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###### Perform Fermi surfaces calculations using PKKprime code
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# Perform Fermi surfaces calculations using PKKprime code
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The computation of Fermi surfaces, or band structures can be easily done
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The computation of Fermi surfaces, or band structures can be easily done
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setting the *RUNOPTION* *qdos* (see [Qdos tutorial](jumu/qdos "wikilink")). The "qdos approach" is based on the scan of the k-space for a given energy (or different energy values if we are interested on band-structure calculations) by the spectral function
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setting the *RUNOPTION* *qdos* (see [Qdos tutorial](jumu/qdos)). The "qdos approach" is based on the scan of the k-space for a given energy (or different energy values if we are interested on band-structure calculations) by the spectral function
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: $`\rho(E+i\eta,k) = \frac{\eta}{\pi}\frac{1}{(E-\epsilon\_k)\^2 + \eta\^2}`$.
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: $`\rho(E+i\eta,k) = \frac{\eta}{\pi}\frac{1}{(E-\epsilon\_k)\^2 + \eta\^2}`$.
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So the density is written as a Lorentzian which
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So the density is written as a Lorentzian which
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reaches its maximum $`\frac{1}{\eta\pi}`$ at $`E=\epsilon\_{\vec{k},\sigma}`$. All the maximums of this spectral
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reaches its maximum $`\frac{1}{\eta\pi}`$ at $`E=\epsilon\_{\vec{k},\sigma}`$. All the maximums of this spectral
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... | @@ -18,7 +18,7 @@ particularly transport ones. However, the \'qdos method\' allows to have |
... | @@ -18,7 +18,7 @@ particularly transport ones. However, the \'qdos method\' allows to have |
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a first glance on the Fermi surface, before launching more accurate
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a first glance on the Fermi surface, before launching more accurate
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computations with the PKKprime code.
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computations with the PKKprime code.
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##### Fermi surface calculation
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## Fermi surface calculation
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The goal is to solve numerically the secular equation of KKR :
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The goal is to solve numerically the secular equation of KKR :
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... | @@ -39,7 +39,7 @@ $`\lambda\_\nu(\vec{k},E)=0`$. |
... | @@ -39,7 +39,7 @@ $`\lambda\_\nu(\vec{k},E)=0`$. |
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k-space, for a fixed energy $`E`$, and find
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k-space, for a fixed energy $`E`$, and find
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$`\min\limits\_{\vec{k},\nu}(\|\lambda\_\nu(\vec{k},E)\|)`$.
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$`\min\limits\_{\vec{k},\nu}(\|\lambda\_\nu(\vec{k},E)\|)`$.
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##### Qualitative explanation of the iterative method
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## Qualitative explanation of the iterative method
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The main feature of this method is that the Brillouin zone, will be
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The main feature of this method is that the Brillouin zone, will be
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divided into cubes and into each cube the secular equation
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divided into cubes and into each cube the secular equation
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