dear Belvasi 

you can use MODIS product for estimating NPP (Net primary product)  i think also carbon index.   

There is no direct carbon index for Landsat images. You have to follow some procedure to derive it by yourself: 1. To produce LAI or other vegetation indices such NDVI, SAVI, EVI, ARVI and so on based on the atmospherically corrected Landsat images; 2. Try to establish satellite-based biomass models by linking the derived indicators (LAI, NDVI....) with the field measured biomass (e.g., grasses, crops or others); 3. Apply your models back to images (NDVI or other) to estimate the biomass of your interested biome in your study area (be careful: different biomes or land cover unit, biomass models are different); 4. Conversion from biomass to carbon in terms of  certain ratio.

However, if you are dealing with forests or woodland, the procedure is much more complicated. You may refer to one of my publications for detail.  Good try!    

Article Assessing woody biomass in African tropical savannahs by mul...

Dear Mehdi

Nasa uses landsat maps to create CO2 maps, you can read more in this article

http://landsat.gsfc.nasa.gov/?p=1159

In this case study, counting carbon, you will be able to find more practical details on the process

http://www.eohandbook.com/eohb2008/casestudy_carbon.html

Regards

FC