Skip to content

Latest commit

 

History

History
89 lines (65 loc) · 4.56 KB

README.md

File metadata and controls

89 lines (65 loc) · 4.56 KB

Transversality-Enforced Tight-Binding (TETB) model

Implemented by Antonio Morales-Pérez, Chiara Devescovi, Yoonseok Hwang, Mikel García-Díez, Barry Bradlyn, Juan L. Mañes, Maia G. Vergniory, and Aitzol García-Etxarri

In this package we define the essential functions necessary to implement the enumeration algorithm, which returns all possible decompositions in terms of elementary bands representations (EBRs) of a "symmetry vector" of a bundle of isolated photonic bands, given a certain number of auxiliary bands.

The analytical framework underlying our implementation of the TETB model is detailed in Ref. [1]. We will use the notation for labelling the space groups (SGs), irreducible representations (irreps) and EBRs presented in Ref. [3].

Installation

Clone the repository and install the package by navigating to the working directory and running

pip install .

Requirements

It requieres three additional packages:

  1. NumPy
  2. SymPy (v1.12)
  3. OR-Tools - Google Optimization Tools (v9.10.4067)

Examples

We provide a set of Jupyter notebooks in ./examples/ for the following cases:

  1. The specific examples studied in Ref. [1] under space groups (SGs) #224 and #221
  2. All first minimal solutions of SG #224, #221, #99 and #2 presented in Ref. [2]

As a first step, it is necessary to define by hand all the EBRs and irreps of the specific SG of the system under study. To accomplish this we forward the user to the tables shown in Ref. [3-5]. There, one can find all EBRs and all irreps tabulated for all magnetic and non-magnetic SGs. More details are given within the examples.

References

Please cite the following paper when using this package:

[1] A. Morales-Pérez, C. Devescovi, Y. Hwang, et al., “Transversality-enforced tight-binding model for 3d photonic crystals aided by topological quantum chemistry,” arXiv preprint arXiv:2305.18257 (2023).

[2] T. Christensen, H. C. Po, J. D. Joannopoulos, and M. Soljačić, “Location and topology of the fundamental gap in photonic crystals,” Phys. Rev. X 12, 021066 (2022).

[3] B. Bradlyn, L. Elcoro, J. Cano, M. G. Vergniory, Z. Wang, C. Felser, M. I. Aroyo & B. A. Bernevig "Topological quantum chemistry" Nature 547, 298-305 (2017).

[4] Bilbao Crystallographic Server -> BANDREP

[5] Bilbao Crystallographic Server -> Representations SG

Acknowledgments

A.G.E., A.M.P, M.G.D., M.G.V. and C.D. acknowledge support from the Spanish Ministerio de Ciencia e Innovación (PID2022-142008NB-I00). A.G.E., A.M.P, and C.D. also acknowledge support from the Basque Government Elkartek program (KK- 533 2023/00016) and the Gipuzkoa Provincial Council within the QUAN-000021-01 project. A.G.E. and M.G.V. acknowledge funding from the IKUR Strategy under the collaboration agreement between Ikerbasque Foundation and DIPC on behalf of the Department of Education of the Basque Government, Programa de Ayuda de Apoyo a los agentes de la Red Vasca de Ciencia, Tecnolog'ia e Innovaci'on acreditados en la categor'ia de Centros de Investigaci'on B'asica y de Excelencia (Programa BERC) from the Departamento de Universidades e Investigaci'on del Gobierno Vasco and Centros Severo Ochoa AEI/CEX2018-000867-S from the Spanish Ministerio de Ciencia e Innovaci'on. M.G.V. thanks support to the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) GA 3314/1-1 – FOR 5249 (QUAST) and partial support from European Research Council (ERC) grant agreement no. 101020833. The work of JLM has been partly supported by the Basque Government Grant No. IT1628-22 and the PID2021-123703NB-C21 grant funded by MCIN/AEI/10.13039/501100011033/ and ERDF; ``A way of making Europe”. The work of B.B. and Y.~H. is supported by the Air Force Office of Scientific Research under award number FA9550-21-1-0131. Y.~H. received additional support from the US Office of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI) grant N00014-20-1-2325 on Robust Photonic Materials with High-Order Topological Protection. C.D. acknowledges financial support from the MICIU through the FPI Ph.D. Fellowship CEX2018-000867-S-19-1. M.G.D. acknowledges financial support from the Government of the Basque Country through the pre-doctoral fellowship PRE_2022_2_0044.

License

This project is released under the GNU GENERAL PUBLIC LICENSE