Mailman 3 August 2018 - Kwant-discuss

Gate-defined Nanowire Quantum Dot
by Jonathan Fields Sept. 15, 2022

Sept. 15, 2022

Dear Reader, I am new to KWANT and trying to figure out if it is suitable for calculating transport properties of gate-defined quantum dots made out of nanowires, along the lines of the structure used in https://arxiv.org/abs/cond-mat/0609463. Now, I understand that the mailing list is not a place to ask people to do my work for me, and my question is also not for someone to do this. What I am looking for is some insights into if this is possible (and not all that difficult) with the package. At first sight (and going through the tutorials as well as the APS March Meeting material) this does not seem straightforward; what I struggle with is how to define this type of dot in KWANT. Now, one way would of course be to built the entire 3D geometry of the system, but this will be computationally expensive, and probably also rather tricky to do in terms of defining everything, from the hexagonal wire itself to all of the gates and oxide layers and such. Some abstraction would be preferred, perhaps even reducing the dimensionality and making a 2D system, such as often done in the tutorial. Is this a good idea? My problem is that if one does this, then I run into the problem of how to model the 'half wrap-around' type gates typically used in these devices. In the transport through barrier section of the APS March Meeting material there is a section on how to model realistic potentials, but this would not work all that well for these wrap around type gates. On the other hand, in a way they are perhaps not so different from the QPC in that section. One could model the three gates as something like https://i.imgur.com/WZC983c.png as they do essentially form channels in the wire. Apart from if this sacrifices too much of the nanowire nature in favor of a 2DEG system, I do suppose such a system should in principle be able to be treated as a quantum dot. I haven't been able to confirm this as I am not yet sure how one can apply a source-drain voltage in KWANT; I first thought that this would probably be related to the energy of the modes, but then again I have not been able to produce Coulomb diamonds in this way. The question is getting rather lenghty, and also a bit unclear at this point. Perhaps I should finish up by stating it in a concise form; would you think that it is possible to simulate the transport of such a gate defined nanowire quantum dot device with KWANT, and if so, is the approach I am suggesting above a viable one, or would you go about it very differently? Kind regards Jonathan <http://aka.ms/weboutlook>

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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))

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Spin polarized transport calculation
by L.M J March 6, 2022

March 6, 2022

Dear Kwant users and developers I have two questions related to the spin calculation using kwant. 1. I'm wondering if we can do spin-polarized transport in kwant? For example, can we can get the separate Conductance Vs Energy diagram for spin up and spin down terms. I'm thinking one way of doing this is to set up the Rashba Hamiltonian as a whole. And then manually extract the spin up and spin down hamiltonian and do the transport calculation separately. But this will eliminate some extra terms that I don't know whether this is correct anymore. Any suggestions? 2. How can we set up the spin polarization for a particular site? For example, in some of the topological insulator, can we set up spin polarization on the edge as up and the other side of the edge as down, and then do the transport? Or this question is completely wrong? Thanks for advance. Sincerely, Liming

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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

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Onsite and hopping values in QHE
by elchatz＠auth.gr Sept. 15, 2018

Sept. 15, 2018

Hello everyone, I am trying to reproduce the QHE bar device calculations http://nbviewer.jupyter.org/github/topocm/topocm_content/blob/master/w3_pum… However, I am having difficulty with the onsite and hopping values as I am using TBModels https://github.com/Z2PackDev/TBmodels and therefore the values are not the same for all sites. The problem is that after the scalar values have been passed on to the Builder, these will then be overriden when using functions for the position-dependent Hamiltonian. I tried making a deep copy of the model, which would then serve as a data structure where to draw the scalar values from when calling the Onsite and Hopping functions. The problem with this is a) I am getting a KeyError which I am still not sure why it happens b) It does not feel very memory-efficient. I am wondering if there is another way that this could be done on the Kwant side that I have not been able to think of. Regards -- Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz(a)auth.gr - tel:+30 2310 998109

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seeking help
by shyam lochan bora Sept. 3, 2018

Sept. 3, 2018

Dear sir, Please help me with the following error in the program from __future__ import print_function from ipywidgets import interact, interactive, fixed, interact_manual import ipywidgets as widgets import kwant from matplotlib import pyplot import numpy as np from holoviews.core.options import Cycle from types import SimpleNamespace def nanowire_chain(): lat = kwant.lattice.chain() sys = kwant.Builder(kwant.TranslationalSymmetry(*lat.prim_vecs)) def onsite(onsite, p): return (2 * p.t - p.mu) * pauli.szs0 + p.B * (np.cos(p.phi)*pauli.s0sz+ np.sin(p.phi)*np.sin(p.theta)*pauli.s0sy+np.sin(p.phi)*np.sin(p.theta)*pauli.s0sx)+ p.delta * pauli.sxs0 sys[lat(0)] = onsite def hop(site1, site2, p): return -p.t * pauli.szs0 - .5j * p.alpha * pauli.szsx sys[kwant.HoppingKind((1,), lat)] = hop return sys def spinful_kitaev_chain(): lat = kwant.lattice.chain() sys = kwant.Builder(kwant.TranslationalSymmetry(*lat.prim_vecs)) def onsite(site, p): return (2 * p.t - p.mu) * pauli.szs0 + p.B * pauli.szsz sys[lat(0)] = onsite def hop(site1, site2, p): return -p.t * pauli.szs0 - 1j * p.delta * pauli.sys0 sys[kwant.HoppingKind((1,), lat)] = hop return sys def find_gap(sys, p, resolution=1e-4): """Find gap in a system by doing a binary search in energy.""" # This tells us if there are modes at a certain energy. if len(sys.modes(energy=0, args=[p])[0].momenta): return 0 gap = step = min(abs(kwant.physics.Bands(sys, args=[p])(k=0))) / 2 while step > resolution: step /= 2 if len(sys.modes(gap, args=[p])[0].momenta): gap -= step else: gap += step return gap def spinorbit_band_gap(sys, mu, t, delta, Bs): sys = sys.finalized() alphas = [0.0, 0.1, 0.2, 0.3] p = SimpleNamespace(mu=mu, t=t, delta=delta,theta=theta,phi=phi) def gap(sys, p, alpha, B): p.alpha = alpha p.B = B return find_gap(sys, p) gaps = [gap(sys, p, alpha, B) for alpha in alphas for B in Bs] gaps = np.reshape(gaps, (len(alphas), -1)) dims = {'kdims': [r'$B$'], 'vdims': ['Band gap']} B_crit = holoviews.VLine(np.sqrt(p.delta**2 + p.mu**2)) plot = [holoviews.Curve((Bs, gaps[i]), label=r'$\alpha={}$'.format( alphas[i]), **dims) * B_crit for i, alpha in enumerate(alphas)] title = r'$\Delta={delta}$, $\mu={mu}$'.format(delta=np.round(p.delta, 2), mu=np.round(p.mu, 2)) style = {'xticks': [0, 0.1, 0.2, 0.3], 'yticks': [0, 0.05, 0.1], 'fig_size': 150} plot = holoviews.Overlay(plot) return plot(plot=style) def title(p): try: title = r"$\alpha={alpha}$, $\mu={mu}$, $B={B}$, $\Delta={delta}$" title = title.format(alpha=np.round(p.alpha, 2), mu=np.round(p.mu, 2), B=np.round(p.B, 2), delta=np.round(p.delta, 2)) except AttributeError: title = r"$\mu={mu}$, $B={B}$, $\Delta={delta}$" title = title.format(mu=np.round(p.mu, 2), B=np.round(p.B, 2), delta=np.round(p.delta, 2)) return title style = {'k_x': np.linspace(-1, 1, 101), 'xdim': r'$k$', 'ydim': r'$E/t$', 'xticks': [-1, 0, 1], 'yticks': [-1, 0, 1], 'xlims': [-1, 1], 'ylims': [-1.5, 1.5], 'title': title} sys = nanowire_chain() p = SimpleNamespace(t=1, mu=0.1, delta=0.1, B=0.3,theta=np.pi/2,phi=np.pi/2) alphas = np.linspace(0, 0.4, 10) holoviews.HoloMap({alpha: spectrum(sys, p.update(alpha=alpha), **style) for alpha in alphas}, kdims=[r'$\alpha$']) c:\python36\lib\site-packages\kwant\linalg\lll.py:103: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions. To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`. coefs = np.linalg.lstsq(vecs_orig.T, vecs.T)[0] c:\python36\lib\site-packages\kwant\linalg\lll.py:144: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions. To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`. center_coords = np.array(np.round(np.linalg.lstsq(basis.T, vec)[0]), int) ---------------------------------------------------------------------------NameError Traceback (most recent call last)<ipython-input-3-9ff9219a759e> in <module>() 2 p = SimpleNamespace(t=1, mu=0.1, delta=0.1, B=0.3,theta=np.pi/2,phi=np.pi/2) 3 alphas = np.linspace(0, 0.4, 10)----> 4 holoviews.HoloMap({alpha: spectrum(sys, p.update(alpha=alpha), **style) for alpha in alphas}, kdims=[r'$\alpha$']) NameError: name 'holoviews' is not defined

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Setting the color scale for kwant.plot
by Eric Mascot Aug. 30, 2018

Aug. 30, 2018

Dear Kwant, I am trying to plot the phase of the hopping term. def hop_c(i,j): return np.angle(sys.hamiltonian(i, j, params=params)[0,0]) kwant.plot(sys, hop_color=hop_c, hop_lw=0.25, site_size=0, cmap=('hsv', 'hsv')); I would like the limits of the colorbar to be -pi to pi but kwant automatically sets the limits to the min and max. Is there a way to set the limits? Thanks, Eric Eric Mascot College of Liberal Arts Graduate Student and Sciences Department of Physics emasco2(a)uic.edu 845 W Taylor St M: 248 433 6435 2158 SES O: 312 413 2109 Chicago, IL 60607

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seeking help
by shyam lochan bora Aug. 28, 2018

Aug. 28, 2018

dear sir, I am working on the assignment problem " tweaking the nanowire" from the online course in topology in condensed matter I am trying to apply the magnetic filed in the nanowire using the following code but I am unable to plot the graph.Please help me in this regard.The code is given below.. import kwant import matplotlib from matplotlib import pyplot import numpy as np def nanowire_chain(): lat = kwant.lattice.chain() sys = kwant.Builder(kwant.TranslationalSymmetry(*lat.prim_vecs)) def onsite(onsite, p): return (2 * p.t - p.mu) * pauli.szs0 + p.B * (np.cos(p.phi)*pauli.s0sz+ np.sin(p.phi)*np.sin(p.theta)*pauli.s0sy+np.sin(p.phi)*np.sin(p.theta)*pauli.s0sx)+ p.delta * pauli.sxs0 sys[lat(0)] = onsite def hop(site1, site2, p): return -p.t * pauli.szs0 - .5j * p.alpha * pauli.szsx sys[kwant.HoppingKind((1,), lat)] = hop return sys def spinful_kitaev_chain(): lat = kwant.lattice.chain() sys = kwant.Builder(kwant.TranslationalSymmetry(*lat.prim_vecs)) def onsite(site, p): return (2 * p.t - p.mu) * pauli.szs0 + p.B * pauli.szsz sys[lat(0)] = onsite def hop(site1, site2, p): return -p.t * pauli.szs0 - 1j * p.delta * pauli.sys0 sys[kwant.HoppingKind((1,), lat)] = hop return sys def find_gap(sys, p, resolution=1e-4): """Find gap in a system by doing a binary search in energy.""" # This tells us if there are modes at a certain energy. if len(sys.modes(energy=0, args=[p])[0].momenta): return 0 gap = step = min(abs(kwant.physics.Bands(sys, args=[p])(k=0))) / 2 while step > resolution: step /= 2 if len(sys.modes(gap, args=[p])[0].momenta): gap -= step else: gap += step return gap def spinorbit_band_gap(sys, mu, t, delta, Bs): sys = sys.finalized() alphas = [0.0, 0.1, 0.2, 0.3] p = SimpleNamespace(mu=mu, t=t, delta=delta,theta=theta,phi=phi) def gap(sys, p, alpha, B): p.alpha = alpha p.B = B return find_gap(sys, p) gaps = [gap(sys, p, alpha, B) for alpha in alphas for B in Bs] gaps = np.reshape(gaps, (len(alphas), -1)) dims = {'kdims': [r'$B$'], 'vdims': ['Band gap']} B_crit = holoviews.VLine(np.sqrt(p.delta**2 + p.mu**2)) plot = [holoviews.Curve((Bs, gaps[i]), label=r'$\alpha={}$'.format( alphas[i]), **dims) * B_crit for i, alpha in enumerate(alphas)] title = r'$\Delta={delta}$, $\mu={mu}$'.format(delta=np.round(p.delta, 2), mu=np.round(p.mu, 2)) style = {'xticks': [0, 0.1, 0.2, 0.3], 'yticks': [0, 0.05, 0.1], 'fig_size': 150} plot = holoviews.Overlay(plot) return plot(plot=style) def title(p): try: title = r"$\alpha={alpha}$, $\mu={mu}$, $B={B}$, $\Delta={delta}$" title = title.format(alpha=np.round(p.alpha, 2), mu=np.round(p.mu, 2), B=np.round(p.B, 2), delta=np.round(p.delta, 2)) except AttributeError: title = r"$\mu={mu}$, $B={B}$, $\Delta={delta}$" title = title.format(mu=np.round(p.mu, 2), B=np.round(p.B, 2), delta=np.round(p.delta, 2)) return title style = {'k_x': np.linspace(-1, 1, 101), 'xdim': r'$k$', 'ydim': r'$E/t$', 'xticks': [-1, 0, 1], 'yticks': [-1, 0, 1], 'xlims': [-1, 1], 'ylims': [-1.5, 1.5], 'title': title} Regards Shyam Lochan Bora

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next nearest neighbour
by Prof. CHAN Kwok Sum Aug. 21, 2018

Aug. 21, 2018

Dear Kwant Developer, I note there was a discussion in the community about next nearest neighbor hopping in the community (Leads with greater than NN hopping<https://www.mail-archive.com/search?l=kwant-discuss@kwant-project.org&q=sub…>). However, I still have the following questions about next nearest neighbour hopping in the lead after reading the discussion. 1. Can we add next nearest neighbour hopping to a lead without expanding the unit cell, if there are only hoppings between nearest neighbouring unit cells even with next nearest neighbour hopping? Can the band structure be calculated properly using the Kwant library? 2. When the lead is attached to the system, will the next nearest neighbour hopping be included in the action automatically? Thank you in advance for your help. KS Chan Disclaimer: This email (including any attachments) is for the use of the intended recipient only and may contain confidential information and/or copyright material. If you are not the intended recipient, please notify the sender immediately and delete this email and all copies from your system. Any unauthorized use, disclosure, reproduction, copying, distribution, or other form of unauthorized dissemination of the contents is expressly prohibited.

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Attaching 3D Leads to a 3D System
by Shivang Agarwal Aug. 20, 2018

Aug. 20, 2018

Hello All, I am trying to attach a 3D lead to a 3D system that I have built, but am facing troubles in the same. I am aware of another thread ( https://mailman-mail5.webfaction.com/pipermail/kwant-discuss/2014-May/00012…) highlighting my question, but having gone through that thread I was still unable to successfully attach a lead to my system. Ideally, I want to attach gold leads to my system but I started by attaching a simple cubic lattice (by breaking it into 2 different lattices). Following is my code. *h = 2.707 * np.cos(13.69*np.pi/180)* *dx = 4.43* *dy = 3.27* *shift_x = 2.164 * np.cos(0.5*98.15*np.pi/180)* *shift_y = 2.164 * np.sin(0.5*98.15*np.pi/180)* *lat0 = kwant.lattice.general([(dx, 0, 0), (0, dy, 0)], [(0, 0, 0), (shift_x, shift_y, 0)])* *lat1 = kwant.lattice.general([(dx, 0, 0), (0, dy, 0)], [(0.5*dx, 0.5*dy, h), (0.5*dx + shift_x, 0.5*dy + shift_y, h)])* *a_const = 2* *b_const = 2* *c_const = 1* *def make_cuboid(a = a_const*dx, b = b_const*dy, c = c_const*h):* * def cuboid_shape(pos):* * x, y, z = pos* * return -a <= x <= a and -b <= y <= b and -c <= z <= c* * sys = kwant.Builder()* * sys[lat0.shape(cuboid_shape, (0, 0, 0))] = None* * sys[lat0.neighbors(1)] = 1* * sys[lat0.neighbors(2)] = 1* * sys[lat1.shape(cuboid_shape, (0.5*dx, 0.5*dy, h))] = None* * sys[lat1.neighbors(1)] = 1* * sys[lat1.neighbors(2)] = 1* * # Diagonally going up-right/down_left bonds* * for j in range(-a_const, a_const):* * for i in range(-b_const, b_const):* * sys[lat0.sublattices[1](j,i), lat1.sublattices[0](j,i)] = 1* * # Diagonally going up-left/down-right bonds* * for m in range(a_const, -a_const, -1):* * for n in range(-b_const, b_const):* * sys[lat0.sublattices[0](m,n), lat1.sublattices[1](m-1,n-1)] = 1* * # Define the leads* * lat0_lead = kwant.lattice.square(dy)* * sym_lead0 = kwant.TranslationalSymmetry((dy, 0))* * lead0 = kwant.Builder(sym_lead0)* * lead0[(lat0_lead(0, i) for i in range(-2,3))] = 0* * lead0[lat0_lead.neighbors()] = 1* * sys[(lat0_lead(3, i) for i in range(-2,3))] = 0* * sys[lat0_lead.neighbors()] = 1* * # Manually attach sites from the base (height=0) lattice to square lattice* * sys[((lat0_lead(3, i), lat0.sublattices[0](2, i)) for i in range(-2,3))] = 1* * def family_colors(site):* * if site.family == lat0.sublattices[0]:* * return 'b'* * elif site.family == lat0.sublattices[1]:* * return 'b'* * elif site.family == lat1.sublattices[0]:* * return 'g'* * elif site.family == lat1.sublattices[1]:* * return 'g'* * kwant.plot(sys, site_size=0.2, hop_lw=0.1, site_color=family_colors)* * return sys.finalized()* *def main():* * sys = make_cuboid()* *if __name__ == '__main__':* * main()* >From my knowledge, this should attach a 2D square lattice lead (or to be precise, just 1 layer of the 2D square lattice lead as shown in https://kwant-project.org/doc/1.3/tutorial/faq) to one side of my 3D system. I would be really glad if someone could help me out with this problem. Best Regards, Shivang -- *Shivang Agarwal* Senior Undergraduate Discipline of Electrical Engineering IIT Gandhinagar Contact: +91-9869321451

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