Sept. 12, 2019
3:55 a.m.
The second problem is solved. I got the landau fan for BHZ model.
Thank you for the support.
On Thu, Sep 12, 2019, 12:46 Naveen Yadav <naveengunwal72@gmail.com> wrote:
> Dear sir,
>
> I have updated KWANT, but it shows the *AttributeError: module
> 'kwant.continuum' has no attribute 'discretize_landau'.* And in browser
> also, it is showing the same error. I have downloaded the landau_levels.py
> file and put it into the continuum folder. But it is not working.
>
>
> On Wed, Sep 11, 2019, 23:47 Naveen Yadav <naveengunwal72@gmail.com> wrote:
>
>> Dear sir,
>>
>> That is exactly what I am looking for.
>> But in my case Hamiltonian is not polynomial in k. It contains Sine and
>> Cosine terms. It's a tight binding Hamiltonian having coupling terms like
>> sigma_x *Sin(kx)+ sigma_y *sin(ky) and mass term in the trignometric form.
>> So, can I proceed by writing the trignometric terms in some lower order
>> polynomial terms? Does that make sense?
>> Please make some comment regarding this.
>> Thank you very much.
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> Naveen
>> Department of Physics & Astrophysics
>> University of Delhi
>> New Delhi-110007
>>
>> On Wed, Sep 11, 2019, 22:18 Anton Akhmerov <anton.akhmerov+kd@gmail.com>
>> wrote:
>>
>>> Dear Naveen,
>>>
>>> If you are dealing with a continuum Hamiltonian (so a polynomial in
>>> k-space), then there is a recent addition to Kwant, that allows to
>>> compute Landau levels. Please check out if this tutorial is what you
>>> are looking for:
>>>
>>> https://kwant-project.org/doc/dev/tutorial/magnetic_field#adding-magnetic-field
>>> (if you click the "activate thebelab" button, you can also play around
>>> with the code in your browser).
>>>
>>> If that suits your needs, you'd need to either install a development
>>> version of Kwant or just get this file:
>>>
>>> https://gitlab.kwant-project.org/kwant/kwant/blob/master/kwant/continuum/landau_levels.py
>>>
>>> Let me know if that answers your question,
>>> Anton
>>>
>>> On Wed, 11 Sep 2019 at 18:39, Naveen Yadav <naveengunwal72@gmail.com>
>>> wrote:
>>> >
>>> > Dear sir,
>>> >
>>> > I understood that this code is off no use. The leads are useless here.
>>> > Actually, I want to plot the Landau fan. Can KWANT do the job here?
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> > Naveen
>>> > Department of Physics & Astrophysics
>>> > University of Delhi
>>> > New Delhi-110007
>>> >
>>> > On Mon, Sep 9, 2019, 00:50 Abbout Adel <abbout.adel@gmail.com> wrote:
>>> >>
>>> >> Dear Naveen,
>>> >>
>>> >> If your concern is the program which is slow, that is not an issue
>>> since it takes just few minutes.
>>> >> Now, if you are talking about the result, I want to be sure that you
>>> notice that your system is not infinite as you claim in your email.
>>> >> You can check that by adding extra cells from the lead"
>>> syst.attach_lead(lead, add_cells=10)
>>> >> Actually, in your case, the presence of the leads is useless since at
>>> the end, you are just diagonalizing the Hamiltonian of the central system.
>>> >> If you want to study an infinite system in x and y, you need to look
>>> at the module "wraparound" and the example of graphene that is in the
>>> archive of kwant.
>>> >> For the magnetic field, you can use the Pierls substitution. check
>>> for example this paper [1]
>>> >>
>>> >> You can also think about the use of continuous Hamiltonian in kwant.
>>> You may find it very useful [2]
>>> >> I hope this helps.
>>> >>
>>> >> Regards,
>>> >> Adel
>>> >>
>>> >>
>>> >> [1] https://arxiv.org/pdf/1601.06507.pdf
>>> >> [2] https://kwant-project.org/doc/1/tutorial/discretize
>>> >>
>>> >> On Sun, Sep 8, 2019 at 6:16 PM Naveen Yadav <naveengunwal72@gmail.com>
>>> wrote:
>>> >>>
>>> >>> Dear Sir,
>>> >>> Thanks for the tips. As you told, I have tried in other way also but
>>> I am getting the same result which are very tedious. I don't know where is
>>> fault.
>>> >>> Now the code looks like
>>> >>>
>>> >>> import kwant
>>> >>> import scipy.sparse.linalg as sla
>>> >>> import matplotlib.pyplot as plt
>>> >>> import tinyarray
>>> >>> import numpy as np
>>> >>> from numpy import cos, sin, pi
>>> >>> import cmath
>>> >>> from cmath import exp
>>> >>>
>>> >>> sigma_0 = tinyarray.array([[1, 0], [0, 1]])
>>> >>> sigma_x = tinyarray.array([[0, 1], [1, 0]])
>>> >>> sigma_y = tinyarray.array([[0, -1j], [1j, 0]])
>>> >>> sigma_z = tinyarray.array([[1, 0], [0, -1]])
>>> >>>
>>> >>>
>>> >>> def make_system(a=1, L=30, W=10, H=10, t=1.0, t_x=1.0, t_y=1.0,
>>> t_z=1.0, lamda=0.1, beta=1.05):
>>> >>> def onsite(site):
>>> >>> return (t_z * cos(beta) + 2 * t) * sigma_z
>>> >>>
>>> >>> def hoppingx(site0, site1):
>>> >>> return (-0.5 * t * sigma_z - 0.5 * 1j * t_x * sigma_x)
>>> >>>
>>> >>> def hoppingy(site0, site1):
>>> >>> return -0.5 * t * sigma_z - 0.5 * 1j * t_y * sigma_y
>>> >>>
>>> >>> def hoppingz(site0, site1, B):
>>> >>> y = site1.pos[1]
>>> >>> return (-0.5 * t_z * sigma_z - 0.5 * 1j * lamda * sigma_0) *
>>> exp(2 * pi * 1j * B * a * (y-40))
>>> >>>
>>> >>>
>>> >>> syst = kwant.Builder()
>>> >>> lat = kwant.lattice.cubic(a)
>>> >>> syst[(lat(z, y, x) for z in range(H) for y in range(W) for x in
>>> range(L))] = onsite
>>> >>> syst[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingz
>>> >>> syst[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingy
>>> >>> syst[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingx
>>> >>>
>>> >>> lead1=kwant.Builder(kwant.TranslationalSymmetry((0,-a,0)))
>>> >>> lead1[(lat(z,y,x) for z in range(H)for y in range(W)for x in
>>> range(L))]=onsite
>>> >>> lead1[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingz
>>> >>> lead1[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingy
>>> >>> lead1[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingx
>>> >>>
>>> >>> syst.attach_lead(lead1)
>>> >>> syst.attach_lead(lead1.reversed())
>>> >>>
>>> >>> lead2=kwant.Builder(kwant.TranslationalSymmetry((-a,0,0)))
>>> >>> lead2[(lat(z,y,x) for z in range(H)for y in range(W)for x in
>>> range(L))]=onsite
>>> >>> lead2[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingz
>>> >>> lead2[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingy
>>> >>> lead2[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingx
>>> >>>
>>> >>> syst.attach_lead(lead2)
>>> >>> syst.attach_lead(lead2.reversed())
>>> >>> syst = syst.finalized()
>>> >>> return syst
>>> >>>
>>> >>> def analyze_system(syst, Bfields):
>>> >>> syst = make_system()
>>> >>> kwant.plot(syst)
>>> >>> energies = []
>>> >>> for B in Bfields:
>>> >>> #print(B)
>>> >>> ham_mat = syst.hamiltonian_submatrix(params=dict(B=B),
>>> sparse=True)
>>> >>> ev, evec = sla.eigsh(ham_mat.tocsc(), k=20, sigma=0)
>>> >>> energies.append(ev)
>>> >>> #print (energies)
>>> >>>
>>> >>> plt.figure()
>>> >>> plt.plot(Bfields, energies)
>>> >>> plt.xlabel("magnetic field [${10^-3 h/e}$]")
>>> >>> plt.ylabel("energy [t]")
>>> >>>
>>> >>> plt.ylim(0, 0.11)
>>> >>> plt.show()
>>> >>> def main():
>>> >>> syst = make_system()
>>> >>> analyze_system(syst, [B * 0.00002 for B in range(101)])
>>> >>> main()
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>> Naveen
>>> >>> Department of Physics & Astrophysics
>>> >>> University of Delhi
>>> >>> New Delhi-110007
>>> >>>
>>> >>> On Sun, Sep 8, 2019, 17:37 Abbout Adel <abbout.adel@gmail.com>
>>> wrote:
>>> >>>>
>>> >>>> Dear Naveen,
>>> >>>>
>>> >>>> Your program works fine. You have just a small problem of
>>> plotting. You can solve that by changing "plt.show" by "plt.show()".
>>> >>>>
>>> >>>> Think about putting print (B) inside the loop when you debug your
>>> program. That will help you for example to see if the program is running
>>> well, and you can detect what may be wrong.
>>> >>>> Think also about returning Energies in your function. This way you
>>> can try potting the result outside the function you called. Don't hesitate
>>> to put some extra lines in your program to follow the progress when you
>>> think that there is a problem.
>>> >>>>
>>> >>>>
>>> >>>> I hope this helps.
>>> >>>> Regards,
>>> >>>> Adel
>>> >>>>
>>> >>>> On Thu, Sep 5, 2019 at 7:32 PM Naveen Yadav <
>>> naveengunwal72@gmail.com> wrote:
>>> >>>>>
>>> >>>>> Dear Sir,
>>> >>>>>
>>> >>>>> I am trying to plot the energy as a function of magnetic field for
>>> a 3D case, but I am getting tedious results. The system is infinite in two
>>> directions and has some width in the third direction. Please have a look at
>>> the code attached below. I tried a lot but failed. Is the code correct or I
>>> am wrong somewhere.
>>> >>>>> Thank you.
>>> >>>>>
>>> >>>>>
>>> >>>>> import kwant
>>> >>>>> import scipy.sparse.linalg as sla
>>> >>>>> import matplotlib.pyplot as plt
>>> >>>>> import tinyarray
>>> >>>>> import numpy as np
>>> >>>>> from numpy import cos, sin, pi
>>> >>>>> import cmath
>>> >>>>> from cmath import exp
>>> >>>>>
>>> >>>>> sigma_0 = tinyarray.array([[1, 0], [0, 1]])
>>> >>>>> sigma_x = tinyarray.array([[0, 1], [1, 0]])
>>> >>>>> sigma_y = tinyarray.array([[0, -1j], [1j, 0]])
>>> >>>>> sigma_z = tinyarray.array([[1, 0], [0, -1]])
>>> >>>>>
>>> >>>>>
>>> >>>>> def make_system(a=1, L=30, W=10, H=10, t=1.0, t_x=1.0, t_y=1.0,
>>> t_z=1.0, lamda=0.1, beta=1.05):
>>> >>>>> def onsite(site):
>>> >>>>> return (t_z * cos(beta) + 2 * t) * sigma_z
>>> >>>>>
>>> >>>>> def hoppingx(site0, site1):
>>> >>>>> return (-0.5 * t * sigma_z - 0.5 * 1j * t_x * sigma_x)
>>> >>>>>
>>> >>>>> def hoppingy(site0, site1):
>>> >>>>> return -0.5 * t * sigma_z - 0.5 * 1j * t_y * sigma_y
>>> >>>>>
>>> >>>>> def hoppingz(site0, site1, B):
>>> >>>>> y = site1.pos[1]
>>> >>>>> return (-0.5 * t_z * sigma_z - 0.5 * 1j * lamda * sigma_0)
>>> * exp(2 * pi * 1j * B * a * (y-40))
>>> >>>>>
>>> >>>>>
>>> >>>>> syst = kwant.Builder()
>>> >>>>> lat = kwant.lattice.cubic(a)
>>> >>>>> syst[(lat(z, y, x) for z in range(H) for y in range(W) for x
>>> in range(L))] = onsite
>>> >>>>> syst[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingz
>>> >>>>> syst[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingy
>>> >>>>> syst[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingx
>>> >>>>>
>>> >>>>> lead1=kwant.Builder(kwant.TranslationalSymmetry((0,-a,0)))
>>> >>>>> lead1[(lat(z,y,x) for z in range(H)for y in range(W)for x in
>>> range(L))]=onsite
>>> >>>>> lead1[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] =
>>> hoppingz
>>> >>>>> lead1[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] =
>>> hoppingy
>>> >>>>> lead1[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] =
>>> hoppingx
>>> >>>>>
>>> >>>>> syst.attach_lead(lead1)
>>> >>>>> syst.attach_lead(lead1.reversed())
>>> >>>>>
>>> >>>>> lead2=kwant.Builder(kwant.TranslationalSymmetry((-a,0,0)))
>>> >>>>> lead2[(lat(z,y,x) for z in range(H)for y in range(W)for x in
>>> range(L))]=onsite
>>> >>>>> lead2[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] =
>>> hoppingz
>>> >>>>> lead2[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] =
>>> hoppingy
>>> >>>>> lead2[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] =
>>> hoppingx
>>> >>>>>
>>> >>>>> syst.attach_lead(lead2)
>>> >>>>> syst.attach_lead(lead2.reversed())
>>> >>>>> syst = syst.finalized()
>>> >>>>> return syst
>>> >>>>>
>>> >>>>> def analyze_system():
>>> >>>>> syst = make_system()
>>> >>>>> kwant.plot(syst)
>>> >>>>> Bfields = np.linspace(0, 0.002, 100)
>>> >>>>> energies = []
>>> >>>>> for B in Bfields:
>>> >>>>> ham_mat = syst.hamiltonian_submatrix(params=dict(B=B),
>>> sparse=True)
>>> >>>>> ev, evec = sla.eigsh(ham_mat.tocsc(), k=20, sigma=0)
>>> >>>>> energies.append(ev)
>>> >>>>> #print(energies)
>>> >>>>>
>>> >>>>> plt.figure()
>>> >>>>> plt.plot(Bfields, energies)
>>> >>>>> plt.xlabel("magnetic field [${10^-3 h/e}$]")
>>> >>>>> plt.ylabel("energy [t]")
>>> >>>>>
>>> >>>>> plt.ylim(0, 0.11)
>>> >>>>> plt.show
>>> >>>>> def main():
>>> >>>>> syst = make_system()
>>> >>>>> analyze_system()
>>> >>>>> main()
>>> >>>>>
>>> >>>>>
>>> >>>>>
>>> >>>>>
>>> >>>>> --
>>> >>>>>
>>> >>>>>
>>> >>>>> With Best Regards
>>> >>>>> NAVEEN YADAV
>>> >>>>> Ph.D Research Scholar
>>> >>>>> Deptt. Of Physics & Astrophysics
>>> >>>>> University Of Delhi.
>>> >>>>
>>> >>>>
>>> >>>>
>>> >>>> --
>>> >>>> Abbout Adel
>>> >>
>>> >>
>>> >>
>>> >> --
>>> >> Abbout Adel
>>>
>>