Mailman 3 March 2015 - Kwant-discuss

How the spin is positioned in the Smatrix?
by Qingtian Zhang March 6, 2022

March 6, 2022

Dear all, I am trying square lattice with spin-orbit coupling and Zeeman splititng just like the example of Tutorial 2.3.1. Now I want to get the spin-dependent conductance：Guu,Gud,Gdu,and Gdd, where "u" indicates up spin, d indicates down spin. We can have the scattering matrix through Smatrix=kwant.smatrix(sys, energy), but how the spin is positioned in the scattering matrix? I have checked some simple cases, it seems the Smatrix is organized like this: | r t | S= | t' r' | but how the spin is included? Thanks in advance. Qingtiian Zhang The code is: import kwant from matplotlib import pyplot from numpy import matrix import tinyarray 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]]) sys=kwant.Builder() lat=kwant.lattice.square() a=1 t=1.0 alpha=0.5 e_z=0.08 W=2 L=2 sys[(lat(x, y) for x in range(L) for y in range(W))] = \ 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Define the left lead. #### lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[(lat(0, j) for j in xrange(W))] = 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Attach the leads and return the finalized system. #### sys.attach_lead(lead) sys.attach_lead(lead.reversed()) kwant.plot(sys) sys=sys.finalized() print "Hamiltonian=" print sys.hamiltonian_submatrix() Smatrix=kwant.smatrix(sys, energy=3.) print "The scattering matrix=" print matrix.round((Smatrix.data),2) print "T=",(Smatrix.transmission(1, 0))

3 3

How to caculate hall resistance
by ZHANG Bing Sept. 12, 2021

Sept. 12, 2021

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

4 3

New instructions for Windows installation
by Michael Wimmer Jan. 15, 2016

Jan. 15, 2016

Dear kwant users, we have posted new instructions for installing kwant on Windows on the kwant website: http://www.kwant-project.org/install The old instructions do not work any more, as the format of the python packages on Christoph Gohlke's webpage have changed. Best regards, the kwant team

3 3

Re: [Kwant] Kwant-discuss Digest, Vol 18, Issue 1
by Lee Kwok-Long May 23, 2015

May 23, 2015

Dear Joe, Thanks, it is very useful for me. I want to know more about how the transmission is related to the wave vector kx, because I want to calculate the transmission contributed from some scale like kx=0~pi. So, how can i know the wave vector for "2" in S10[3, 2] ? I tried "modes = Smatrix.lead_info", it seems that it does not give the kx information. I can take graphene as an example, we have two valleys K and K' in graphene. Since the wave vectors kx for the two valleys are different, we can calculate the transmission contributed from K valley and K' valley separately, but of course we need to know "transmission-mode-kx" first. Maybe this can be easily solved in another way. Kwok-Long Lee On Fri, Feb 6, 2015 at 8:03 PM, <kwant-discuss-request(a)kwant-project.org> wrote: > Send Kwant-discuss mailing list submissions to > kwant-discuss(a)kwant-project.org > > To subscribe or unsubscribe via the World Wide Web, visit > https://mailman-mail5.webfaction.com/listinfo/kwant-discuss > or, via email, send a message with subject or body 'help' to > kwant-discuss-request(a)kwant-project.org > > You can reach the person managing the list at > kwant-discuss-owner(a)kwant-project.org > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Kwant-discuss digest..." > > > Today's Topics: > > 1. Transmission of each propagating mode (Lee Kwok-Long) > 2. Re: Transmission of each propagating mode (Joseph Weston) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Fri, 6 Feb 2015 16:43:23 +0800 > From: Lee Kwok-Long <kwoklonglee(a)gmail.com> > To: kwant-discuss(a)kwant-project.org > Subject: [Kwant] Transmission of each propagating mode > Message-ID: > < > CAMzfLzK0z7uFZGB54o71i8yr0hb2hf1D9GXxEhckubFYuQC5_g(a)mail.gmail.com> > Content-Type: text/plain; charset="utf-8" > > Dear all, > I want to calculate the transmission of each propagating mode separately, > but I do not know how the propagating modes are related to the scattering > matrix. For example, we can read from the bandstructure and find a mode at > E=0.2，kx=0.95pi, how to find the transmission for this mode. Or, we have > the transmission and how to find the contributions from each mode? Thanks > in advance! > Kwok-Long Lee >

2 3

bug in plotting a 3D system (matplotlib 1.4.3)
by Rafał Skolasiński March 25, 2015

March 25, 2015

Hi All, I noticed a bug in kwant.plot that occurs when one try to plot 3D system with matplotlib 1.4.3. http://nbviewer.ipython.org/urls/dl.dropboxusercontent.com/u/75521386/bug.i… Best, Rafal

2 2

about QHE Hall bar code
by ANANT VIJAY VARMA March 24, 2015

March 24, 2015

In the following code what about the parameter 'energy' for smatrix function Isn't it required for transmission function? And if not in what range the conductance is being calculated .Please explain more about this parameter 'energy' ? Also, when we are calculating resistance by applying voltages is it required or not in KWANT to put this 'energy' parameter.? def calculate_sigmas(G): # smat = smat.data # smat = abs(smat)**2 # reduce by one dimension G -> G[temp, temp] temp = [0, 1, 3, 4, 5] G = G[temp, :] G = G[:, temp] # invert R = G^-1 # find out whether it is a numpy object r = np.linalg.inv(G) # Voltages follow: V = R I[temp] V = r.dot(np.array([0, 0, 0, 1, -1])) # Completely solved the six terminal system. # Consider the 2x2 conductance now: Use I = sigma U E_x = V[1] - V[0] E_y = V[1] - V[3] #formula above sigma_xx = E_x / (E_x**2 + E_y**2) sigma_xy = E_y / (E_x**2 + E_y**2) return sigma_xx, sigma_xy sys = qhe_hall_bar(L=60, W=100, w_lead=90, w_vert_lead=28) par = SimpleNamespace(t=1.0, mu=0.3, mu_lead=0.3, B=None) sigmasxx = [] sigmasxy = [] Bs = np.linspace(.02, .15, 200) for par.B in Bs: s = kwant.smatrix(sys, args=[par]) G = np.array([[s.transmission(i, j) for i in range(len(sys.leads))] for j in range(len(sys.leads))]) G -= np.diag(np.sum(G, 0)) sigma = calculate_sigmas(G) sigmasxx.append(sigma[0]) sigmasxy.append(sigma[1])

2 1

Adding leads to a 4-layer system
by Lee Kwok-Long March 24, 2015

March 24, 2015

Dear all, I want to consider a four-layer structure, so I define the lattice for the four layers like: lat_layer1 = kwant.lattice.square(name='layer1') lat_layer2 = kwant.lattice.square(name='layer2') lat_layer3 = kwant.lattice.square(name='layer3') lat_layer4 = kwant.lattice.square(name='layer4') And then i set the hoppings for all the layers and hoppings between the layers. My question is about adding the lead. Can I do it like this: I have four left leads according to the sys region. I use a lead0 to include all the left leads like: lead0=kwant.Builder(sym) lead0+=lead_La1 lead0+=lead_La2 lead0+=lead_La3 lead0+=lead_La4 At last, i add the hoppings between layers in lead0. I calculate the bandstructure of led0. Can I do it like this? Kwok-Long Lee

2 2

SdHo oscillations
by ANANT VIJAY VARMA March 21, 2015

March 21, 2015

Hello everyone! I am calculating the longitudinal resistance (SdHo oscillation) using a square lattice.The order of leads is as follows: #Left Lead sys.attach_lead(leadA)# lead no. 0 #right lead sys.attach_lead(leadA.reversed())# lead no. 1 # First upper lead sys.attach_lead(leadB)# lead no. 2 # First lower lead sys.attach_lead(leadB.reversed())# lead no. 3 # Second upper lead sys.attach_lead(leadC) # lead no. 4 #second lower lead sys.attach_lead(leadC.reversed()) # lead no. 5 And using the Folowing piece of code to calculate the Longitudinal resistance: energy =2 def plot_conductance(sys, energy, Bs): data = [] for B in Bs: smatrix = kwant.smatrix(sys, energy, args=[B]) Trans = np.array([[smatrix.transmission(i, j) for j in xrange(6)] for i in xrange(6)]) Trans -= np.diag(Trans.sum(axis=0)) cm = Trans[:-1, :-1] resistance = np.linalg.solve(cm, [-1,1,0, 0, 0])[3] data.append(resistance) My question is that it is correct also what is the unit of current being used here, and units of rest of the quantities?Also How I am supposed to write code gate voltage. I am trying the same way accept now my arguement is not B but G (gate voltage). But its wrong I know.Please help me about these questions. Thank you in advance.

2 1

Hexagonal quantum ring
by Jonas da Silva Nascimento March 21, 2015

March 21, 2015

Hi, I want make a hexagonal quantum ring. I thought about using straight-lines (12-lines) for limit the points between its, but I will have many lines code. Has someone a better idea? Other thing, I want calculate the current density as function of a defect in a of the arm. Is it possible? Thank for help me. Jonas

2 1

Lead around a corner
by Pijnenburg Jana March 19, 2015

March 19, 2015

Hi, I have a rectangular shaped system that should be completely coupled to leads at one side . This means I have leads attached along the horizontal direction as well as the vertical direction. Now, the corners (the transition between the vertical and horizontal leads) act as scatterers. I was wondering if there is some way to define a lead around a corner? Thanks in advance, Jana

2 1