Dear Adel,
Thanks a lot. Your suggestions are very helpful. Indeed, we can use k---->
k-eA to implement the magnetic field.
Regarding this, I have another question: Starting from the continuum
Hamiltonian H=alpha*(k_x**2+k_y**2), I would like to add a magnetic field along
z direction [with the gauge given by A=(-By, 0, 0)]. I am work with a
Hamiltonian where k_x and k_y have a unit of Angstrum^-1 and energy have an
unit of eV. By k----> k-eA substitution, I need to consider the Hamiltonian
H=alpha*[(k_x-e/hbar*B*y)**2+k_y**2]. Here, e = -1.602176634e-19 C, hbar =
1.05457266e-34 J s. To let k_x - e/hbar*B*y have a unit of Angstrum^-1 (units
of B and y are Tesla and Angstrum, respectively), the unit of the "e/hbar“
coefficient should be Tesla/Angstrum^2. In such sense, I have the "e/hbar“
coefficient as -1.519266e-05 Tesla/Angstrum^2.
Now I generate a model with alpha = -8 eV Angstrum^2 and e/hbar =
-1.519266e-05 Tesla/Angstrum^2. When doing the calculations, I found that when
magnetic field is of the order of 10 Tesla, adding a magnetic field almost did
nothing (i.e., the change of conductance is very small). When further
increasing the magnetic field to e.g., 1000 T, indeed, the conductance changes
much.
I guess there may be something wrong when setting the coefficient "e/hbar“.
But I do not know what happens. Could you please further help me with this
issue? Thanks in advance!
