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Commit dea00c59 authored by Iacopo Bertelli's avatar Iacopo Bertelli
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Update 12_band_structures_in_higher_dimensions.md

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...@@ -214,7 +214,7 @@ Consider a rectangular lattice with lattice constants $a_x$ and $a_y$. ...@@ -214,7 +214,7 @@ Consider a rectangular lattice with lattice constants $a_x$ and $a_y$.
Suppose the hopping parameters in the two directions to be $t_1$ and $t_2$. Suppose the hopping parameters in the two directions to be $t_1$ and $t_2$.
Consider a single orbital per atom and only nearest-neighbour interactions. Consider a single orbital per atom and only nearest-neighbour interactions.
1. Write down a 2D tight-binding Hamiltonian (expand to 2D the results of 1D). 1. Write down a 2D tight-binding Schrodinger equation (expand to 2D the results of 1D).
2. Formulate the Bloch ansatz for the wave function. 2. Formulate the Bloch ansatz for the wave function.
3. Calculate the dispersion relation of this model. 3. Calculate the dispersion relation of this model.
4. What Fermi surface shape would this model have if the atoms are monovalent? 4. What Fermi surface shape would this model have if the atoms are monovalent?
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