Longitudinal and Transverse effective mass of graphene

[paramjot]

how can we calculate Longitudinal and Transverse effective mass of graphene. Can anyone help

[Petr Khomyakov]

Please provide a definition of those masses for a graphene monolayer.

[paramjot]

Hi,  actually I want to calculate the effective mass at the bottom valley of the conduction band of bandstructure of graphene which is at K point and in the direction from K to M point. Also, I want to find the electron affinity of this monolayer

[Petr Khomyakov]

In graphene, the conduction and valence bands are linear (non-parabolic) near the K-point. How do you define an effective mass then? You may define the Fermi velocity at the K-point as hbar x velocity_F = e_k/k where k is a k-point near the K symmetry point, e.g., see Phys. Rev. B 82, 115437 (2010). You can then define the Dirac particle mass as discussed at https://uwaterloo.ca/institute-for-quantum-computing/sites/ca.institute-for-quantum-computing/files/uploads/files/lecture-5.pdf

Graphene has zero gap, so affinity and work function have the same magnitude. So, you just have to compute the work function as usual by calculating the Fermi energy with respect to the vacuum level, see https://docs.quantumatk.com/tutorials/work_function_ag_100/work_function_ag_100.html.

[paramjot]

Thanks a lot for your help, sir. Actually I want to calculate effective density of states of electrons and holes (Nc and Nv) for which I need Longitudinal and Transverse effective mass of grapheneKPM

[Petr Khomyakov]

Regarding computing the density of states of graphene near the K-point, see Appendix in Phys. Rev. B 87, 075414 (2013). I do no think you need any kind of effective masses, as the density of states can be computed directly in QuantumATK.

[paramjot]

Sir , I want to calculate effective DOS which is different from the conventional DOS as shown in link 1 . For which I need effective DOS mass which calculated in Link2.
[1] https://ecee.colorado.edu/~bart/book/ex019.htm
[2] https://docs.quantumwise.com/tutorials/effective_mass/effective_mass.html

[Anders Blom]

I suggest to have a look at https://arxiv.org/abs/1206.6100 to better understand the concept of effective mass in graphene, and why the same methodology as for Si etc cannot be used for materials with a linear dispersion

[Petr Khomyakov]

Sir , I want to calculate effective DOS which is different from the conventional DOS as shown in link 1 . For which I need effective DOS mass which calculated in Link2.
[1] https://ecee.colorado.edu/~bart/book/ex019.htm
[2] https://docs.quantumwise.com/tutorials/effective_mass/effective_mass.html

Formulas in Link1 are not applicable for graphene's bands near the K-point, because of its non-parabolic bands, as I mentioned in previous posts. Please take a look at some text books on Solid State Physics (e.g., by Neil W. Ashcroft & N. David Mermin) where general relation between the band structure and DOS is explained and examples for parabolic bands are given.

[paramjot]

When I make armchair graphene nanoribbon using a nanoribbon plugin instead of a graphene sheet that case, we obtain the bandstructure that has parabolic structure.  Does that formula I depicted above will stay right in this case? I attach the pic of that bandstructure  ( bandgap occur due to doping)

[Anders Blom]

Yes