Dear Sir,
I am a PhD student of Hong Kong University of Science and Technology. I
want to use KWANT to caculate Hall resistance of a Hall bar structure.We
can get the conductance between 6 electrodes, but how to get hall
resistance? Can you give me some help? Thank you very much.
Best Regards,
Zhang Bing

Hello everyone, I would appreciate any suggestion you could give me to
solve this:
Im currently working on a 2D finite monolayer of certain material that is
coupled to a pair of leads in both left and right sides, the thing is: how
can I get rid of the dangling bonds that appears in the edges of the
nanoribbon?, I cant use the function "eradicate dangling" because the
dissapearing atoms will just generate new dangling bonds.
(By the way: I tried to use this function just to see what happens but
nothing changed in the structure, is that normal?)
So, Is there a way to automatically fill the dangling bonds with Hydrogen
atoms? Or do I have to do it manually?
Thanks in advance.

Dear Kwant developers,
I created a general lattice with 10 million orbitals in Kwant and I obtained the Hamiltonian(H).
At some point, I need to solve the inhomogeneous matrix equation H u = v, where u is the vector of unknowns and v is a constant vector.
My life will be easier if I could use MUMPS solver provided by Kwant to obtain u.
Is there any chance?
Best regards,Hadi

Thanks Adel, I realized that I used round function instead of floor and that caused the difference.
Best,
Ran
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Dear Adel,
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Thank you for the additional remark. Yes, for near zero energies this "arcos formula" gives the same with Datta's simple expression. However, since you said it is exact for KWANT's discrete model, I tried to compare it with KWANT's results and I found discrepancy. Please see the attached figure.
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In the Figure, you will see that I reduced "a" from 1 to 0.1 and KWANT results (blue curve) and it gave much closer to Datta's expression (yellow curve) now, as Joe predicted in the previous message. However, this "arcos expression" (green curve) does not give the same results with KWANT. And the results do not change much when decrease the lattice parameter a much lower like 0.00001. Am I doing sth wrong here or did I misinterpret your point?
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Best,
Ran
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Dear Mutcran,
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I would like just to make an additional remark. Indeed, the formula in Datta's book is for a continuous model where the maximum number of modes is given by� M=2 W/ \lambda_f�� (\lambda_f is the Fermi wavelength).
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In the case of a discrete model, like in Kwant, you can deduce M from the band structure. In fact, we have:
E=4t -2t cos(kx)-2t cos(m pi/(N+1)), where N is the number of sites for one transversal cell.
The maximum number of transmitted modes is obtained when the longitudinal kinetic energy is 0 (kx~0).
so we get M= (N+1)/pi��� arcos((E-2t)/(-2t))������ (you need to take the integer part of this expression).
This result is exact for a discrete square lattice model.
A simple Taylor expansion around E~0 will give you the Datta's formula��� (where W=(N+1)a).
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As a conclusion, the number of transmitted modes for a given discrete model is obtained from the form of the Band structure. This allows you to calculate it for any complex lattice (as long as you can get analytically the band structure).
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I hope this helps,
Adel
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On Tue, Jan 22, 2019 at 11:22 PM mutcran <mutcran(a)mynet.com> wrote:
Thanks Joe! That was indeed the case! It became much closer with small a.
Best,
Ran
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Hi Ran, > I tried to compare KWANT’s results for transmission with Datta’s ballistic transport formalism where total transmission is written as > > Ttot=T(E)M(E) > > Here Datta takes T(E)=1 for ballistic transport (please see: J. Appl. Phys. 105, 034506, 2009) and M(E) is the number of modes in transverse direction. When I compared KWANT's results with Datta’s expression, for the system given in “quantum_wire_revisited.py”, I found different results (please see the attached figure where I tried to put every relevant thing in the calculation). Since the reflectance is zero for that system and so transmission is 1 for each mode, shouldn’t it give the same results with Datta’s transmission expression? > Nice question! Looking at your results it seems that the energies at which new modes ope n is shifted with respect to Datta's result. I believe that this is simply due to the fact that your discretization is not fine enough. Datta's result
is valid in the continuum limit, whereas the Kwant simulation (in the case presented) uses a finite-difference discretization to render the problem discrete. If you decrease the 'a' parameter, you should see the discrepancy between the two result decrease. Happy Kwanting, Joe
--
Abbout Adel

Dear Adel,
�
Thank you for the additional remark. Yes, for near zero energies this "arcos formula" gives the same with Datta's simple expression. However, since you said it is exact for KWANT's discrete model, I tried to compare it with KWANT's results and I found discrepancy. Please see the attached figure.
�
In the Figure, you will see that I reduced "a" from 1 to 0.1 and KWANT results (blue curve) and it gave much closer to Datta's expression (yellow curve) now, as Joe predicted in the previous message. However, this "arcos expression" (green curve) does not give the same results with KWANT. And the results do not change much when decrease the lattice parameter a much lower like 0.00001. Am I doing sth wrong here or did I misinterpret your point?
�
Best,
Ran
�
�
Dear Mutcran,
�
I would like just to make an additional remark. Indeed, the formula in Datta's book is for a continuous model where the maximum number of modes is given by� M=2 W/ \lambda_f�� (\lambda_f is the Fermi wavelength).
�
In the case of a discrete model, like in Kwant, you can deduce M from the band structure. In fact, we have:
E=4t -2t cos(kx)-2t cos(m pi/(N+1)), where N is the number of sites for one transversal cell.
The maximum number of transmitted modes is obtained when the longitudinal kinetic energy is 0 (kx~0).
so we get M= (N+1)/pi��� arcos((E-2t)/(-2t))������ (you need to take the integer part of this expression).
This result is exact for a discrete square lattice model.
A simple Taylor expansion around E~0 will give you the Datta's formula��� (where W=(N+1)a).
�
As a conclusion, the number of transmitted modes for a given discrete model is obtained from the form of the Band structure. This allows you to calculate it for any complex lattice (as long as you can get analytically the band structure).
�
I hope this helps,
Adel
�
�
�
�
On Tue, Jan 22, 2019 at 11:22 PM mutcran <mutcran(a)mynet.com> wrote:
Thanks Joe! That was indeed the case! It became much closer with small a.
Best,
Ran
�
Hi Ran, > I tried to compare KWANT’s results for transmission with Datta’s ballistic transport formalism where total transmission is written as > > Ttot=T(E)M(E) > > Here Datta takes T(E)=1 for ballistic transport (please see: J. Appl. Phys. 105, 034506, 2009) and M(E) is the number of modes in transverse direction. When I compared KWANT's results with Datta’s expression, for the system given in “quantum_wire_revisited.py”, I found different results (please see the attached figure where I tried to put every relevant thing in the calculation). Since the reflectance is zero for that system and so transmission is 1 for each mode, shouldn’t it give the same results with Datta’s transmission expression? > Nice question! Looking at your results it seems that the energies at which new modes open is shifted with respect to Datta's result. I believe that this is simply due to the fact that your discretization is not fine enough. Datta's result is
valid in the continuum limit, whereas the Kwant simulation (in the case presented) uses a finite-difference discretization to render the problem discrete. If you decrease the 'a' parameter, you should see the discrepancy between the two result decrease. Happy Kwanting, Joe
--
Abbout Adel

Dear Colleagues,
I want to build a structure as shown in picture. There are 5 parts.
I want to construct it by define the shape function shown in TUTORIAL: Nontrivial shapes. However, when I want to attach a 1D lead on the two-side, I get a message:
ValueError: Sites with site families (kwant.lattice.Monatomic([[1.0, 0.0], [0.0, 1.0]], [0.0, 0.0], '', 4),) do not appear in the system, hence the system does not interrupt the lead.
Can you give me some hints?
Maybe my description is not clear, I attach the code in the e-mail to reproduce this question.
Best wishes.
Jinlong Zhang
jlzhang1996(a)163.com

Thanks Joe! That was indeed the case! It became much closer with small a.
Best,
Ran
�
Hi Ran, > I tried to compare KWANT’s results for transmission with Datta’s ballistic transport formalism where total transmission is written as > > Ttot=T(E)M(E) > > Here Datta takes T(E)=1 for ballistic transport (please see: J. Appl. Phys. 105, 034506, 2009) and M(E) is the number of modes in transverse direction. When I compared KWANT's results with Datta’s expression, for the system given in “quantum_wire_revisited.py”, I found different results (please see the attached figure where I tried to put every relevant thing in the calculation). Since the reflectance is zero for that system and so transmission is 1 for each mode, shouldn’t it give the same results with Datta’s transmission expression? > Nice question! Looking at your results it seems that the energies at which new modes open is shifted with respect to Datta's result. I believe that this is simply due to the fact that your discretization is not fine enough. Datta's result is
valid in the continuum limit, whereas the Kwant simulation (in the case presented) uses a finite-difference discretization to render the problem discrete. If you decrease the 'a' parameter, you should see the discrepancy between the two result decrease. Happy Kwanting, Joe

Hi,
I tried to compare KWANT’s results for transmission with Datta’s ballistic transport formalism where total transmission is written as
Ttot=T(E)M(E)
Here Datta takes T(E)=1 for ballistic transport (please see: J. Appl. Phys. 105, 034506, 2009) and M(E) is the number of modes in transverse direction. When I compared KWANT's results with Datta’s expression, for the system given in “quantum_wire_revisited.py”, I found different results (please see the attached figure where I tried to put every relevant thing in the calculation). Since the reflectance is zero for that system and so transmission is 1 for each mode, shouldn’t it give the same results with Datta’s transmission expression?
Best,
Ran
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Dear all,
I receive the following error when I call kpm.spectraldesnisty with a "bounds" keyword.
Here is the error:
in _rho = kwant.operator.Density(syst, sum=True, where=in_circle, bounds=[lw_bound, up_bound])
File "kwant/operator.pyx", line 735, in kwant.operator.Density.__init__
TypeError: __init__() got an unexpected keyword argument 'bounds'
I do not provide my own code since I think this is a kwant internal error.
Thanks and best regards,Hadi

Hi,
For the calculation of the conductance in the tutorial file “quantum_wire_revisited.py”, instead of giving arbitrary energies like [0.01 * i for i in range(100)], can I give the real energy values of the system by:
E=(pi^2*hbar^2)/(2m)*(nx^2/L^2+ny^2/W^2)
where I took transport direction length (L) as very long, say 100 times larger than the width (W). (Since the transport direction is practically open in KWANT)
This gives very different results than using arbitrary energies. What is the problem with this approach and is there a way to explicitly account the discrete energies of the system (not the arbitrary ones)?
Best,
Ran
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