Kwant Topological Edge Transport Study
A completed condensed matter physics study of topological edge transport, disorder, conductance, and finite width effects in the spinless Haldane model.
Software compatibility
The released results use Kwant 1.5.0, NumPy 1.26.4, and Python 3.12 on macOS ARM. A Linux ARM container run also passed, but other architectures and Kwant releases are not verified.
Project definition
Problem statement
A topological label alone does not prove that a finite device carries a robust edge channel. Lead modes, sample width, Fermi energy, disorder, boundaries, and finite size can all change the measured conductance.
The physics problem is to construct a controlled Haldane ribbon, compare topological and trivial cases, retain local and transport evidence, and explain where the ideal edge response begins to fail.
Project objectives
- Construct a finite honeycomb ribbon with matched semi-infinite leads using the spinless Haldane model.
- Compare clean topological and trivial conductance over the same 61-point energy grid.
- Calculate lead bands and local scattering density at the selected probe energy.
- Measure conductance under four disorder strengths using twelve deterministic realizations per strength.
- Study six finite widths and six staggered mass values against the analytical phase boundary.
Project structure
Project components
Haldane model
Defines the honeycomb lattice, nearest and complex second-neighbour hopping, staggered mass, leads, and seeded onsite disorder.
Transport solver
Uses Kwant scattering matrices to calculate two-terminal conductance and the available lead modes.
Band and density analysis
Calculates lead dispersions and the normalized spatial density of the injected scattering state.
Parameter studies
Runs the clean energy scan, disorder ensemble, finite width comparison, and fixed-energy mass response.
Evidence
Retains CSV, JSON, eight labelled figures, tests, references, and complete documentation.
Methodology
Project workflow
- 01Build the ribbon
A validated configuration declares the hopping terms, geometry, masses, disorder strengths, and probe energy.
- 02Finalize the system
Kwant creates the finite scattering region and attaches two clean matched leads.
- 03Run transport
The solver calculates conductance, propagating modes, lead bands, and local scattering density.
- 04Compare cases
Retained tables and figures expose phase, disorder, width, and mass trends.
- 05Verify
Tests, coverage, dependency audit, container execution, and repository checks confirm the release.
Demonstration scenario
At energy 0.1 t, the reference topological ribbon carries one conductance quantum while the matched trivial ribbon carries none. More than 99.9 percent of the normalized scattering density lies in the declared edge region. The median remains 0.998945 at disorder W = 1 and falls to 0.957135 at W = 2, allowing the student to explain both robustness and its finite-device limits.
Engineering
Tools and method
- Tools
- The project uses Kwant 1.5.0, Python 3.12, NumPy 1.26.4, SciPy, Pandas, Matplotlib for subject analysis, simulation, and results.
- Quantum transport
- Kwant 1.5.0 constructs the tight-binding device and solves its coherent scattering problem.
- Model control
- Python validates the study configuration and applies deterministic disorder with Kwant digest salts.
- Numerical analysis
- NumPy, SciPy, and Pandas retain and summarize the transport evidence.
- Figures
- Matplotlib and Seaborn generate eight report figures directly from the retained results.
- Reproducibility
- Pinned dependencies, Docker, exact configuration, automated tests, raw evidence, Word files, and PDFs support independent reruns.
Testing
Evaluation
Evaluation measures
- Topological and trivial conductance across 61 energies each
- Lead dispersion and propagating modes at the probe energy
- Fraction of scattering density contained in the declared edge region
- Median, 5th percentile, 95th percentile, and plateau robustness under disorder
- Finite width mode onset and conductance response
- Fixed-energy mass response compared with the analytical Haldane boundary
Project boundaries
- The completed model is a coherent spinless tight-binding simulation, not a fabricated device or material measurement.
- The conductance values use dimensionless model units and do not predict the resistance of a specific material sample.
- The fixed-energy mass sweep is interpreted with the analytical Haldane boundary and is not a numerical Chern-number calculation.
- Interactions, phonons, dephasing, contacts beyond ideal matched leads, temperature broadening, and experimental calibration are outside the completed scope.
Included
- 01Complete Python and Kwant source code
- 02One hundred and twenty-two clean conductance solves across topological and trivial phases
- 03Forty-eight deterministic disorder runs
- 04Six ribbon widths and six mass cases
- 05Six retained CSV result tables and one JSON study summary
- 06Eight labelled result figures in PNG and SVG formats
- 07Three literature images with source and licence records
- 08Thirty automated tests with 100 percent statement and branch coverage
- 09Complete project files, calculations, results, and analysis material in a private GitHub repository
- 1079-page project documentation in PDF and editable Word formats
- 119-page setup and usage guide in PDF and editable Word formats
- 12Fifty annotated references, including work published in 2025 and 2026
Project record
No information is collected on this page.
- Permanent project ID
- GP-PH-1WWN3NS
- Catalogued
- 21 Aug 2026
- Completed
- 26 Aug 2026
- Verified
- 26 Aug 2026
- Demonstration
- Included in repository
Handover
After purchase
- 01Payment is confirmed
The project is marked unavailable and cannot be purchased again.
- 02Repository access is granted
The buyer's submitted GitHub account receives access to the private repository.
- 03The purchase record is delivered
The certification sheet is prepared from the reviewed buyer details and sent privately by email.