mirror of
https://github.com/triqs/dft_tools
synced 2024-12-22 12:23:41 +01:00
53 lines
1.1 KiB
ReStructuredText
53 lines
1.1 KiB
ReStructuredText
.. index:: Transport
|
|
|
|
.. _Transport:
|
|
|
|
Transport calculations
|
|
======================
|
|
|
|
.. index:: Theory
|
|
|
|
Formalism
|
|
---------
|
|
The optical conductivity and the Seebeck coefficient in the direction :math:`\alpha\beta` are defined as
|
|
|
|
.. math::
|
|
|
|
\sigma_{\alpha\beta} = \beta e^{2} A_{0,\alpha\beta} \ \ \ \text{and} \ \ \ S_{\alpha\beta} = -\frac{k_B}{|e|}\frac{A_{1,\alpha\beta}}{A_{0,\alpha\beta}}
|
|
|
|
in which the kinetic coefficients :math:`A_{n,\alpha\beta}` are given by
|
|
|
|
.. math::
|
|
|
|
A_{n,\alpha\beta} = N_{sp} \pi \hbar \int{d\omega \left(\beta\omega\right)^n f\left(\omega\right)f\left(-\omega\right)\Gamma_{\alpha\beta}\left(\omega\right)}
|
|
|
|
with the transport distribution
|
|
|
|
.. math::
|
|
|
|
\Gamma_{\alpha\beta}\left(\omega\right) = \frac{1}{V} \sum_k Tr\left(v_{k,\alpha}A_{k}\left(\omega\right)v_{k,\beta}A_{k}\left(\omega\right)\right)
|
|
|
|
.. index:: Prerequisite
|
|
|
|
Prerequisites
|
|
-------------
|
|
|
|
.. note::
|
|
Coming soon!
|
|
|
|
|
|
.. index:: Using the transport code.
|
|
|
|
Using the transport code
|
|
------------------------
|
|
|
|
.. note::
|
|
Coming soon!
|
|
|
|
|
|
.. index:: References
|
|
|
|
References
|
|
----------
|
|
|