TBMethod

1. Installation & Uninstallation

1.1 Installation

Programming environment version: the latest the best

1.1.1 Offline

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

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

1.1.2 Online

• Outstanding

1.2 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`"]

This can be initialized automatically by putting the init.m file to the directory SystemOpen[$UserBaseDirectory <> "/Kernel"]. The first line of init.m sets the number of parallel cores. I usually use the available logical cores.

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.

1.3 Uninstallation

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

2. 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

3. Documentation

MMA-style documentation under construction

Cooperation is highly welcome.

A tutorial in Zhihu Column is also under compilation.

4. My Two Tips

1. The CSR is the smallest union of all physical nonperiodicities; the leads are asymptotic.
2. Do not introduce abruptness or discontinuity unless they are themselves physical.

5. Related Publications

1. arXiv: 2604.01596.
2. npj Quant. Mater. 10, 48 (2025).
3. Phys. Rev. B 111, 085137 (2025).
4. Phys. Rev. B 111, 155303 (2025).
5. Phys. Rev. Lett. 133, 246606 (2024).
6. Phys. Rev. Lett. 131, 086601 (2023).
7. Phys. Rev. B 107, 075303 (2023).
8. Phys. Rev. B (Letter) 106, L201407 (2022).
9. Front. Phys. 17, 63503 (2022).
10. Appl. Phys. Lett. 120, 084002 (2022).
11. Chin. Phys. Lett. 39, 017302 (2022).
12. Phys. Rev. B 101, 235432 (2020).
13. Phys. Rev. B 100, 205408 (2019).
14. Phys. Rev. B 95, 045424 (2017).

6. Incomplete References

6.1 Topological Models & Characterization

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).

6.2 Lattice Green's Function Formalism

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).

6.3 Slater-Koster Method

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).

6.4 Other Theoretical Considerations

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).