Recommended by

Indexed by

Single-point spin Chern number in a supercell framework

Roberta Favata1*, Antimo Marrazzo1*

1 Dipartimento di Fisica, UniversitĂ  di Trieste, Strada Costiera 11, I-34151 Trieste, Italy

* Corresponding authors emails: roberta.favata@phd.units.it, antimo.marrazzo@units.it
DOI10.24435/materialscloud:tx-ke [version v1]

Publication date: Jan 30, 2023

How to cite this record

Roberta Favata, Antimo Marrazzo, Single-point spin Chern number in a supercell framework, Materials Cloud Archive 2023.22 (2023), doi: 10.24435/materialscloud:tx-ke.


We present an approach for the calculation of the Z2 topological invariant in non-crystalline two-dimensional quantum spin Hall insulators. While topological invariants were originally mathematically introduced for crystalline periodic systems, and crucially hinge on tracking the evolution of occupied states through the Brillouin zone, the introduction of disorder or dynamical effects can break the translational symmetry and imply the use of larger simulation cells, where the k-point sampling is typically reduced to the single Γ-point. Here, we introduce a single-point formula for the spin Chern number that enables to adopt the supercell framework, where a single Hamiltonian diagonalisation is performed. Our single-point approach allows to calculate the spin Chern number even when the spin operator does not commute with the Hamiltonian, as in the presence of Rashba spin-orbit coupling. This archive entry contains the results of the single-point calculations of the topological invariant on the tight-binding Kane-Mele model for large supercells (up to 7200 sites). Convergence tests as function of the supercell size are reported, both in the pristine case and in presence of Anderson disorder. Single-point calculations of the spin Chern number are carried out over the entire phase diagram of the Kane-Mele model. The study of topological phase transitions due to disorder is performed in terms of single-point spin Chern number by averaging over several realisations of the Anderson disorder in the supercell.

Materials Cloud sections using this data

No Explore or Discover sections associated with this archive record.


File name Size Description
1.2 MiB Results of tight-binding calculations: single-point topological invariant and band gap


Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.


Spin Chern number Supercell framework Topological insulators Kane-Mele model Anderson disorder

Version history:

2023.22 (version v1) [This version] Jan 30, 2023 DOI10.24435/materialscloud:tx-ke