Density of state of 2D material

[ramkrishna]

Dear Sir,
        I am trying to calculate the density of states of MoS2 monolayer sheet. Please find the attached figure (band structure and band gap gives satisfying results). In  2D case, we know that DOS is a constant but in this 2D system I am not getting such things. And even in the following  paper http://link.springer.com/article/10.1140%2Fepjb%2Fe2012-30070-x we can see that DOS is also not like a constant. I have  tried so many times by considering all kind of combination but got almost same result. What I feel is that, the calculation may correct but I am not able to understand the physics behind this. Can you please explain this elaborately then it will be very helpful for me to understand this?

one more thing, the unit here is written just 1/eV in case of both sheet as well as ribbon. will it also be per area for sheet and per width for ribbon?? 

Regards
Ramkrishna

[kstokbro]

For a 2-D free electron gas you will get a constant DOS. The electrons in a real material are never completely free and the DOS of a 2-d system only approximately constant. Often the electrons are covalently bound, and in this case the DOS may have other shapes.

Also note that it is important that you have many k-points in the DOS

[ramkrishna]

Thank you for your kind reply. But what about the unit?

[kstokbro]

In ATK we always calculate the DOS of your unit cell,
DOS unit 1/eV, i.e. number of states per energy and unit cell