We present the results of a high-throughput, first principles search for topological materials based on identifying materials with band inversion induced by spin-orbit coupling. Out of the currently available 30000 materials in our database, we investigate more than 4507 non-magnetic materials having heavy atoms and low bandgaps. We compute the spillage between the spin-orbit and non-spin-orbit wave functions, resulting in more than 1699 high-spillage candidate materials. We demonstrate that in addition to Z2 topological insulators, this screening method successfully identifies many semimetals and topological crystalline insulators. Our approach is applicable to the investigation of disordered or distorted materials, because it is not based on symmetry considerations, and it can be extended to magnetic materials. After our first screening step, we use Wannier-interpolation to calculate the topological invariants and to search for band crossings in our candidate materials. We discuss some individual example materials, as well as trends throughout our dataset, that is available at JARVIS-DFT website: http://jarvis.nist.gov

1. Database of Topological Materials
&
Spin-orbit Spillage
Kamal Choudhary, Kevin Garrity, Francesca Tavazza
NIST
American Physical Society
March 7, 2019
1
https://jarvis.nist.gov/

2. Motivation
2
https://doi.org/10.1093/nsr/nww026
Device perspective Exotic physics
• Dissipation-less spintronic devices
• Quantum computer
• Magnetic monopole
• Quantum anomalous Hall Effect
• Dirac-cones,…
Email: kamal.choudhary@nist.gov

3. Topological materials
New class of materials
(electronic bandgap perspective)
3
Email: kamal.choudhary@nist.gov
https://phys.org/news/2014-01-quantum-natural-3d-counterpart-graphene.html
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSzMKD5ICIkR9neJRre3prqIjp_iqLMu6TQp7mXKJqmmh-HqjFB
No U-turn material
(2016 Nobel prize)
Metal
Semiconductor
Insulator

4. Spin-orbit Spillage
• Majority of the topological materials driven by spin-orbit coupling (SOC)
• Simple idea: Compare wavefunctions of a material with and without SOC?
• Spillage initially proposed for insulators only, now extended to metals also
• Advantages over symmetry-based approaches:
disordered and magnetic mats.
• For trivial materials, spillage 0.0, non-trivial materials ≥ 0.5
• Starting from 30000 materials in JARVIS-DFT database:
1868 high-spillage materials found
4
https://www.ctcms.nist.gov/~knc6/jsmol/JVASP-1067
𝜂 𝐤 = 𝑛 𝑜𝑐𝑐(𝐤) − Tr 𝑃 ෨𝑃 ; 𝑃 𝐤 = ෍
𝑛=1
)𝑛 𝑜𝑐𝑐(𝐤
ۧ|𝜓 𝑛𝐤 ൻ𝜓 𝑛𝐤|
Liu and Vanderbilt, Phys. Rev. B 90, 125133 (2014).
https://arxiv.org/abs/1810.10640
Email: kamal.choudhary@nist.gov

5. Spillage and other distributions analysis
5
30000 materials
Bandgap<1 eV, atomic
weight>65, non-magnetic
(4835)
Spillage>0.5
(1868)
Wannier calc. for
289
High-symmetry and ternary structures favored
For trivial mats (red) generally SOC/NSOC bandgap same
Email: kamal.choudhary@nist.gov

6. Wannier function, band-crossings, inversion…
6
Email: kamal.choudhary@nist.gov
https://arxiv.org/abs/1810.10640
Examples after spillage-based narrowing down the list of materials…
PbS, P63/mmc, Z2 TI
Band-inv. at Г
Dirac cone for (001) at Г
LiBiS2, P4/mmm, weak TI
Band-inv. at R
Dirac at M and Z
KHgAs, P63/mmc, CTI InSb, P63mc, bulk Dirac cone at Г-A
GaSb, P63mc, two Dirac cones at Г-A
Weyl crossing along Γ – K and Γ – M

7. Periodic table and dimensionality trends
7
Email: kamal.choudhary@nist.gov
High-spillage materials generally with Pb, Bi,…
https://arxiv.org/abs/1810.10640
More than 10% low-dimensional
89.61
10.39
Dimensionality distribution
3D 2D+1D+0D
89.61
10.39
Dimensionality distribution
3D 2D+1D+0D

8. Demo
8
Got to https://jarvis.nist.gov/
Then JARVIS-DFT ; click ‘Bi and ‘Se’ then click ‘Search’
https://www.ctcms.nist.gov/~knc6/JVASP.html
Click on JVASP-1067 for R-3m Bi2Se3
Scroll-down to spillage-section
Email: kamal.choudhary@nist.gov

9. Summary and Future Work
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➢Simple and robust criteria to identify topological materials, can be complimentary to
symmetry-based approaches
➢Publicly available database: https://jarvis.nist.gov/
➢Coupled with other databases such as for optoelectronic, mechanical, thermoelectric,
electronic properties: a great resource to accelerate material-design
➢On-going work for 2D, disordered and magnetic materials
Thank you for your time!
Email: kamal.choudhary@nist.gov