

 ... ... @@ -82,7 +82,7 @@ Here the coupling strength $W = \langle \psi_+ | V(x) | \psi_- \rangle$ is the m We need to diagonalize a 2x2 matrix Hamiltonian. The answer is $$E(\delta k) = E_0 \pm \sqrt{v^2\hbar^2\delta k^2 + |W|^2}$$ In one of the exercises you will encounter the details of this calculation. Check out section 15.1.1 of the book for the details of this calculation. #### Physical meaning of $W$ ... ... @@ -176,7 +176,12 @@ The resulting band structure looks like this (in the extended Brillouin zone sch Observe that the top of the first band is above the bottom of the lowest band. Therefore if $V$ is sufficiently weak, the material can be conducting even with 2 electrons per unit cell! A larger $V$ makes the Fermi surface more square-like and eventually makes the material insulating. A larger $V$ makes the Fermi surface more distorted and eventually makes the material insulating. Let's compare the almost parabolic dispersion of the nearly free electron model with a tight-binding model in 2D. We now have a dispersion relation $E = E_0 + 2t(\cos k_x a + \cos k_y a)$, which looks like this: ### Light adsorption ... ...