Kwant-discuss March 2015

kwant-discuss@python.org

13 participants
15 discussions

Query about longitudinal and hall conductance in 4 terminal
by Sudin Ganguly 18 Mar '15

18 Mar '15

Dear Sir, I am using Kwant for 2 months. I've studied the conductance behaviour in a square lattice for two terminal case. But for the 4 terminal case I've some confusion about the hall conductance. I've read your post about the hall resistance. You wrote there, nonlocal_resistance = np.linalg.solve(cm, [1, 0, -1])[1] Why did you put the currents I_0=1, I_1=0 and I_2=-1? Also can you please tell me how do I calculate the longitudinal conductance for the 4 terminal case. With regards, Sudin Sudin Ganguly Research Scholar Dept. of Physics IIT Guwahati Assam,India-781039

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plot wavefunction
by 宋志刚 06 Mar '15

06 Mar '15

Dear prpfessor: I have studied Kwant six month. Recently, some obstacle confused me. When I define a topological insulator system with two-oribits, the wave function alaways cannot be obtained. The error as follows: File "interpnd.pyx", line 104, in scipy.interpolate.interpnd.NDInterpolatorBase._check_init_shape (scipy\interpolate\interpnd.c:2724) ValueError: different number of values and points. I hope you can give some value advice to get correct wave function. Thank you! Song Zhigang My code as follows: # Tutorial 2.4.2. Closed systems # ============================== # # Physics background # ------------------ # Fock-darwin spectrum of a quantum dot (energy spectrum in # as a function of a magnetic field) # # Kwant features highlighted # -------------------------- # - Use of `hamiltonian_submatrix` in order to obtain a Hamiltonian # matrix. import tinyarray from cmath import exp import numpy as np import kwant # For eigenvalue computation import scipy.sparse.linalg as sla # For plotting from matplotlib import pyplot 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, t=1.0, r=10): # Start with an empty tight-binding system and a single square lattice. # `a` is the lattice constant (by default set to 1 for simplicity). lat = kwant.lattice.square(a) sys = kwant.Builder() # Define the quantum dot def circle(pos): (x, y) = pos rsq = x ** 2 + y ** 2 return rsq < r ** 2 def hopx(site1, site2, B=0): # The magnetic field is controlled by the parameter B y = site1.pos[1] return -t * exp(-1j * B * y)* sigma_0 sys[lat.shape(circle, (0, 0))] = 4 * t * sigma_0 # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = -t * sigma_0 # It's a closed system for a change, so no leads return sys def plot_spectrum(sys, Bfields): # In the following, we compute the spectrum of the quantum dot # using dense matrix methods. This works in this toy example, as # the system is tiny. In a real example, one would want to use # sparse matrix methods energies = [] for B in Bfields: # Obtain the Hamiltonian as a dense matrix ham_mat = sys.hamiltonian_submatrix(args=[B], sparse=True) # we only calculate the 15 lowest eigenvalues ev = sla.eigsh(ham_mat, k=15, which='SM', return_eigenvectors=False) energies.append(ev) pyplot.figure() pyplot.plot(Bfields, energies) pyplot.xlabel("magnetic field [arbitrary units]") pyplot.ylabel("energy [t]") pyplot.show() def plot_wave_function(sys): # Calculate the wave functions in the system. ham_mat = sys.hamiltonian_submatrix(sparse=True) evecs = sla.eigsh(ham_mat, k=20, which='SM')[1] # Plot the probability density of the 10th eigenmode. kwant.plotter.map(sys, np.abs(evecs[:, 9])**2, colorbar=False, oversampling=1) def main(): sys = make_system() # Check that the system looks as intended. kwant.plot(sys) # Finalize the system. sys = sys.finalized() # The following try-clause can be removed once SciPy 0.9 becomes uncommon. try: # We should observe energy levels that flow towards Landau # level energies with increasing magnetic field. plot_spectrum(sys, [iB * 0.002 for iB in xrange(100)]) # Plot an eigenmode of a circular dot. Here we create a larger system for # better spatial resolution. sys = make_system(r=30).finalized() plot_wave_function(sys) except ValueError as e: if e.message == "Input matrix is not real-valued.": print "The calculation of eigenvalues failed because of a bug in SciPy 0.9." print "Please upgrade to a newer version of SciPy." else: raise # Call the main function if the script gets executed (as opposed to imported). # See <http://docs.python.org/library/__main__.html>. if __name__ == '__main__': main()

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kwant.plotter.plot site_color 'order' on tutorial
by Julian Moreno 05 Mar '15

05 Mar '15

Hi! I'm trying to plot (map) the potential on each site of a system (quantum wire in this case) - In which order 'site_color' passes the values to cmap, or what's happening here? I'd like to see the top line of sites whiter - I get the same color for each atom when I run several times. Is this because 'kwant.digest.uniform' is not so random? Thanks in advance Julian -- ------------------------------ This message and its contents, including attachments are intended solely for the original recipient. If you are not the intended recipient or have received this message in error, please notify me immediately and delete this message from your computer system. Any unauthorized use or distribution is prohibited. Please consider the environment before printing this email.

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hall resistance
by Nilo Maurício Sotomayor Choque 05 Mar '15

05 Mar '15

Dear Sir, I am a researcher from UFT-Brazil. I am trying to calculate Hall and longitudinal resistances at six terminal bar with antidots. I have some doubts about the order assigned to the leads because i create them in pairs. I sent part of the python code. # DEFINE-SE A REGIAO DE ESPALHAMENTO INCLUI ANTIDOT def rect(pos): (x, y) = pos return (0 <= x <= L and 0 <= y <= W ) # DEFINE-SE O CAMPO MAGNÉTICO CONTROLADO POR B def hopx(site1, site2, B=0): y = site1.pos[1] return -t * exp(-1j * B * y) # energia dos sitios sys[lat.shape(rect, (0, 0))] = 4 * t # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = -t #DEFINEM-SE OS CONTATOS ############################################################ # left and right leads sym_lead = kwant.TranslationalSymmetry((-a, 0)) lead = kwant.Builder(sym_lead) def lead_shape(pos): (x, y) = pos return (0 <= y <= W) lead[lat.shape(lead_shape, (0, 0))] = 4 * t lead[lat.neighbors()] = -t #### FIXAR OS DOIS CONTATOS RIGHT AND LEFT #### sys.attach_lead(lead) sys.attach_lead(lead.reversed()) ############################################################ # top lead 1 lead = kwant.Builder(kwant.TranslationalSymmetry((0, a))) lead[(lat(j+(L/5), 0) for j in xrange(W))] = 4 * t lead[lat.neighbors()] = -t #### FIXAR CONTATO SUPERIOR E INFERIOR #### sys.attach_lead(lead) sys.attach_lead(lead.reversed()) ############################################################ # top lead 2 lead = kwant.Builder(kwant.TranslationalSymmetry((0, a))) lead[(lat(j+(3*L/5), 0) for j in xrange(W))] = 4 * t lead[lat.neighbors()] = -t #### FIXAR CONTATO SUPERIOR E INFERIOR #### sys.attach_lead(lead) sys.attach_lead(lead.reversed()) ############################################################ # return sys # def plot_conductance(sys, energy, Bfields): data = [] for B in Bfields: smatrix = kwant.smatrix(sys, energy, args=[B]) cond = np.array([[smatrix.transmission(i, j) for j in xrange(6)] for i in xrange(6)]) cond -= np.diag(cond.sum(axis=0)) cm = cond[:-1, :-1] nonlocal_resistance = np.linalg.solve(cm, [-1, 1, 0, 0, 0])[2] print nonlocal_resistance data.append(nonlocal_resistance) local_dos = kwant.ldos(sys, energy = 0.25) pyplot.figure() pyplot.plot(Bfields, data) pyplot.xlabel("magnetic field [T]") pyplot.ylabel("rxy") pyplot.show() kwant.plotter.map(sys, local_dos, num_lead_cells=10) # def main(): sys = make_system() # Check that the system looks as intended. kwant.plot(sys) # Finalize the system. sys = sys.finalized() plot_conductance(sys, energy=0.3, Bfields=[i* 0.002 for i in xrange(200)]) The order of the leads determine the solution of the linear system of cm. Could you give me some help? With the best regards, M. Sotomayor

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Bug report
by Bas Nijholt 03 Mar '15

03 Mar '15

I’ve found a bug in add_site_family(), the input for other_vectors should be a list, but I used a tulpe, the error message I got is not correct. Code: lat = kwant.lattice.general([(1, 0), (sin_30, cos_30)], [(0, 0), (0, 1 / sqrt(3))]) a, b = lat.sublattices sym_lead = kwant.TranslationalSymmetry(lat.vec((1, 0))) sym_lead.add_site_family(a, other_vectors=(1, -2)) Error message: --------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-73-c9cfa5f61ce2> in <module>() 4 sym_lead = kwant.TranslationalSymmetry(lat.vec((1, 0))) 5 ----> 6 sym_lead.add_site_family(a, other_vectors=(1, -2)) /usr/local/lib/python2.7/site-packages/kwant/lattice.pyc in add_site_family(self, fam, other_vectors) 572 573 if np.linalg.matrix_rank(m) < num_vec: --> 574 raise ValueError('other_vectors and symmetry periods are not ' 575 'linearly independent.') 576 ValueError: other_vectors and symmetry periods are not linearly independent.

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Kwant-discuss March 2015