Mailman 3 November 2024 - Kwant-discuss

conservation_law and particle_hole in finite systems
by Konner Feldman Dec. 14, 2024

Dec. 14, 2024

I am trying to simulate a finite size rectangular 2d electron gas inside a josephson junction. There is one rectangular scattering region on each end that is coupled to a different superconductor, while the middle rectangular scattering region is just a part of the semiconductor 2DEG. I am only simulating the 2DEG and not the superconductors, but there is still spin-orbit coupling and hole interactions. I was told that the "conservation_law" and "particle_hole” parameters are not needed for systems such as this one that do not have infinite length regions, but I don't understand why. Could somebody please help me understand this?

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Armchair/zig-zag Haldane model
by Lorenzo CAVICCHI Nov. 21, 2024

Nov. 21, 2024

Dear all, I am trying to implement a transport calculation for the Haldane model on armchair and zig-zag graphene nanoribbons (with open boundary conditions along the y-direction and periodic boundary conditions along the x-direction, i.e., the transport direction). In particular, my system consists of a finite-sized scatterer attached to two semi-infinite leads. The system is "homogeneous," meaning that all three components (left lead, scatterer, and right lead) share the same Haldane Hamiltonian (https://doi.org/10.1103/PhysRevLett.61.2015). I am writing to seek assistance because I am encountering two major problems when extracting the eigenstates of the scatterer at a fixed energy: 1)When the system is constructed with zig-zag edges, I find a limit on the width of the sample in the y-direction, beyond which the wave functions cannot be calculated using the kwant.wave_function() method. Specifically, if the ribbon exceeds this width, for certain energy values, calling kwant.wave_function(sys, energy) produces the following error: "RuntimeError: Numbers of left- and right-propagating modes differ, possibly due to a numerical instability." This appears to result from an accumulation of lead bands, which makes the identification of propagating modes inaccurate. 2)When the system is constructed with armchair edges, the kwant.wave_function(system, energy) method again fails to properly return the eigenstates of the scatterer. However, in this case, the error occurs for all ribbon widths (in the y-direction) and seems unrelated to the energy value. The error is: "LinAlgError: Reordering failed; problem is very ill-conditioned." I have not been able to resolve these issues and would greatly appreciate any insights or suggestions you might have for addressing them. Thank you for your time. Best regards, Lorenzo Cavicchi

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Graphene sheet with 4-atom rectangular unitcell
by Masoumeh Alihosseini Nov. 21, 2024

Nov. 21, 2024

Hi dear all, I have a question, I want to work with rectangular graphene cell with 4 atoms in the unitcell. Like zigzag nanoribbon but I want to apply periodicity in y direction for both scattering region and leads. Could you please help me? Thank you, Masoumeh

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Current-voltage
by Masoumeh Alihosseini Nov. 21, 2024

Nov. 21, 2024

Dear all, I want to calculate current-voltage curve for graphene. For this purpose, I wrote the following code, but I need to ensure that it works properly or not. Another question is that can I use tkwant to do these computations. Thank you in advance for your help #current-voltage#### def fermi_dirac(energy, mu, T): return 1 / (np.exp((energy - mu) / (k_B * T)) + 1) for voltage in voltages: mu_left = voltage / 2 mu_right = -voltage / 2 # Compute the current using the Landauer-Büttiker formula I = 0 # Loop over energy intervals and compute contributions for e1, e2, g1, g2 in zip(energies[:-1], energies[1:], conductance[:-1], conductance[1:]): # Compute Fermi-Dirac distributions at e1 and e2 for left and right reservoirs f_left_e1 = fermi_dirac(e1, mu_left, temperature) f_right_e1 = fermi_dirac(e1, mu_right, temperature) f_left_e2 = fermi_dirac(e2, mu_left, temperature) f_right_e2 = fermi_dirac(e2, mu_right, temperature) # Current calculation using trapezoidal integration delta_E = e2 - e1 I += ((g1 + g2) / 2) * ((f_left_e1 - f_right_e1) + (f_left_e2 - f_right_e2)) / 2 * delta_E # Convert from eV to Amperes current.append(I * e/h * 1e6) # Multiply by e to convert the current to Amperes return current Masoumeh Alihosseini

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About the running speed of kwant code
by sfhuang＠iphy.ac.cn Nov. 8, 2024

Nov. 8, 2024

I was surprised to find that the same program runs faster on the Apple Silicon M1 Max chip than on the M2 Ultra. This shouldn’t happen, as the latter is supposed to have more cores and higher computational performance. I’d appreciate it if somebody can give me an explanation about this.

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