Hello everyone.
I am trying to calculate and plot dispersion relation for a 4x4 matrix
model. But I want to use 4 different lattices with names a_up, b_up,a_down,
B_down. That is my basis. But I am not able to reproduce the same structure
when I am using four different lattices instead 4x4 matrices.
Here are my codes
# Code With Matrix use:
" #Onsite energy\n",
" sys[lat.shape(cube,(0,0,0))] = (C + 2 * D1 + 4 * D2) * s0s0 + (M
+ 2 * B1 + 4 * B2) *s0sz\n",
" #hopping in x direction \n",
" sys[kwant.builder.HoppingKind((1, 0,0), lat,lat)] = - D2 * s0s0
- B2 * s0sz +A2 * 0.5j * sxsx\n",
" #hopping in y direction \n",
" sys[kwant.builder.HoppingKind((0,1,0), lat,lat)] = - D2 *s0s0
-B2 * s0sz + A2 * 0.5j * sysx\n",
" #hopping in z direction \n",
" sys[kwant.builder.HoppingKind((0,0,1), lat,lat)] = - D1 * s0s0
-B1 * s0sz + A1 * 0.5j * szsx \n",
#Code with lattice desription:
"a_up = kwant.lattice.general([(1,0,0),(0,1,0),(0,0,1)], name=
'a_up')\n",
"b_up = kwant.lattice.general([(1,0,0),(0,1,0),(0,0,1)], name=
'b_up')\n",
"a_down = kwant.lattice.general([(1,0,0),(0,1,0),(0,0,1)], name=
'a_down')\n",
"b_down= kwant.lattice.general([(1,0,0),(0,1,0),(0,0,1)], name=
'b_down')"
" # ONSITE POTENTIAL\n",
" \n",
" \n",
" sys[a_up.shape(cube,(0,0,0))] = (M + 2 * B1 + 4 * B2)\n",
" sys[b_up.shape(cube,(0,0,0))] = -(M + 2 * B1 + 4 * B2)\n",
" sys[a_down.shape(cube,(0,0,0))] = (M + 2 * B1 + 4 * B2)\n",
" sys[b_down.shape(cube,(0,0,0))] = -(M + 2 * B1 + 4 * B2)\n",
" \n",
" # HoppING TERM along x-direction\n",
" \n",
" #1. Diagonal terms\n",
" sys[kwant.builder.HoppingKind((1,0,0),a_up, a_up)] = -B2\n",
" sys[kwant.builder.HoppingKind((1,0,0),b_up, b_up)] = B2\n",
" sys[kwant.builder.HoppingKind((1,0,0),a_down, a_down)] = -B2\n",
" sys[kwant.builder.HoppingKind((1,0,0),b_down, b_down)] = B2\n",
" \n",
" #2. Non-Diagonal terms\n",
" sys[kwant.builder.HoppingKind((1,0,0), a_up,b_down)] = A2 *
0.5j\n",
" sys[kwant.builder.HoppingKind((1,0,0), a_down,b_up)] = A2 *
0.5j\n",
" sys[kwant.builder.HoppingKind((1,0,0), b_down,a_up)] = A2 *
0.5j\n",
" sys[kwant.builder.HoppingKind((1,0,0), b_up,a_down)] = A2 *
0.5j\n",
" \n",
" \n",
" # Hopping along y-direction\n",
" \n",
" #1. Diagonal Terms\n",
" sys[kwant.builder.HoppingKind((0,1,0),a_up, a_up)] = -B2\n",
" sys[kwant.builder.HoppingKind((0,1,0),b_up, b_up)] = B2\n",
" sys[kwant.builder.HoppingKind((0,1,0),a_down, a_down)] = -B2\n",
" sys[kwant.builder.HoppingKind((0,1,0),b_down, b_down)] = B2\n",
" \n",
" #2. non diagoal terms\n",
" sys[kwant.builder.HoppingKind((0,1,0), a_up,b_down)] = -1j* A2
* 0.5j\n",
" sys[kwant.builder.HoppingKind((0,1,0), a_down,b_up)] = -1j* A2
* 0.5j\n",
" sys[kwant.builder.HoppingKind((0,1,0), b_down,a_up)] = 1j* A2
* 0.5j\n",
" sys[kwant.builder.HoppingKind((0,1,0), b_up,a_down)] = 1j* A2
* 0.5j\n",
" \n",
" \n",
" \n",
" # Hopping along z-direction\n",
" \n",
" #1. Diagonal Terms\n",
" sys[kwant.builder.HoppingKind((0,0,1),a_up, a_up)] = -B1\n",
" sys[kwant.builder.HoppingKind((0,0,1),b_up, b_up)] = B1\n",
" sys[kwant.builder.HoppingKind((0,0,1),a_down, a_down)] = -B1\n",
" sys[kwant.builder.HoppingKind((0,0,1),b_down, b_down)] = B1\n",
" \n",
" #2. non diagoal terms\n",
" sys[kwant.builder.HoppingKind((0,0,1), b_up,a_up)] = A1 *
0.5j\n",
" sys[kwant.builder.HoppingKind((0,0,1), a_up,b_up)] = A1 *
0.5j\n",
" sys[kwant.builder.HoppingKind((0,0,1), b_down,a_down)] = A1 *
0.5j\n",
" sys[kwant.builder.HoppingKind((0,0,1), b_down,b_down)] = A1 *
0.5j\n",
" \n",
My problem is I am not getting the same band structure from both the codes.
I know there is some problem with the way I have put my hoppings in the
second code.
But I have no clear idea about hoppingkind function. I think I should not
use in the later case. Please help me correct the problem.
Thanks!
ANANT VIJAY VARMA
Research Scholar
IISER-KOLKATA
WEST BENGAL.
