A. Basic usage: supercells, stripes and flakes, all out of the box!
Here we use only the honeytools and honeyplots high-level modules:
use honeytools ! We import only the top-level API here
use honeyplots ! And the bindings to matplotlib and gnuplot
use stdlib_strings, only: str => to_string ! Just for I/O
implicit none
type(xy_lattice) :: hlattice
type(unit_cell) :: mylayout
integer :: i
logical,allocatable :: NN(:,:),NNN(:,:)Where in hlattice we would store the generated x,y coordinates, their "A" or "B" sublattice-character and integer indices to build consistently the nearest and next-nearest neighbors matrices. Anyhow you probably don't care, just declare a type(xy_lattice variable.
You would probably care instead about unit-cell initialization, which is done by passing a predefined orientation field (armchair or zigzag, they are constant expressions exported by the library, in most cases you don't want to customize your own orientation object, so we provide these two 🙃). You can instead change the lattice spacing and the origin, by passing the size and origin optional parameters (default values are 1 and [0,0]).
Finally NN and NNN are two logical masks two identify which lattice points are to be connected by a nearest-neighbors or next-nearest-neighbors hoppings (or something else[1]). These are accepted by the plotting routines too, to allow easier visual exploration.
So, let's start with the examples!
mylayout = unit_cell(orientation=armchair)
do i = 1,5
hlattice = get_flake(radius=i,layout=mylayout)
if(i==1)then
call xy_print(hlattice)
print*
print*, "NN matrix:"
do j = 1,hlattice%size
write(*,*) (NN(j,k), k=1,hlattice%size)
enddo
call plot(hlattice,backend='gnuplot',set_terminal='dumb')
endif
call xy_nearest_neighbors(lattice=hlattice,nn_mask=NN)
call plot(hlattice,NN,figure_name='flake'//str(i)//'.svg')
enddoWould print to standard output:
site # 1 [x,y]: -0.99999999999999989 0.0000000000000000
site # 2 [x,y]: -1.9999999999999998 2.2204460492503131E-016
site # 3 [x,y]: -2.5000000000000000 -0.86602540378443849
site # 4 [x,y]: -2.0000000000000004 -1.7320508075688770
site # 5 [x,y]: -1.0000000000000007 -1.7320508075688776
site # 6 [x,y]: -0.50000000000000000 -0.86602540378443882
site # 7 [x,y]: -0.99999999999999989 1.7320508075688772
site # 8 [x,y]: -1.9999999999999998 1.7320508075688774
site # 9 [x,y]: -2.5000000000000000 0.86602540378443871
site # 10 [x,y]: -0.50000000000000000 0.86602540378443837
site # 11 [x,y]: 0.50000000000000011 -0.86602540378443860
site # 12 [x,y]: -0.50000000000000044 -2.5980762113533156
site # 13 [x,y]: 0.49999999999999928 -2.5980762113533160
site # 14 [x,y]: 1.0000000000000000 -1.7320508075688774
site # 15 [x,y]: 0.50000000000000011 0.86602540378443860
site # 16 [x,y]: 1.0000000000000000 -2.4492935982947064E-016
site # 17 [x,y]: 0.50000000000000011 2.5980762113533160
site # 18 [x,y]: -0.49999999999999978 2.5980762113533160
site # 19 [x,y]: 1.0000000000000000 1.7320508075688770
site # 20 [x,y]: 2.0000000000000000 0.0000000000000000
site # 21 [x,y]: 1.9999999999999993 -1.7320508075688776
site # 22 [x,y]: 2.5000000000000000 -0.86602540378443882
site # 23 [x,y]: 2.0000000000000000 1.7320508075688772
site # 24 [x,y]: 2.5000000000000000 0.86602540378443837
NN matrix:
F T F F F T F F F T F F F F F F F F F F F F F F
T F T F F F F F T F F F F F F F F F F F F F F F
F T F T F F F F F F F F F F F F F F F F F F F F
F F T F T F F F F F F F F F F F F F F F F F F F
F F F T F T F F F F F T F F F F F F F F F F F F
T F F F T F F F F F T F F F F F F F F F F F F F
F F F F F F F T F T F F F F F F F T F F F F F F
F F F F F F T F T F F F F F F F F F F F F F F F
F T F F F F F T F F F F F F F F F F F F F F F F
T F F F F F T F F F F F F F T F F F F F F F F F
F F F F F T F F F F F F F T F T F F F F F F F F
F F F F T F F F F F F F T F F F F F F F F F F F
F F F F F F F F F F F T F T F F F F F F F F F F
F F F F F F F F F F T F T F F F F F F F T F F F
F F F F F F F F F T F F F F F T F F T F F F F F
F F F F F F F F F F T F F F T F F F F T F F F F
F F F F F F F F F F F F F F F F F T T F F F F F
F F F F F F T F F F F F F F F F T F F F F F F F
F F F F F F F F F F F F F F T F T F F F F F T F
F F F F F F F F F F F F F F F T F F F F F T F T
F F F F F F F F F F F F F T F F F F F F F T F F
F F F F F F F F F F F F F F F F F F F T T F F F
F F F F F F F F F F F F F F F F F F T F F F F T
F F F F F F F F F F F F F F F F F F F T F F T F
> Gnuplot GUI popping up...
3 +-------------------------------------+
| G G |
| |
2 |-+ |
| G G G G |
| |
1 |-+ |
| G G G G |
| |
0 |-+ G G G |
y | G |
| |
| G G G G |
-1 |-+ |
| |
| G G G G |
-2 |-+ |
| |
| + + G + G + + |
-3 +-------------------------------------+
-3 -2 -1 0 1 2 3
x
And save to disk:
radius=1 |
radius=2 |
radius=3 |
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radius=4 |
radius=5 |
radius=6 |
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mylayout = unit_cell(armchair,size=1,origin=[-5,-18])
hlattice = get_supercell(5,3,mylayout)
call xy_next_nearest_neighbors(hlattice,NNN,NN)
call plot(hlattice,NN,NNN,figure_name='supercell_armchair.svg')
mylayout = unit_cell(zigzag,size=3,origin=[-9,-9])
hlattice = get_supercell(3,5,mylayout)
call xy_next_nearest_neighbors(hlattice,NNN,NN)
call plot(hlattice,NN,NNN,figure_name='supercell_zigzag.svg')Would draw also next-neighbor links!
supercell_armchair.svg |
supercell_zigzag.svg |
|---|---|
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mylayout = unit_cell(armchair)
hlattice = get_stripe(5,9,mylayout)
call xy_next_nearest_neighbors(hlattice,NNN,NN)
call plot(hlattice,NN,NNN,figure_name='stripe_armchair.svg')
mylayout = unit_cell(zigzag)
hlattice = get_stripe(7,5,mylayout)
call xy_next_nearest_neighbors(hlattice,NNN,NN)
call plot(hlattice,NN,NNN,figure_name='stripe_zigzag.svg')stripe_armchair.svg |
stripe_zigzag.svg |
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do i = 2,5 ! triangles of size = 1 cannot exist
hlattice = get_triangle(i,unit_cell(zigzag))
call xy_next_nearest_neighbors(hlattice,NNN,NN)
call plot(hlattice,NN,NNN,figure_name='triangle'//str(i)//'.svg')
enddosize=2 |
size=3 |
size=4 |
size=5 |
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[1]: We also provide facilities to build nth-order shells, just call the xy_shells subroutine and build yourself the mask as shell_table == distance_set(n) (these are the two intent(out) variables in the call). Maybe I'll add an explicit example in the future.