Set up the sample

In this tutorial, we show how to build a sample using the Cython-based modeling tools. Cython tools are orders of magnitudes faster than their Python counterparts, and are designed for constructing large models with millions or billions of orbitals. We demonstrate the usages of these tools by reproducing the models in Build complex primitive cells. The scripts can be found at examples/sample/model.

Construct graphene nano-ribbon

Similar as Build complex primitive cells, we need the rectangular primitive cell to construct graphene nano-ribbons. We import it from the repository by:

import tbplas as tb

rect_cell = tb.make_graphene_rect()

A nano-ribbon with armchair edges can be formed by extending the rectangular cell and enforcing periodic boundary conditions along \(b\) direction only. We do this by:

sc_am = tb.SuperCell(rect_cell, dim=(3, 3, 1), pbc=(False, True, False))
gnr_am = tb.Sample(sc_am)
gnr_am.plot()

Firstly, we create a supercell sc_am from the SuperCell class. The dim argument specifies how many times the primitive cell is replicated along \(a\), \(b\) and \(c\) directions, while the pbc argument gives the boundary condition. Then we create a sample gnr_am from the Sample class. The output is shown in the left panel of the figure:

Graphene nano-ribbon with armchair edges (GNR-AM) or zigag edges (GNR-ZZ).

Similarly, we can make a nano-ribbon with zigzag edges, by extending the rectangular cell and enforcing periodic boundary conditions along \(a\) direction only:

sc_zz = tb.SuperCell(rect_cell, dim=(3, 3, 1), pbc=(True, False, False))
gnr_zz = tb.Sample(sc_zz)
gnr_zz.plot()

The output is shown in the right panel of the figure.

Graphene with vacancies

After demonstrating the basic usage of SuperCell and Sample classes, we then build the graphene model with vacancies. We have a look at the model without vacancies first:

prim_cell = tb.make_graphene_diamond()
sc = tb.SuperCell(prim_cell, dim=(3, 3, 1), pbc=(True, True, False))
sample = tb.Sample(sc)
sample.plot()

The output is shown in the left panel of the figure:

Graphene samples without and with vacancies and after trimming dangling terms. Cells are labeled with blue texts. Removed and dangling orbitals are indicated with blue and green circles, respectively.

In Build complex primitive cells we introduce vacancies into the model by removing orbital #8 and #14. However, in SuperCell class the orbitals are numbered in a different scheme. We identify orbital #8 as \((1, 1, 0, 0)\) and #14 as \((2, 1, 0, 0)\), where the first 3 integers indicate the cell index and the 4th integer is the orbital index. That’s to say, orbital #8 is the 0th orbital in cell \((1, 1, 0)\) and #14 is the 0th orbital in cell \((2, 1, 0)\). We remove these orbitals by calling the set_vacancies() method of SuperCell class:

sc.unlock()
sc.set_vacancies(vacancies=[(1, 1, 0, 0), (2, 1, 0, 0)])
sample = tb.Sample(sc)
sample.plot()

The output is shown in the middle panel of the figure. Obviously, there is a dangling orbital, as indicated by the green circle. We can remove it by calling the trim() method of SuperCell class:

sc.unlock()
sc.trim()
sample = tb.Sample(sc)
sample.plot()

The output is shown in the right panel of the figure.