Dear all,
I have a code for the Mobius structure, using python scripts. However, I want to construct a structure by adding hexagonal lattices in a Mobius structure. How can I do this using Kwant.
Thank you in advance. Best, Nuwan, MSU, Starkville
P.S.: The python script for the mobius structure is as follows:
import numpy as np import matplotlib.pyplot as plt import matplotlib.tri as mtri
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure(figsize=plt.figaspect(0.5))
u = np.linspace(0, 2.0 * np.pi, endpoint=True, num=50) v = np.linspace(0.5, 0.5, endpoint=True, num=10) u, v = np.meshgrid(u, v) u, v = u.flatten(), v.flatten()
x = (1 + 0.5 * v * np.cos(u / 2.0)) * np.cos(u) y = (1 + 0.5 * v * np.cos(u / 2.0)) * np.sin(u) z = 0.5 * v * np.sin(u / 2.0)
tri = mtri.Triangulation(u, v)
ax = fig.add_subplot(1, 2, 1, projection='3d') ax.plot_trisurf(x, y, z, triangles=tri.triangles) ax.set_zlim(1, 1)
plt.show()
Dear Nuwan,
What you shared here is a true 3D Mobius. Now, the question which is important in this problem is: Do you change the value of the hoppings between the sites or no? I mean the value of the hoppings between the sites in the flat lattice and in the Mobius one.
If you do not take into account the effect of the distortion, the solution is simple:
1) Get a flat lattice with width W and length L. 2) Add a hopping between the following sites (1, y) and (L, Wy) for y in W .
This system is exactly equivalent to a Mobius one (where we suppose that the hopping value depends only on whether two sites are connected or not and not on the distance between them )
I hope this helps. Adel
On Mon, Jul 8, 2019 at 10:50 PM Nuwan Chaminda Gunawardhana Waduge < gn212@msstate.edu> wrote:
Dear all,
I have a code for the Mobius structure, using python scripts. However, I want to construct a structure by adding hexagonal lattices in a Mobius structure. How can I do this using Kwant.
Thank you in advance. Best, Nuwan, MSU, Starkville
P.S.: The python script for the mobius structure is as follows:
import numpy as np import matplotlib.pyplot as plt import matplotlib.tri as mtri
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure(figsize=plt.figaspect(0.5))
u = np.linspace(0, 2.0 * np.pi, endpoint=True, num=50) v = np.linspace(0.5, 0.5, endpoint=True, num=10) u, v = np.meshgrid(u, v) u, v = u.flatten(), v.flatten()
x = (1 + 0.5 * v * np.cos(u / 2.0)) * np.cos(u) y = (1 + 0.5 * v * np.cos(u / 2.0)) * np.sin(u) z = 0.5 * v * np.sin(u / 2.0)
tri = mtri.Triangulation(u, v)
ax = fig.add_subplot(1, 2, 1, projection='3d') ax.plot_trisurf(x, y, z, triangles=tri.triangles) ax.set_zlim(1, 1)
plt.show()
participants (2)

Abbout Adel

Nuwan Chaminda Gunawardhana Waduge