band structure of bulk Black phosphorus

[victor]

Dear Staff,

I want to calculate band structure of bulk Black phosphorus. Basically i followed the tutorial provided in your website. So far i basically can get the band structure for monolayer, which gives 0.98 ev around (very close to 1 eV given in the literature).
But when i calculated the band struture for bulk black phosphorus with the same unit cell (4 atoms) and ATK-DFT, GGA-PBE, FHI, 8*8*8 sampling points, i got band structure with lines crossing fermi level, which is unlikely for bulk BP. Then i  used the 8 atoms structures (given by tutorial) as primitive cell to calculate, but again i cannot obtain the band gap of 0.3 eV around. Could you help me on this regard? appreciate.

[Daniele Stradi]

It is difficult to say what's wrong without seeing your atkpython input and log files. If you can attach them here, we could have a look...

[victor]

Dear Daniele Stradi,

Thanks for your reply. please see attached figures demonstrating how i calculated bulk band structure of Black phosphorus.

[zh]

The screenshot figures of your calculations show that you used the LDA functional for the bulk BP. The tutorial in the following webpage is given for a monolayer BP with the GGA functional:
http://docs.quantumwise.com/tutorials/crystal_builder/crystal_builder.html
Please follow exactly the parameters given in the tutorial to reproduce the calculations.

[victor]

Thanks for your kind suggestion, actually, i already did the calculation for monolayer BP, which basically reproduces the band gap 0.88 eV around Gamma point. please see attached figures. But when i use the primitive cell to calculate bulk band structure, i did not produce 0.3 eV band gap.

[Daniele Stradi]

As far as I can see the cell vectors in the bulk BP are not aligned in the same way as in Phosphorene. In the former, the C axis lies parallel to the staking plane, whereas in the latter is lies perpendicular to this plane. This second orientation of the cell vectors is the correct one.

I would try to repeat the calculation for BP by swapping the axes so that the C axis lies perpendicular to the stacking plane.

[victor]

Thank very much for your help Daniele Stradi. I will be looking forward to your further instruction after your calculations.

[victor]

Dear Daniele Stradi,

How is your testing about the band structure of bulk black phosphorus?

[Daniele Stradi]

If you want to calculate the band structure of BP and compare it that of phosporene, once you have built the BP conventional cell as described in the tutorial (http://docs.quantumwise.com/tutorials/crystal_builder/crystal_builder.html) do the following operations:

1. Open the Bulk Tools ‣ Swap Axes tool and click B-C and Y-Z in order to align the phosphorene plane perpendicular to the C axis.
2. The lattice type has now been reset. You therefore need to open Bulk Tools ‣ Lattice Parameters and select Simple Orthorhombic as the lattice type.

Then you can calculate the band structure of BP in the same way as explained in the tutorial for phosphorene (same k-point sampling, same basis set, same exchange-correlation functional).

[victor]

Dear Daniele Stradi,

I followed your instruction to recalculate the band structure of bulk BP, but the calculated result is incorrect. Because the band gap at Z point is not 0.3 plus eV. please find the attached figure. One more question, i learn from literature that the lattice type is base-center orthorhombic not simple-orthorhombic. 

[victor]

Dear Daniele Stradi,

please look at the attached band structure of bulk BP, given in the paper [Nature Nanotechnology 9, 372–377 (2014)]. The first brillouin region is base-like center orthorhomic not simple orthorhomic. I tried alot of times, but i cannot reproduce the band structure with band gap equal to 0.3 eV around.

Remark: I can reproduce the band structure of monolayer BP (so called phosporene). But i am unable to get correct band gap for bulk BP.

[Daniele Stradi]

Dear Victor,

the calculations in the paper you mention have been performed using the HSE06 hybrid functional. GGA functionals such as PBE (the one you used in your calculations if you followed the tutorial) give too small band gap and in your particular case predict BP to be metallic.
Hybrid functionals will be available in ATK starting from ATK2017. In the meanwhile you can try the MGGA functional and the PseudoPotentialProjectorShift method, which also can be used to get a better gap compared to PBE:

http://docs.quantumwise.com/manuals/Types/ExchangeCorrelation/ExchangeCorrelation.html
http://docs.quantumwise.com/manuals/Types/PseudoPotentialProjectorShift/PseudoPotentialProjectorShift.html

Regards,
Daniele.

[zh]

Additional comment: the Brillouin zone of base-center orthorhombic is different from that of simple-orthorhombic,  so the position of some special k-points even with the same notations (except Gamma) may be different in two cases.