Dear Zhao,
In two dimensional electronic gases (2DEG) where the electrons are
described by your hamiltonian, we have to use the effective mass of the
electron and not the exact mass m_e:
m*=0.067 me in semiconducting heterostructures giving 2DEG.
with this value, the hopping parameter t =150 mev
t=hbar^2/(2m* a^2)
Usually in the simulation we take the Fermi energy typically EF=0.1 t
But we know that EF=k^2 a^2 t (hbar^2 k^2/2m ), a is the
lattice constant
So, k^2 a^2= 0.1 => k=0.3/a
The electronic wavelength lambda =2 pi/ k =21 a
Typically, in SGM experiments, we have lambda around 20 nm this means
that a=10 anstrom
with 10 T, you have the magnetic length, L_b=100 angstrom=10 a.,
The wavelength has the same order as the magnetic length, which should be
fine.
You might have to look at the change induced in the band structure and not
directly in the transmission because it might be sometimes misleading
especially for uniform systems.
Please check the development version of kwant [1] which has an interesting
new feature for implementing the magnetic field.
I hope this helps,
Adel
[1] https://kwant-project.org/doc/dev/tutorial/magnetic_field
On Sun, Jan 15, 2023 at 9:11 AM <[email protected]> wrote:
> 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!
>
--
Abbout Adel
