TBMethod

Installation & Uninstallation

Installation

Programming environment version: the latest the best

Offline

1. Download the latest "TBMethod-<\*version #\*>.paclet" file to one's local machine;

2. Run PacletInstall["<*path-to-download*>/TBMethod-<*version #*>.paclet"].

Online

• Outstanding

<!-- **Run** `PacletInstall["https://github.com/AlexanderZ11234/TBMethod/releases/download/0.2.1/TBMethod-0.2.1.paclet"]` -->

Installation Test (1 → 3 or 2 → 3)

1. For single kernel, load the package by

<!---->

Needs["TBMethod`"]

2. For parallel computation, load it by

<!---->

Needs["TBMethod`"]
ParallelNeeds["TBMethod`"]

3. Check the installation by

<!---->

Scan[Echo @* Information] @ {"TBMethod`MDConstruct`*", "TBMethod`EigenSpect`*", "TBMethod`LGFF`*", "TBMethod`DataVisualization`*"}

and four lists of functions should be indexed out.

Uninstallation

• Run PacletUninstall["TBMethod"] for uninstallation or reinstallation.

Functionality Highlights

• External degree of freedom (real-space coordinate): sufficient employment of the NNS (nearest neighbor search) algorithm, so that the total computation complexity tends to be fine as:

  • Model construction linear in system's size $ \text{O}(n) $:

    • Generation of Hamiltonian matrices,
    • Adaptive partition of central scattering region

  • Calculation of transport related quantities:

    • 5-terminal Hall calculation in $ \text{O}(n^{1.7}) $

• Internal degree of freedoms: spin, atomic orbital, (BdG) particle-hole, (Floquet) photon block, and lattice vibration polarization

• Workflow coordinated with DeePTB on Slater-Koster model construction and transport calculation with nonidentity overlapping matrices

Documentation

<a href="#" class="magic-button" title="Onsite testable"> MMA-style </a> documentation under construction

Cooperation is highly welcome.

A tutorial in Zhihu Column is also under compilation.

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Related Publications

</summary>

1. npj Quant. Mater. 10, 48 (2025).
2. Phys. Rev. B 111, 085137 (2025).
3. Phys. Rev. B 111, 155303 (2025).
4. Phys. Rev. Lett. 133, 246606 (2024).
5. Phys. Rev. Lett. 131, 086601 (2023).
6. Phys. Rev. B 107, 075303 (2023).
7. Phys. Rev. B (Letter) 106, L201407 (2022).
8. Front. Phys. 17, 63503 (2022).
9. Appl. Phys. Lett. 120, 084002 (2022).
10. Chin. Phys. Lett. 39, 017302 (2022).
11. Phys. Rev. B 101, 235432 (2020).
12. Phys. Rev. B 100, 205408 (2019).
13. Phys. Rev. B 95, 045424 (2017).

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Incomplete References

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Topological Models & Characterization

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1. Bernevig, Topological Insulators and Topological Superconductors, PUP, 2013.
2. Shen, Topological Insulators: Dirac Equation in Condensed Matters, Springer, 2017.
3. Phys. Rev. Lett. 61, 2015 (1988).
4. Phys. Rev. Lett. 95, 146802 (2005).
5. Phys. Rev. Lett. 95, 226801 (2005).
6. Phys. Rev. B 82, 161414(R) (2010).
7. Phys. Rev. B 84, 075119 (2011).
8. Phys. Rev. Lett. 112, 037001 (2014).
9. Phys. Rev. B 95, 195102 (2017).
10. Phys. Rev. B 95, 245433 (2017).
11. Phys. Rev. Lett. 124, 136403 (2020).
12. Phys. Rev. Lett. 124, 166804 (2020).

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Lattice Green's Function Formalism

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1. Datta, Electronic Transport in Mesoscopic Systems, CUP, 1995.
2. Datta, Quantum Transport: Atom to Transistor, CUP, 2005.
3. Wimmer, Quantum transport in nanostructures: From computational concepts to spintronics in graphene and magnetic tunnel junctions, Ph.D. Dissertation, Universität Regensburg, 2008.
4. Qiao, Charge and Spin Transport in Two-Dimensional Mesoscopic Systems, Ph.D. Dissertation, HKU, 2009.
5. Papior, Computational Tools and Studies of Graphene Nanostructures, Ph.D. Dissertation, TUD, 2016.
6. J. Phys. F: Met. Phys. 14, 1205 (1984).
7. J. Phys. F: Met. Phys. 15, 851 (1985).
8. Phys. Rev. Lett. 97, 066603 (2006).
9. Nanotechnology 18, 435402 (2007).
10. Phys. Rev. B 83, 085412 (2011).
11. Phys. Rev. B 91, 125408 (2015).
12. Phys. Rev. B 97, 165405 (2018).
13. Phys. Rev. B 100, 195417 (2019).

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Slater-Koster Method

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1. Saito, Physical Properties of Carbon Nanotubes, ICP, 1998.
2. Phys. Rev. 94, 1498 (1954).
3. Phys. Rev. B 74, 165310 (2006).
4. Phys. Rev. B 82, 245412 (2010).
5. Nat. Commun. 15, 6772 (2024).
6. Phys. Rev. B 110, 235130 (2024).

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Other Theoretical Considerations

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1. Z. Phys. 64, 629 (1930).
2. Z. Phys. 80, 763 (1933).
3. Phys. Rev. B 40, 8169 (1989).
4. Phys. Rev. B 79, 081406(R) (2009).
5. Phys. Rev. B 84, 235108 (2011).
6. Phys. Rev. Lett. 114, 056801 (2015).

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